diff --git "a/batch_s000048.csv" "b/batch_s000048.csv" new file mode 100644--- /dev/null +++ "b/batch_s000048.csv" @@ -0,0 +1,10410 @@ +source,target + WASP-30b has the secoud simallest commpanion-to-star size ratio (AF=nz32 0.0050) of all sub-stellar yodics so far discovered by erouud-based trausit survevs., WASP-30b has the second smallest companion-to-star size ratio $\Delta F = R_{\rm p}^2/R_*^2 = 0.0050$ ) of all sub-stellar bodies so far discovered by ground-based transit surveys. + The star in the system with the Μπα: size ratio. ILAT-P-ll (V29.6AF=0.0033:Bakosetal.2010)... is ὃ times brighter than WASP-30.," The star in the system with the smaller size ratio, HAT-P-11 \citep[$V$ = 9.6; $\Delta F = 0.0033$;][]{2010ApJ...710.1724B}, is 8 times brighter than WASP-30." + As it is fay easier to find such an object around a smaller. cooler star. the discovery of WASP-30b sugeests that hieh-niass. sub-stellar objects in short orbits around cooler stars are rare.," As it is far easier to find such an object around a smaller, cooler star, the discovery of WASP-30b suggests that high-mass, sub-stellar objects in short orbits around cooler stars are rare." + WASP-South is hosted dy the South Africau Astronomical Observatory and SuperWASP-N is hosted by the Issac Newton Group ou La Palma., WASP-South is hosted by the South African Astronomical Observatory and SuperWASP-N is hosted by the Issac Newton Group on La Palma. + We are grateful for their ongoing support and assistance., We are grateful for their ongoing support and assistance. + Funding for WASP comes froin consortimu universities and from the Ul& Science and Technology. Facilities Council., Funding for WASP comes from consortium universities and from the UK's Science and Technology Facilities Council. + M. Gillon acknowledecss support from the Beleian SciencePolicy Office in the form of a Return Craut., M. Gillon acknowledges support from the Belgian SciencePolicy Office in the form of a Return Grant. + WASP.," WASP," +simultaneously fitted a svnthetic ΤΟΠ ΟΠΗ spectra. using the 18 PCIE;O0IT transitions in the observed frequency range. using (hie same constraints as lor the απο fit.,"simultaneously fitted a synthetic $^{13}$ $_3$ OH spectra, using the 18 $^{13}$ $_3$ OH transitions in the observed frequency range, using the same constraints as for the $^+$ line fit." + The fit reproduces most of the observed features and shows that the emission from ΤΟΠ ΟΠΗ may explain (he observed non Gaussian — proliles., The fit reproduces most of the observed features and shows that the emission from $^{13}$ $_3$ OH may explain the observed non Gaussian $^+$ profiles. + Onlv the parameters derived [or the three most intense components in (he group are given in Table 1.., Only the parameters derived for the three most intense components in the group are given in Table \ref{tab:gaussfit}. + This is (he first (nme that the EC isotopologue of methanol is detected towards an extragalactic source., This is the first time that the $^{13}$ C isotopologue of methanol is detected towards an extragalactic source. + Regarding the accuracy of the fitted parameters presented in Table 1.. the integrated line intensities derived for and ΟΠ ΟΠ are likely underestimated by —20% due to the baseline determination.," Regarding the accuracy of the fitted parameters presented in Table \ref{tab:gaussfit}, the integrated line intensities derived for $^+$ and $^{13}$ $_3$ OH are likely underestimated by $\sim20\%$ due to the baseline determination." + In the next Section. we diseuss the detection of ΟΠ ΟΠ in the context of the derived abundances with respect to those of the main methanol isotopologue.," In the next Section, we discuss the detection of $^{13}$ $_3$ OH in the context of the derived abundances with respect to those of the main methanol isotopologue." + We have estimated the fractional abundances of the newly observed species in 2253 assumine oplically thin emission. LTE conditions. aud similar spatial distribution Lor all species.," We have estimated the fractional abundances of the newly observed species in 253 assuming optically thin emission, LTE conditions, and similar spatial distribution for all species." +" Under these assumptions. we have caleulated the column densities of 000 . IICO. and for an excitation temperature ἕως=1545 NIN and an estimated source extent for each velocity component of 10""."," Under these assumptions, we have calculated the column densities of $^{13}$ $^+$ , $^+$ , HCO, and $^+$ for an excitation temperature $T_{\rm ex}=15\pm5$ K and an estimated source extent for each velocity component of $10''$." + The Ti.=15zx 5IXIN is assumed based on the average rotational temperatures derived [rom most of the species detected towards 2253 (Martinetal.2006b)., The $T_{\rm ex}=15\pm5$ K is assumed based on the average rotational temperatures derived from most of the species detected towards 253 \citep{Martin06b}. +. Indeed (he non detection of 3—2 implies low excitation temperatures of Ti. LOW. Both the excitation temperature and (he emission extent have an important impact in the absolute derived column densities by up (o a factor of 2. however. the fractional abundances ancl abundance ratios are mostly independent of these assumptions.," Indeed the non detection of $^+\,3-2$ implies low excitation temperatures of $T_{\rm ex}\sim10$ K. Both the excitation temperature and the emission extent have an important impact in the absolute derived column densities by up to a factor of 2, however, the fractional abundances and abundance ratios are mostly independent of these assumptions." + We asstune that the emission extent is similar for all observed species., We assume that the emission extent is similar for all observed species. + Table 2. presents the column densiües and fractional abundance ratios wilh respect to II» for all the species., Table \ref{tab:abunRatios} presents the column densities and fractional abundance ratios with respect to $_2$ for all the species. + The total IL;columndensity has been derived [rom the CO colunn, The total $_2$columndensity has been derived from the $^{18}$ O column +has not yet been addressed.,has not yet been addressed. +the luminosity function of LMXBs (Gilfanov.2004).,the luminosity function of LMXBs \citep{gilfanov}. +". In the luminosity range of 2-1076—2.10°""eres7!. the X-ray to K- luminosity ratio is =I4-1075ergs7!Li. in the 2—10 keV band."," In the luminosity range of $ 2 \cdot 10^{36} - 2 \cdot 10^{37} \ \mathrm{erg \ s^{-1}} $, the X-ray to K-band luminosity ratio is $ \approx 1.4 \cdot 10^{28} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $ in the $2-10$ keV band." +" To convert this value to the 0.3—0.7 keV energy range we used the average spectrum of LMXBS. described by a power-law model with a slope ofΓ=1.56 (Irwinetal..2003) and assumed a column density of Nj,=4-102em7."," To convert this value to the $ 0.3-0.7 $ keV energy range we used the average spectrum of LMXBS, described by a power-law model with a slope of $ \Gamma = 1.56 $ \citep{irwin2} and assumed a column density of $ N_{H} = 4 \cdot 10^{20} \ \mathrm{cm^{-2}} $." + The result is Lx/Lgs(1.720.1)-1077eigs!Li.. Which 15 in reasonable agreement with the value obtained from the first method.," The result is $L_{\mathrm{X}}/L_{\mathrm{K}} \approx (1.7\pm0.1) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $, which is in reasonable agreement with the value obtained from the first method." + Both methods are based on the assumption that the X/K ratio for LMXBs ts the same for all galaxies in the sample., Both methods are based on the assumption that the X/K ratio for LMXBs is the same for all galaxies in the sample. + This assumption may be contradicted by the fact that in NGC 3377 and NGC 3585 the predicted luminosity of unresolved LMXBs exceeds the observed luminosity of unresolved emission (Table 3))., This assumption may be contradicted by the fact that in NGC 3377 and NGC 3585 the predicted luminosity of unresolved LMXBs exceeds the observed luminosity of unresolved emission (Table \ref{tab:fit}) ). + Incidentally or not. these are the two youngest galaxies in our sample.," Incidentally or not, these are the two youngest galaxies in our sample." + The possible age dependence of the LMXB X/K ratio cannot be excluded but still needs to be established., The possible age dependence of the LMXB X/K ratio cannot be excluded but still needs to be established. + On the other hand. the correction due to unresolved LMXBs ts less than €40% of the observed value of Ly/Ly (Table 4)).," On the other hand, the correction due to unresolved LMXBs is less than $\la 40\%$ of the observed value of $L_X/L_K$ (Table \ref{tab:xtok}) )." + This accuracy is sufficient for the present study. whose purpose is to constrain the luminosity of nuclear-burning white dwarfs.," This accuracy is sufficient for the present study, whose purpose is to constrain the luminosity of nuclear-burning white dwarfs." + Therefore we defer further investigation of the possible effect of inconstant LMXB X/K ratio for a follow-up study., Therefore we defer further investigation of the possible effect of inconstant LMXB X/K ratio for a follow-up study. + The X-ray to K-band luminosity ratios transformed to the same point source detection sensitivity are listed in Table 4.., The X-ray to K-band luminosity ratios transformed to the same point source detection sensitivity are listed in Table \ref{tab:xtok}. + These numbers are fairly uniform Lx/Lg=(2.440.45-1077ergs!Ly! where. as before. the cited error refers to the rms of the measured values.," These numbers are fairly uniform $ L_{\mathrm{X}}/L_{\mathrm{K}} = (2.4 \pm 0.4) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $ , where, as before, the cited error refers to the rms of the measured values." + The excellent source detection sensitivity. achieved in the bulge of M31. and the large number of compact X-ray sources in this galaxy allows us to estimate the contribution of unresolved LMXBs having the luminosities below the adopted threshold of 2-10°°ergs| to the Ly/Ly ratio.," The excellent source detection sensitivity, achieved in the bulge of M31, and the large number of compact X-ray sources in this galaxy allows us to estimate the contribution of unresolved LMXBs having the luminosities below the adopted threshold of $2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$ to the $L_X/L_K$ ratio." + We consider the inner 6’ of the bulge where the source detection is complete down to 2-10?ergs7! (Voss&Gilfanov.2007).., We consider the inner $ 6 \arcmin $ of the bulge where the source detection is complete down to $ 2 \cdot 10^{35} \ \mathrm{erg \ s^{-1}} $ \citep{voss}. + In this region we collected all compact sources with the luminosity in the range 2-10?—2.1079eres7!. excluding those classified as supersoft sources.," In this region we collected all compact sources with the luminosity in the range $2 \cdot 10^{35} - 2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$, excluding those classified as supersoft sources." + The combined X-ray luminosity of these sources is divided by the near-infrared luminosity of the same region. to produce Ly/Ly=(3.6€0.3)-1075ergs!Ly...," The combined X-ray luminosity of these sources is divided by the near-infrared luminosity of the same region, to produce $L_X/L_K= (3.6 \pm 0.3) \cdot 10^{26} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $." + This number represents the Lx/Ly ratio in the soft band of low-mass X-ray binaries with luminosities in the 2-10?—10°°ergs7! range., This number represents the $L_X/L_K$ ratio in the soft band of low-mass X-ray binaries with luminosities in the $2 \cdot 10^{35} - 2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$ range. + We conclude that LMXBs contribute ~15 per cent to the Lx/Ly ratio derived above., We conclude that LMXBs contribute $ \sim 15 $ per cent to the $L_X/L_K$ ratio derived above. + The possible effect of the interstellar absorption on the observed X-ray luminosities. depends on the energy spectra of the main X-ray emitting components — active binaries and supersoft sources.," The possible effect of the interstellar absorption on the observed X-ray luminosities, depends on the energy spectra of the main X-ray emitting components – active binaries and supersoft sources." + ABs have significantly harder spectra than supersoft sources. which is illustrated in Fig. 3..," ABs have significantly harder spectra than supersoft sources, which is illustrated in Fig. \ref{fig:softsrc}." + The class of ABs ts represented by V711 Tau. it was observed by for 3.2 ks in Obs-ID 0116340601. while RX JO439.8- is an example of steady hydrogen-burning sources. based on a exposure with 8.1 ks in Obs-ID 83.," The class of ABs is represented by V711 Tau, it was observed by for $ 3.2 $ ks in Obs-ID 0116340601, while RX J0439.8-6809 is an example of steady hydrogen-burning sources, based on a exposure with $ 8.1 $ ks in Obs-ID 83." + As a consequence of the harder spectra. ABs are less affected by the interstellar absorption.," As a consequence of the harder spectra, ABs are less affected by the interstellar absorption." + In Fig., In Fig. +" + we plot the corrected X/K ratio ((Ly/L4), in Table 3) against the Galactic column density.", \ref{fig:xtokplot} we plot the corrected X/K ratio $\left(L_X/L_K\right)_{corr}$ in Table 3) against the Galactic column density. + A weak anti- between these two quantities appears to exist., A weak anti-correlation between these two quantities appears to exist. + This dependence or. rather. absence of a stronger one. can be used. in principle. to further constrain the contribution of sources," This dependence or, rather, absence of a stronger one, can be used, in principle, to further constrain the contribution of sources" +WOS5S mask. shown in figure laa. bv those of simulation B shown in figure 2bb. After this replacement the smoothing of LO” is applied.,"KQ85 mask, shown in figure \ref{Fig:KQ85_masks_nside_512_and_nside_16}a a, by those of simulation B shown in figure \ref{Fig:CutSky_Info_Input_maps}b b. After this replacement the smoothing of $10^\circ$ is applied." + Phe last step transfers now the “wrong” information to the pixels outside the mask., The last step transfers now the “wrong” information to the pixels outside the mask. + This smootheed map is shown in figure 2cc. Downgrading this map to Naas=16 provides the data outside the mask which are used for the reconstruction., This smoothed map is shown in figure \ref{Fig:CutSky_Info_Input_maps}c c. Downgrading this map to $N_{\hbox{\scriptsize side}} =16$ provides the data outside the mask which are used for the reconstruction. + Lf the reconstruction would not use the information within the mask. the reconstructed map of figure 3aa should reappear.," If the reconstruction would not use the information within the mask, the reconstructed map of figure \ref{Fig:CutSky_Info_Extraction_lmax_10}a a should reappear." + However. as revealed in figure Sec. the reconstruction algorithm generates within the mask the main structures of simulation D. which is. displayed in ligure 2bb. This clearly demonstrates the information transfer. so that one has to be careful in testing the reconstruction algorithm.," However, as revealed in figure \ref{Fig:CutSky_Info_Extraction_lmax_10}c c, the reconstruction algorithm generates within the mask the main structures of simulation B, which is displayed in figure \ref{Fig:CutSky_Info_Input_maps}b b. This clearly demonstrates the information transfer, so that one has to be careful in testing the reconstruction algorithm." + This leads to the question whether the reconstruction can be carried out using only unsmootheel maps where no information about pixels within the mask is, This leads to the question whether the reconstruction can be carried out using only unsmoothed maps where no information about pixels within the mask is +across a fare.,across a flare. + The light curves in Fie., The light curves in Fig. + 6 clearly reveal (hie. presence of rapid flares (hat last [ον less (han an hour., 6 clearly reveal the presence of rapid flares that last for less than an hour. + Panel {shows a beautiful example of such a flare., Panel f shows a beautiful example of such a flare. + In fact. (here are significant sub-structures associated with the event. suggesting the presence of two overlapping Lares of even shorter cdurations.," In fact, there are significant sub-structures associated with the event, suggesting the presence of two overlapping flares of even shorter durations." + Interestingly. (he X-ray spectrum of the source varies little across (his flare (see Panel [in Fig.," Interestingly, the X-ray spectrum of the source varies little across this flare (see Panel f in Fig." + 7)., 7). + The effort to precisely determine the duration of each flare was. in general. complicated bx (he presence of data gaps. as well as (he co-existence of fIares on a wide range of timescales.," The effort to precisely determine the duration of each flare was, in general, complicated by the presence of data gaps, as well as the co-existence of flares on a wide range of timescales." + Sometimes. only a portion of a flare is seen.," Sometimes, only a portion of a flare is seen." + The shortest rise or decay lime seen is about. 1000 s. although it can be argued that it might be even shorter in some cases (see. e.g.. Panel e of Fig.," The shortest rise or decay time seen is about 1000 s, although it can be argued that it might be even shorter in some cases (see, e.g., Panel e of Fig." + 6)., 6). + The observed. variability may extend to shorter timescales. on which individual X-ray flares become unresolvable.," The observed variability may extend to shorter timescales, on which individual X-ray flares become unresolvable." + The collective effects of such variability can be investigated by adopting a more sophisticated time-domain or Fourier-domain based technique., The collective effects of such variability can be investigated by adopting a more sophisticated time-domain or Fourier-domain based technique. + We chose to follow the latter approach to obtain a representative power-clensily spectrum (PDS) οἱ Alrk 421 in the low or flaring state., We chose to follow the latter approach to obtain a representative power-density spectrum (PDS) of Mrk 421 in the low or flaring state. + We selected a subset of the 1997 observations Chat are relatively long for the low state ancl. similarly. a subset of the 2001 observations for the flaring state.," We selected a subset of the 1997 observations that are relatively long for the low state and, similarly, a subset of the 2001 observations for the flaring state." + The total exposure (ime is comparable lor the two data sets., The total exposure time is comparable for the two data sets. + For each observation. we made a lisht curve from the data that has a tme resolution of 1/8 s (but no energv resolution).," For each observation, we made a light curve from the data that has a time resolution of 1/8 s (but no energy resolution)." + We then broke the light curve into segments. each of which is 4096 s long (which requires the padding of data gaps or shorter segments wilh the average count rate).," We then broke the light curve into segments, each of which is 4096 s long (which requires the padding of data gaps or shorter segments with the average count rate)." + We performed Fast-Fourier transformation on each segment to obtain a PDS., We performed Fast-Fourier transformation on each segment to obtain a PDS. + The PDS was normalized according to a scheme proposed by Leahy et al. (, The PDS was normalized according to a scheme proposed by Leahy et al. ( +1983).,1983). + The individual PDSs of the segments were (hen weighted (bv the total number of photons) aud averaged to obtain the PDS for the observation., The individual PDSs of the segments were then weighted (by the total number of photons) and averaged to obtain the PDS for the observation. + To further improve statistics. we weighted and averaged the PDSs of the selected observations in a similar manner.," To further improve statistics, we weighted and averaged the PDSs of the selected observations in a similar manner." + From the resulted PDS. we subtracted olf noise power due to Poisson counting statistics to obtain the PDS of the source.," From the resulted PDS, we subtracted off noise power due to Poisson counting statistics to obtain the PDS of the source." + Fie., Fig. + 9 shows the final PDS for each state., 9 shows the final PDS for each state. +" The observed PDS can be fitted bv a simple power law. 1//"". where a=1.9-Ε0.2 for the low state and 2.26£0.06 for the flaring state. although statistics is quite limited for the low state."," The observed PDS can be fitted by a simple power law, $1/f^{\alpha}$, where $\alpha=1.9\pm 0.2$ for the low state and $2.26\pm 0.06$ for the flaring state, although statistics is quite limited for the low state." + The latter value is in general agreement with the published results for the [Iaring state (Ixataoka et al., The latter value is in general agreement with the published results for the flaring state (Kataoka et al. + 2001: Brinkmann et al., 2001; Brinkmann et al. + 2003)., 2003). + The PDS appears to fall more steeply in (he flaring state. although the difference is only of marginal statistical significance.," The PDS appears to fall more steeply in the flaring state, although the difference is only of marginal statistical significance." + The power-law type of PDS is twpical of AGN., The power-law type of PDS is typical of AGN. + What is remarkable here is (hat the variability, What is remarkable here is that the variability +)unded by. Aj=1.,bounded by $\Delta_b = 1$. + Each segmoeut is composed of teus o hmndreds of exid cells; cach with width z Lian |.," Each segment is composed of tens to hundreds of grid cells, each with width $\approx 1~$ km $^{-1}$." + For each overdeuse segment. our scheme attenuates the ionizing backeround (half of which is assumed to cuter roni each side) based ou the amount aud distribution of11.," For each overdense segment, our scheme attenuates the ionizing background (half of which is assumed to enter from each side) based on the amount and distribution of." +".. The scheme starts the assumption that ⋅ ≓↽⊀ ∪↥∎⋜↧∐↸⋡↸∖∐↴∖↴⋜↧↸⋡↥∎∪↴∖↴↴∖↴↑↕↓↸∖↴∖↴↸∖∶↰⋎↕⊔↸∖∐↑∙↖↖↽∐↸∖↥⋅↸∖∣↕⋜∏⋝↸∖↕↴∖↴↑∐↸∖↸⊳↸∖∐TyDQyvolwithue""⋅⇁ ⊔∐⊔↴⋝↸∖↥⋅∙⋜⋯≺∟∖∐↖⋅⊔⋜⋯≺↧⋅∫∣⊽≼∑⋟⋜⋯∖↥⋅↸∖↴∖↴↻↸∖↸⋡↑↕↖⊽↸∖↕⋅↖⊽↾↕⊔∖∐↸∖∐ ↸⋡⋯↕⋯⊔∐≺∐∖∐↴∖↴↕↑⋅↖⊽⋜⋯≺↧↕∐∏≺∐∖∐↑↕↕↑↸∖∐↴∖↴↕↑⋅↖⊽↑∪≼⋡↸∖∐∣↕↥⋅∩⋯ ∕∙"," The scheme starts with the assumption that $x_{{\rm HeII}, {\it i}} = 1$ and $J_{i}(E) = J(E)^{\rm void} \,\exp[-\sigma_{\rm HeII}(E) \, N_{{\rm HeII}, {\it i}}]$ for all cells across the segment, where $i$ labels the cell number, and $N_{{\rm HeII}, {\rm i}}$ and $J_{i}(E)$ are respectively the column density and incident intensity to cell $i$ from $< i$." +≋↕⋯∐⋜∐⋅↕⋅↖⇁∙↑∐∖↥⋅↸∖↕↴∖↴⋜↧↸⊳∪∐↑↥⋅∏∏↕↑↕∪∐↑∪⋅∫∣⇁⋖⊏⋝↕⋟↥⋅∪⋯ >7.," Similarly, there is a contribution to $J_{i}(E)$ from $>\,i$." + Next. the scheme iterates to converge to Dur; and οι. assume photoionization equilibrium.," Next, the scheme iterates to converge to $\Gamma_{{\rm HeII}, {\it i}}$ and $x_{{\rm HeII}, {\it i}}$, assuming photoionization equilibrium." + For our calculations. J(Ey? is set to have a spectral iudex of 1.5. as expected for quasars.," For our calculations, $J(E)^{\rm void}$ is set to have a spectral index of $-1.5$, as expected for quasars." + LLve forest sigltlines show that Typ fluctuates wildly ⊲ ∙∖↽↕⊰↸∖↕⋯↸∖↥⋅↴∖↴⊇∩∩⊤⋟⋈↖↖⊽↸∖≺↧∪∐∪↑⋜↧↑↑↸∖∐∏≻↑↑∪↕⊔∪≼∐∖↕↑∐↸," $\alpha$ forest sightlines show that $\Gamma_{\rm HeII}$ fluctuates wildly on scales of $\gtrsim10~$ cMpc \citep{zheng04, fechner07}." +∖↴∖↴↸∖∪↕↴∖↴↸⊳⋜↧↕↸∖↴∖↴∪↕≼↓∩↸⊳⋀∖↕↻↸⊳⋖∑↕∐∖∐∶↴⋁↸∖↑⋜↧↕∙−≻∩∩↓∶⊟∖↸⊳∐∐↸∖↥⋅ ∏⋯⊳↑∏⋜↧↑↕∪∐↴∖↴∐↸∖↥⋅↸∖∙↴⋝∏↑↖↖↽↕∐↸⊳∪∐∐⊔↸∖∐↑∪∐∐∪↖↖↽↑," We do not attempt to model these fluctuations here, but will comment on how they could affect our conclusions." +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐��⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕��↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖��↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions +∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions +ways.,ways. +" For example. nonlinear interactions among Alfvénn waves occur only between waves propagating in opposite directions in the plasma frame (Iroshnikov 1963. Kraichnan 1965). and so if the energy in waves propagating towards the Sun is very small. then the energy cascade rate and turbulent heating rate also become small (Dobrowolny et al 1980. Hossain et al 1995, Chandran et al 2009)."," For example, nonlinear interactions among Alfvénn waves occur only between waves propagating in opposite directions in the plasma frame (Iroshnikov 1963, Kraichnan 1965), and so if the energy in waves propagating towards the Sun is very small, then the energy cascade rate and turbulent heating rate also become small (Dobrowolny et al 1980, Hossain et al 1995, Chandran et al 2009)." + Finite cross helicity may also modify the wavenumber scalings of the inertial-range power spectra of the density. magnetic field. and velocity.," Finite cross helicity may also modify the wavenumber scalings of the inertial-range power spectra of the density, magnetic field, and velocity." +" Because the “minority” Sunward Alfvénn waves and the passive scalar fluctuations are both cascaded by the ""dominant anti-Sunward Alfvénn waves. the passive scalar spectrum Is expected to have the same inertial-range scaling as the Sunward waves (Lithwick Goldreich 2003; Chandran 2008b)."," Because the “minority” Sunward Alfvénn waves and the passive scalar fluctuations are both cascaded by the “dominant” anti-Sunward Alfvénn waves, the passive scalar spectrum is expected to have the same inertial-range scaling as the Sunward waves (Lithwick Goldreich 2003; Chandran 2008b)." + In some studies of Alfvennic turbulence with cross helicity (e.g.. Grappin et al. 1983: Chandran 2008a: Beresnyak Lazarian 2009) the minority Alfvénn waves have a shallower power spectrum than the dominant Alfvénn waves. suggesting that the passive scalar spectrum is shallower than the magnetic spectrum in highly imbalanced turbulence.," In some studies of Alfvénnic turbulence with cross helicity (e.g., Grappin et al 1983; Chandran 2008a; Beresnyak Lazarian 2009) the minority Alfvénn waves have a shallower power spectrum than the dominant Alfvénn waves, suggesting that the passive scalar spectrum is shallower than the magnetic spectrum in highly imbalanced turbulence." + This finding may be related to the shallow density spectra seen in radio observations of the corona. in which the turbulence is expected to be highly “imbalanced™ (Cranmer van Ballegooijen 2005. Verdini Velli However. a number of other studies find that the inertial-range spectra of the minority waves and dominant waves scale with wavenumber in the same way (Lithwick. Goldreich. Sridhar 2007: Perez Boldyrev 2009: Podesta Bhattacharjee 2009).," This finding may be related to the shallow density spectra seen in radio observations of the corona, in which the turbulence is expected to be highly “imbalanced” (Cranmer van Ballegooijen 2005, Verdini Velli However, a number of other studies find that the inertial-range spectra of the minority waves and dominant waves scale with wavenumber in the same way (Lithwick, Goldreich, Sridhar 2007; Perez Boldyrev 2009; Podesta Bhattacharjee 2009)." + Moreover. the different studies cited above disagree over Whether the spectra of the minority and dominant waves are equal at the dissipation scale (“pinning”).," Moreover, the different studies cited above disagree over whether the spectra of the minority and dominant waves are equal at the dissipation scale (“pinning”)." + Because imbalanced Alfvénnic turbulence is still not fully understood. and is likely the norm in the solar wind. we are only able to derive upper limits on the turbulent heating rates from the density observations. às discussed further below.," Because imbalanced Alfvénnic turbulence is still not fully understood, and is likely the norm in the solar wind, we are only able to derive upper limits on the turbulent heating rates from the density observations, as discussed further below." + In addition. this uncertainly implies that the precise power-law scalings for in Figures 1 and 2. should not be taken too literally. althoughIP we believe that our conclusions about the relative contribution of the active and passive density fluctuations are robust.," In addition, this uncertainly implies that the precise power-law scalings for $\Phi_{\rm ne}^{\rm 1D}$ in Figures \ref{fig:dn_sw} and \ref{fig:dn_cor} should not be taken too literally, although we believe that our conclusions about the relative contribution of the active and passive density fluctuations are robust." + In this section. we discuss observational constraints on density fluctuations in the solar corona and solar wind. and their implications for low-frequency Alfvénnic turbulence models.," In this section, we discuss observational constraints on density fluctuations in the solar corona and solar wind, and their implications for low-frequency Alfvénnic turbulence models." +" Coles Harmon (1989) analyzed the spectral broadening of Arecibo radar observations of Venus near superior conjunction to determine the. three-dimensional power spectrum of electron density fluctuations «b,(7:K). (treated as an isotropic function. of wave vector k) at a range of heliocentric distances r in the slow solar wind."," Coles Harmon (1989) analyzed the spectral broadening of Arecibo radar observations of Venus near superior conjunction to determine the three-dimensional power spectrum of electron density fluctuations $\Phi_{ne}(r,k)$ (treated as an isotropic function of wave vector ${\bf k}$ ) at a range of heliocentric distances $r$ in the slow solar wind." +" They were able to fit ,,(&) at r25R. with one power law at em7! sa slightly shallower power law atkj. and an exponential or Gaussian at &>Kj. where is the ""inner-scale"" wave number at r=5R.."," They were able to fit $\Phi_{ne}(r,k)$ at $r=5 R_{\sun}$ with one power law at $k < 10^{-7} \mbox{ cm}^{-1}$ , a slightly shallower power law at, and an exponential or Gaussian at $k> k_i$, where is the “inner-scale” wave number at $r=5 R_{\sun}$." + They found that atk =k; and r=5R.. δι~9.0<10°em?km? (see their Fig.," They found that at $k= k_i$ and $r= 5 R_{\sun}$, $\Phi_{ne} \simeq 9.0 \times 10^3 +\mbox{ cm}^{-6} \mbox{ km}^3$ (see their Fig." + 4)., 4). + We focus on the inner scale for reasons that will become clearer below., We focus on the inner scale for reasons that will become clearer below. +" Coles et al (1991) found that ϱ,, is a factor of 215 smaller in coronal holesthan in the slow wind. and thus we set The rms electron density fluctuation δη, is given by ont~Atk?b,(K;). which implies ón,~87em? at r25R.."," Coles et al (1991) found that $\Phi_{ne}$ is a factor of $\simeq 15$ smaller in coronal holesthan in the slow wind, and thus we set The rms electron density fluctuation $\delta n_{k_i}$ is given by $\delta n_{k_i}^2 \simeq 4\pi k_i^3 \Phi_{ne}(k_i)$ , which implies $\delta n_{k_i} \simeq 87 \mbox{ cm}^{-3}$ at $r=5 R_{\sun}$." + We estimate the coronal-hole electron density from Eqn. (, We estimate the coronal-hole electron density from Eqn. ( +"4) of Feldman et al (1997). which gives n,=5.9«10°em? at rF—SR. this is very close to the value inferred by Fisher Guhathakurta (1995) from observations taken with the Spartan 201-01 coronagraph.","4) of Feldman et al (1997), which gives $n_e = 5.9 \times 10^3 \mbox{ cm}^{-3}$ at $r= 5R_{\sun}$; this is very close to the value inferred by Fisher Guhathakurta (1995) from observations taken with the Spartan 201-01 coronagraph." + This value forthe background density then gives atr —5R.., This value forthe background density then gives at $r=5 R_{\sun}$. +" An upper limit on the rms amplitude of the Alfvénnic velocity fluctuation at perpendicular scale kel, denoted ὄνς,. can be obtained by assuming that the density fluctuations at scale ko! arise entirely from KAWs."," An upper limit on the rms amplitude of the Alfvénnic velocity fluctuation at perpendicular scale $k_i^{-1}$, denoted $\delta +v_{k_i}$, can be obtained by assuming that the density fluctuations at scale $k_i^{-1}$ arise entirely from KAWs." +" Using the linear eigenfunctions of KAWs. we can write If the compressibility of the KAWs noticeably affects the density spectrum from 1077em!«k107 em-!, as conjectured above and as is suggested by Figure 2.. then Óv,, may beclose to the upper limit given in equation (7)): this is because the fraction of ®,,. that arises from KAWs increases at larger κ (Fig. 2))."," Using the linear eigenfunctions of KAWs, we can write If the compressibility of the KAWs noticeably affects the density spectrum from $10^{-7} \mbox{ cm}^{-1} < k < 10^{-5} \mbox{ cm}^{-1}$ , as conjectured above and as is suggested by Figure \ref{fig:dn_cor}, then $\delta v_{k_i}$ may beclose to the upper limit given in equation \ref{eq:deltan}) ); this is because the fraction of $\Phi_{ne}$ that arises from KAWs increases at larger $k$ (Fig. \ref{fig:dn_cor}) )." + To evaluate the right-hand side of equation (7)) we assume y;=| and 7;=2.0«10° K and adopt the coronal-hole magnetic field model of Cranmer van Ballegooijen (2005) (their eq.," To evaluate the right-hand side of equation \ref{eq:deltan}) ) we assume $\gamma_i = 1$ and $T_i = +2.0\times 10^6$ K and adopt the coronal-hole magnetic field model of Cranmer van Ballegooijen (2005) (their eq." + 2). which gives By=5.8ν107 G at r25...," 2), which gives $B_0 = +5.8 \times 10^{-2}$ G at $r=5 R_{\sun}$." +" These parameters give p;=2.3101em. di2341054em. v4=1.6«107m/s. and or. equivalently. Atk—Kj.the density spectrum at r=5R. is still close to the value obtained by extrapolating a power-law fit to ®,,, for values of k between 1077em7! and 1075em7!."," These parameters give $\rho_i = 2.3 \times 10^{4} \mbox{ cm}$, $d_i = 3 \times 10^{5} \mbox{ + cm}$, $v_{\rm A} = 1.6 \times 10^8 \mbox{ cm/s}$, and or, equivalently, At $k = k_i$,the density spectrum at $r=5 R_{\sun}$ is still close to the value obtained by extrapolating a power-law fit to $\Phi_{ne}$ for values of $k$ between $10^{-7} \mbox{ cm}^{-1}$ and $10^{-6} \mbox{ + cm}^{-1}$." +" We can thus assume that most of the cascade power is still present atk,κι and that most of the dissipation occurs at k4.7 ky.", We can thus assume that most of the cascade power is still present at $k_\perp=k_i$ and that most of the dissipation occurs at $k_\perp >k_i$ . +" Moreover. because k;p;—0.2. the kinetic energy and magnetic energy of Alfvénnie fluctuations at 4,=κι are comparable. as in incompressible MHD. but not like the short-wavelength regime kp;>> |. in which the magneticenergy dominates."," Moreover, because $k_i \rho_i \simeq 0.2$, the kinetic energy and magnetic energy of Alfvénnic fluctuations at $k_\perp = k_i$ are comparable, as in incompressible MHD, but not like the short-wavelength regime $k_\perp \rho_i \gg 1$ , in which the magneticenergy dominates." + The energy density of Alfvénnic fluctuations at scale ko! Is thus ~ pov; ," The energy density of Alfvénnic fluctuations at scale $k_i^{-1}$ is thus $\simeq \rho \delta +v_{k_i}^2$ ." +The time required for the fluctuationenergy at ky=Κι to cascade to ky> 2A. denoted {.. ct satisfies the inequality," The time required for the fluctuationenergy at $k_\perp += k_i$ to cascade to $k_\perp \geq 2 k_i$ , denoted $t_c$ , satisfies the inequality" +in Figure 7..,in Figure \ref{figrv}. + The fleure has suggested that there is a correlation between A: aud log(P)., The figure has suggested that there is a correlation between $R_V$ and $\log(P)$. + However. if we adopt such a period dependency of Ry and apply this to our OGLE data (with the OGLE extinction map). we still obtain a significant detection of noulinearity of the P-L relation with F=6.71.," However, if we adopt such a period dependency of $R_V$ and apply this to our OGLE data (with the OGLE extinction map), we still obtain a significant detection of nonlinearity of the P-L relation with $F=6.74$." + Therefore a period dependency of Ay still caunot explain the observed nonlinear LMC P-L relation., Therefore a period dependency of $R_V$ still cannot explain the observed nonlinear LMC P-L relation. + Another piece of evidence against extinction errors causing the observed ποποσα P-L relation is the P-C relation at παπα elt., Another piece of evidence against extinction errors causing the observed nonlinear P-L relation is the P-C relation at maximum light. + The observed P-C relation for the Galactic aud LAIC long period Cepheids is shown to be flat at the maxima light (Code1917:Ikaubur&Necow2001).," The observed P-C relation for the Galactic and LMC long period Cepheids is shown to be flat at the maximum light \citep{cod47,kan04}." +. There is a souncl plivsical reason behind the flatuess of the P-C relation at the masximaun liebt (Simonetal.1993:IkauburNecow2006):: the interaction of hydrogen ionization front (IF) aud plotosphere at the maximal ieht.," There is a sound physical reason behind the flatness of the P-C relation at the maximum light \citep{sim93,kan04a,kan06}: the interaction of hydrogen ionization front (HIF) and photosphere at the maximum light." + As period increases. Cepheids can only ect cooler or stay roughly in the same temperature range (i.c. he P-C relation is flat) at maxima light.," As period increases, Cepheids can only get cooler or stay roughly in the same temperature range (i.e. the P-C relation is flat) at maximum light." + If an additional amount of extinction 1s needed to make the P-C relation linear at the mean lieht. the the same amount of extinction would force the Cepheids to become totter as period increases at miaxinmun light.," If an additional amount of extinction is needed to make the P-C relation linear at the mean light, the the same amount of extinction would force the Cepheids to become hotter as period increases at maximum light." + This is iu serious contradiction with the pulsation theories and observations., This is in serious contradiction with the pulsation theories and observations. + Iu fact. some researcliers have used the flatuess of the P-C relation at the παπα light O crive the extinction values (Sinonctal.1993:Feruie1991).," In fact, some researchers have used the flatness of the P-C relation at the maximum light to derive the extinction values \citep{sim93,fer94}." +. Furthermore. the multi-phase study of he LMC P-L and P-C relatious implies that the LAIC P-L aud P-C relations are nonlinear at most ofthe phases over the pulsation evcle. especially at pliases near 0.8 (Necow&Ixaubur 2006b)..," Furthermore, the multi-phase study of the LMC P-L and P-C relations implies that the LMC P-L and P-C relations are nonlinear at most ofthe phases over the pulsation cycle, especially at phases near $0.8$ \citep{nge06}. ." + Based on the above aretunents and the aremmeuts preseuted in Waubur&Necow(200L).. Saudageetal.(2001)... (2005) aud Ἱναια&Necow(2006).. we believe that frou the current available extinction studies.," Based on the above arguments and the arguments presented in \citet{kan04}, \citet{san04}, \citet{nge05} and \citet{kan06}, we believe that from the current available extinction studies." + The P-L relation aud the period-color (P-C) relation for Cepheid variables are not independent of eac[um other., The P-L relation and the period-color (P-C) relation for Cepheid variables are not independent of each other. + Madore&Freecanan(1991). have eiven a thorough review for the physics behind the Cephlieid P-L and P-C relations., \citet{mad91} have given a thorough review for the physics behind the Cepheid P-L and P-C relations. + At mean light in the optical bands. a nonlinear P-L relation will imply that the P-C relation is also nonlinear and vice versa.," At mean light in the optical bands, a nonlinear P-L relation will imply that the P-C relation is also nonlinear and vice versa." + The maxima belt P-C relation shows a slightly different behavior. see Necow&Ixaubur(2006b).," The maximum light P-C relation shows a slightly different behavior, see \citet{nge06}." +. Compared to the P-L relation. the nonlinearity of the P-C relation is compelling and easier to visualize (seetheP-CplotsinTamunanu&Reindl2002:ἹναονNecow2001:Sandageetal.2001:Necowetal.2005:IKaubur& 2006).," Compared to the P-L relation, the nonlinearity of the P-C relation is compelling and easier to visualize \citep[see the P-C plots in][]{tam02,kan04,san04,nge05,kan06}." +. Towever the evidence for the uoulinear LMC P-C relation is larecly ignored when the detection of nonlinear P-L relation is criticized., However the evidence for the nonlinear LMC P-C relation is largely ignored when the detection of nonlinear P-L relation is criticized. + The large scatter at eiven period in the P-C relation is Ooeven as an example of possible errors iu extinction., The large scatter at given period in the P-C relation is given as an example of possible errors in extinction. + However. we state againOo that if the extinction errors are ercat. they should also affect the PC relation at 1naxiumua belt but the P-C relation at mmaxinuun light is flat as predicted by theory.," However, we state again that if the extinction errors are great, they should also affect the PC relation at maximum light but the P-C relation at maximum light is flat as predicted by theory." + The F-test applied to the P-C relation has already been discussed ii Ianbur&Necow(2001.2006) and Necowetal.(2005). and will not be repeated here.," The $F$ -test applied to the P-C relation has already been discussed in \citet{kan04,kan06} and \citet{nge05} and will not be repeated here." + The results again strouely support the nonlinear P-C relation., The results again strongly support the nonlinear P-C relation. + Unless new evidence aud/or new theory emerges to show that the Cepheid P-L aud P-C relations should be totally independent. r," Unless new evidence and/or new theory emerges to show that the Cepheid P-L and P-C relations should be totally independent, ." +"elation, There is a nis-conception that if the P-Lrelation is nonlinear in the optical (BV RI) bauds. then the"," There is a mis-conception that if the P-Lrelation is nonlinear in the optical $BVRI$ ) bands, then the" +spectra were then normalized. via Legendre polvnomial fits to the continuum regions.,spectra were then normalized via Legendre polynomial fits to the continuum regions. + The empirical S/N ratios in the normalized spectra range from about 35r to LOO per half resolution clement for the ECII-D cata and from about SO to 150 for the lower resolution GIGOAL cata., The empirical S/N ratios in the normalized spectra range from about 35 to 100 per half resolution element for the ECH-B data and from about 80 to 150 for the lower resolution G160M data. + More detailed discussions of the GIRS data and our adopted: reduction and analysis procedures may be found. in. Welty ο al. (, More detailed discussions of the GHRS data and our adopted reduction and analysis procedures may be found in Welty et al. ( +1999b).,1999b). + The normalized. line profiles for and toward LD 72127. and LD 72127D are shown in Fig. 1.., The normalized line profiles for and toward HD 72127A and HD 72127B are shown in Fig. \ref{fig:naca}. + In cach case. the stronger member of the doublet. (if present). is shown at à continuum level of 1.0. and the weaker member of the doublet. GÉ present) is olfsetbv. | 0.2.," In each case, the stronger member of the doublet (if present) is shown at a continuum level of 1.0, and the weaker member of the doublet (if present) is offsetby $+$ 0.2." + Velocities with respect to the local standard of rest (LSR) may be obtained w subtracting13.4 km + from the heliocentrie velocities shown in theLigure’., Velocities with respect to the local standard of rest (LSR) may be obtained by subtracting13.4 km $^{-1}$ from the heliocentric velocities shown in the. +.. Several previously observed. proliles or LD 72127 and from 1988 (EWIIM ~ 2527 km +: Hobbs et al., Several previously observed profiles for HD 72127A – and from 1988 (FWHM $\sim$ 2.5–2.7 km $^{-1}$; Hobbs et al. + 1991) and from. 1994 (FNLIN ~ 0.3 kmsI: Welty et al., 1991) and from 1994 (FWHM $\sim$ 0.3 km $^{-1}$; Welty et al. + 1996) are included or comparison., 1996) – are included for comparison. + Spectra of some of the weaker optical lines are shown in Fig. 2..," Spectra of some of the weaker optical lines are shown in Fig. \ref{fig:weak}," + where the profile for WD 72127. is ollset above the one for LID 72127D in cach case (ancl note he expanded vertical scale for all the lines)., where the profile for HD 72127A is offset above the one for HD 72127B in each case (and note the expanded vertical scale for all the lines). + Profiles of some of the UV absorption lines toward HD 72127X are shown in Lig.e 3..," Profiles of some of the UV absorption lines toward HD 72127A are shown in Fig. \ref{fig:uv}," + where (again)o the vertical scale has been expauded or the weaker lines., where (again) the vertical scale has been expanded for the weaker lines. + Equivalent widths for the various lines measured from the normalized optical and UV. spectra are isted in Table 1:: for comparison. values reported for LL. Sin. and by Wallerstein et al. (," Equivalent widths for the various lines measured from the normalized optical and UV spectra are listed in Table \ref{tab:ewids}; for comparison, values reported for , , and by Wallerstein et al. (" +1995b). (from. GLIRS,1995b) (from GHRS +whereαρ is the incidence angle for a source on-axis.,where$\alpha_0$ is the incidence angle for a source on-axis. + However. we lack a with a given reflective coating. as a function of the off-axis angle of the X-ray source.," However, we lack a with a given reflective coating, as a function of the off-axis angle of the X-ray source." + In this paper. we present a solution to that problem.," In this paper, we present a solution to that problem." + We develop an analytical approach that can be applied to double cone grazing-incidence X-ray mirrors and. with reasonable accuracy. to Wolter-I. mirrors (unless the f-number is small).," We develop an analytical approach that can be applied to double cone grazing-incidence X-ray mirrors and, with reasonable accuracy, to Wolter-I mirrors (unless the f-number is small)." + The limits of this approximation are discussed in Sect. 2.., The limits of this approximation are discussed in Sect. \ref{DC_WI}. + In Sect. 3..," In Sect. \ref{EffArea}," + we derive general integral formulae (such as Eq. (25))), we derive general integral formulae (such as Eq. \ref{eq:Aeff_fin_offaxis}) )) + to compute the off-axis effective area for a double-reflection X-ray mirror with shallow incident angles. for reflective coating.," to compute the off-axis effective area for a double-reflection X-ray mirror with shallow incident angles, for reflective coating." + As a particular case. in Sect.," As a particular case, in Sect." + 4 we obtain some algebraic expressions for the geometric area and verify that the well-known Eq. (1)), \ref{Geometric} we obtain some algebraic expressions for the geometric area and verify that the well-known Eq. \ref{eq:SC_formula}) ) + can be derived as a particular case., can be derived as a particular case. + In Sect. 5..," In Sect. \ref{Comp}," + the predictions of the analytical approach are validated. for some particular cases. by means of a compariso with the outputs of a ray-tracing routine.," the predictions of the analytical approach are validated, for some particular cases, by means of a comparison with the outputs of a ray-tracing routine." + The results are briefly discussed in Sect. 6.., The results are briefly discussed in Sect. \ref{Final}. + We note that we assume that the off-axis mutual obstructio of mirrors in densely nested mirror assemblies has a negligible effect., We note that we assume that the off-axis mutual obstruction of mirrors in densely nested mirror assemblies has a negligible effect. + Therefore. the results are valid. for either isolated double cone or Wolter-I mirrors. or for mirror modules know to be neghgibly obstructed. such that their effective area simply equals the sum of the contributions of the individual mirrors.," Therefore, the results are valid for either isolated double cone or Wolter-I mirrors, or for mirror modules known to be negligibly obstructed, such that their effective area simply equals the sum of the contributions of the individual mirrors." + The quantification of the off-axis obstruction m mirror assemblies will be considered in future., The quantification of the off-axis obstruction in mirror assemblies will be considered in future. +We consider. in a preliminary way. a grazing-1incidence | mirror. and an on-axis photon source (Fig. 1)).,"We consider, in a preliminary way, a grazing-incidence Wolter-I mirror, and an on-axis photon source (Fig. \ref{fig:mirror_section}))." + The optical axis is aligned with the z axis., The optical axis is aligned with the $z$ axis. +" We define Ry, to be the radius at the parabolic end (1.e.. the maximum radius). Ro the radius at =0 (the plane). Δι the radius at the hyperbolic end (ie. the minimum radius). F the focal point. and f the distance of F from the intersection plane (1.e.. the focal distance)."," We define $R_{\mathrm M}$ to be the radius at the parabolic end (i.e., the maximum radius), $R_0$ the radius at $z=0$ (the ), $R_m$ the radius at the hyperbolic end (i.e., the minimum radius), $F$ the focal point, and $f$ the distance of $F$ from the intersection plane (i.e., the focal distance)." +" In general. we refer to ""primary"" and ""secondary"" segments. instead of “parabola” and “hyperbola”."," In general, we refer to “primary” and “secondary"" segments, instead of “parabola"" and “hyperbola""." +" We denote with Z, the primary segment length along the z axis. and {5 that of the secondary."," We denote with $L_1$ the primary segment length along the $z$ axis, and $L_2$ that of the secondary." + The polar coordinate ts ᾧ., The polar coordinate is $\varphi$. + Because of the surface curvature. the incidence angles on the two surfaces vary in general with the z coordinate.," Because of the surface curvature, the incidence angles on the two surfaces vary in general with the $z$ coordinate." + We define a(z) to be this angle on the primary (0$ 27000 K and $>$ 4.0) we found from lines, as from lines, substantially greater values, 5.8 on average." + In accordance with this finding. we selected from the lists of Daflon et al. (," In accordance with this finding, we selected from the lists of Daflon et al. (" +2003. 2004a.b) two groups of stars. namely the stars with i:25500 A andthestarsmwith (2Y000A: inbotheaseslos (4.0.,"2003, 2004a,b) two groups of stars, namely the stars with $<$ 25500 K and the stars with $>$ 27000 K; in both cases $>$ 4.0." +" E hecorrespondingmeanW, vvalues are compared with our data in Table 3.", The corresponding mean values are compared with our data in Table 3. +" One may see from Table 3 that there is a significant difference inl, ffor both groups between our and Daflon et al", One may see from Table 3 that there is a significant difference in for both groups between our and Daflon et al. +s (2003) results. while the difference with Daflon et al. (,"'s (2003) results, while the difference with Daflon et al. (" +2004a.b) is markedly smaller.,"2004a,b) is markedly smaller." + It is necessary to remember that we have used the vvalues averaged on aand lines. so our real mean vvalues are somewhat smaller than in Table 3.," It is necessary to remember that we have used the values averaged on and lines, so our real mean values are somewhat smaller than in Table 3." + It is important to note once again that we determined independently from lines of three chemical elements. namelyI.. aandΠ.," It is important to note once again that we determined independently from lines of three chemical elements, namely, and." +. Moreover. the Vt determination from aand llines was implemented by the standard method. but that from lines was effected by a quite different method (Paper TT).," Moreover, the Vt determination from and lines was implemented by the standard method, but that from lines was effected by a quite different method (Paper III)." + Nevertheless. all three sets of aare in rather good agreement.," Nevertheless, all three sets of are in rather good agreement." +" In particular. for the B stars with i:25500 A we foundlhal(i)individualV, vvalues range. as a rule. between and 5Iz Gi) mean vvalues are 1.0. 0.5 and 2.5 fforHe. παπάOL. respectively. ("," In particular, for the B stars with $<$ 25500 K we found that (i) individual values range, as a rule, between 0 and 5; (ii) mean values are 1.0, 0.5 and 2.5 for, and, respectively. (" +"Note that we have not found reasons to prefer ID) over 1,(@O1D). so we used an averaged value 102).","Note that we have not found reasons to prefer ) over ), so we used an averaged value ))." + Thus. our results fromr. aand llines confirm that our lower sscule is preferable to the higher sscule of Daflon et al. (," Thus, our results from, and lines confirm that our lower scale is preferable to the higher scale of Daflon et al. (" +2003. 2004a.b).,"2003, 2004a,b)." +" It is important to remember as well that our mean Mg abundance 7.59 obtained with the 1D) values from the AAS| line is precisely contirmed from an analysis of the weak TISTI line that is insensitive to1,.", It is important to remember as well that our mean Mg abundance 7.59 obtained with the ) values from the 4481 line is precisely confirmed from an analysis of the weak 7877 line that is insensitive to. +. We implemented trial determinations of logz(Mg) with various for some stars from first and second groups.," We implemented trial determinations of $\log \varepsilon({\rm +Mg})$ with various for some stars from first and second groups." +" The changes in ogz(Mg) depend substantially on the effective temperature7,41 nevertheless. the final conclusion is clear: the differences in the vvalues explain completely the above-mentioned discrepancies between our and Daflon et al"," The changes in $\log \varepsilon({\rm Mg})$ depend substantially on the effective temperature; nevertheless, the final conclusion is clear: the differences in the values explain completely the above-mentioned discrepancies between our and Daflon et al." +’s (2003) mean magnesium abundance.,'s (2003) mean magnesium abundance. + It is interesting to note that. according to Daflon (2004). the ower vvalues can be a result of the cooler effective temperatures7;r.," It is interesting to note that, according to Daflon (2004), the lower values can be a result of the cooler effective temperatures." +. The difference between our and Daflon et al, The difference between our and Daflon et al. +/s sscales cannot be sufficient to cause a marked change in thermal velocities and. hence. a change in;.,"'s scales cannot be sufficient to cause a marked change in thermal velocities and, hence, a change in." +". We believe that the difference inl; ddiscussed above may be connected with a rough correlation between the observed equivalent widths 11 and excitation potentials x: lines with higher x, tend to show lower IV on average.", We believe that the difference in discussed above may be connected with a rough correlation between the observed equivalent widths $W$ and excitation potentials $\chi_e$: lines with higher $\chi_e$ tend to show lower $W$ on average. + These lines are more sensitive to tthan weaker lines. so their calculated ΤΕ values change more significantly when increases.," These lines are more sensitive to than weaker lines, so their calculated $W$ values change more significantly when increases." + In this case one should increase tto eliminate a discrepancy in the derived abundances between relatively weak and strong lines., In this case one should increase to eliminate a discrepancy in the derived abundances between relatively weak and strong lines. + For more than ten years the C. N. and O abundances have been considered as indicators of the metallicity of early B stars in reference to the Sun.," For more than ten years the C, N, and O abundances have been considered as indicators of the metallicity of early B stars in reference to the Sun." + However. it is gradually becoming clear that this choice is not the best one.," However, it is gradually becoming clear that this choice is not the best one." + On the one hand. there are empirical data that mixing exists in the early B-type MS stars between their interiors and surface layers. so the observed abundances of the CNO-cycle elements may be affected by evolutionary alterations.," On the one hand, there are empirical data that mixing exists in the early B-type MS stars between their interiors and surface layers, so the observed abundances of the CNO-cycle elements may be affected by evolutionary alterations." + On the other hand. the solar C. N and O abundances were continuously revised and tended to decrease during this period.," On the other hand, the solar C, N and O abundances were continuously revised and tended to decrease during this period." + Unfortunately. it was impossible in these cases to use the accurate meteoritic abundances. because C. N and O are incompletely condensed in meteorites. so their meteoritic abundances are signiticantly lower than the solar ones.," Unfortunately, it was impossible in these cases to use the accurate meteoritic abundances, because C, N and O are incompletely condensed in meteorites, so their meteoritic abundances are significantly lower than the solar ones." + Magnesium. unlike C. N and O. does not have such demerits.," Magnesium, unlike C, N and O, does not have such demerits." + First. this chemical element should not alter markedly its abundance in B stars during the MS phase.," First, this chemical element should not alter markedly its abundance in B stars during the MS phase." + Second. its solar abundance is known now very precisely from spectroscopic and meteoritic data.," Second, its solar abundance is known now very precisely from spectroscopic and meteoritic data." + Displaying the rather strong LHH8I.2À line in spectra of early and medium B stars. this element is appropriate as a reliable indicator of their metallicity.," Displaying the rather strong 4481.2 line in spectra of early and medium B stars, this element is appropriate as a reliable indicator of their metallicity." + Using the high-resolution spectra of 52 B stars we effected a non-LTE analysis of the A4481.2 lline and determined the magnesium abundance., Using the high-resolution spectra of 52 B stars we effected a non-LTE analysis of the 4481.2 line and determined the magnesium abundance. + We studied the role of the neighbouring, We studied the role of the neighbouring +curve to the right).,curve to the right). + This is not unexpected and is discussed in Section 3.3. below., This is not unexpected and is discussed in Section \ref{ssechighm} below. + “Phere is no evidence of a departure [rom the PS curve at amass of 64. corresponding to the size of smoothing blocks of side 4 (this is in contrast to the ηΞ case. discussed below).," There is no evidence of a departure from the PS curve at a mass of 64, corresponding to the size of smoothing blocks of side 4 (this is in contrast to the $n=-2$ case, discussed below)." + The maximum mass of collapsed halos is quite small. less than 125 even for the largest box. L=256.," The maximum mass of collapsed halos is quite small, less than 125 even for the largest box, $L=256$." + Given that the smallest halos to collapse in our nmoclel (apart from isolated cells) have mass 8. then this gives avery small cvnamic range.," Given that the smallest halos to collapse in our model (apart from isolated cells) have mass 8, then this gives a very small dynamic range." + We could. force larger objects to form by allowing a larger fraction of the box to collapse (this would be legitimate if. for example. one were to regard the whole box as a single collapsed halo) however one would not then expect the evolution to be self-similar.," We could force larger objects to form by allowing a larger fraction of the box to collapse (this would be legitimate if, for example, one were to regard the whole box as a single collapsed halo) however one would not then expect the evolution to be self-similar." + The curves for the steeper spectrum. m=2. extend to much higher masses because the spectrum has much more power on large scales than for n=Q0.," The curves for the steeper spectrum, $n=-2$, extend to much higher masses because the spectrum has much more power on large scales than for $n=0$." + Lere we cdo see evidence of kinks at the blocking masses of 64. 512 and 4096. especially at the final output time when half the box has collapsed: there is an excess of halos of slightly higher mass and a deficit of slightlv lower mass than these.," Here we do see evidence of kinks at the blocking masses of 64, 512 and 4096, especially at the final output time when half the box has collapsed: there is an excess of halos of slightly higher mass and a deficit of slightly lower mass than these." + Overall the spectrum is a reasonable Gt to the PS prediction at masses above 100. but shows and excess between masses of SN and 100.," Overall the spectrum is a reasonable fit to the PS prediction at masses above 100, but shows and excess between masses of 8 and 100." + 6 shows a projection of the largest halos in one L=128 box of cach spectral type at a time when half the mass has collapsed into halos., \ref{fig:proj} shows a projection of the largest halos in one $L=128$ box of each spectral type at a time when half the mass has collapsed into halos. + Many of the irregular shapes which are visible are due to projection ellects., Many of the irregular shapes which are visible are due to projection effects. + Our halos tend to exhibit more variety of axial ratios than in theAloclel., Our halos tend to exhibit more variety of axial ratios than in the. +. Phere the relative length of the major- and minor-axes is fixed all times at approximately 1:11.59. whereas ours start with more typically 1:1 (for collapse of isolated. blocks as in 2bb) or 1:1.5 (for the collapse of overlapping blocks as in 2ec). developping rapidlv to more complex structures with a great. variety of shapes.," There the relative length of the major- and minor-axes is fixed all times at approximately 1:1.59, whereas ours start with more typically 1:1 (for collapse of isolated blocks as in \ref{fig:halo}b b) or 1:1.5 (for the collapse of overlapping blocks as in \ref{fig:halo}c c), developping rapidly to more complex structures with a great variety of shapes." + S shows the distribution of axial ratios for all halos of mass greater than or equal to 8 for η=0 and greater than, \ref{fig:axes} shows the distribution of axial ratios for all halos of mass greater than or equal to 8 for $n=0$ and greater than +the initial separation and the initial orbital energy such that models which start with a larger separation require a smaller initial eccentricity.,the initial separation and the initial orbital energy such that models which start with a larger separation require a smaller initial eccentricity. + In all cases. the apparent orbit of the two galaxies becomes (or was to beein with) nearly parabolic at the present (ime. consistent with recent estimates. of the Milky WayAndromeda orbit. (see.e$...2)..," In all cases, the apparent orbit of the two galaxies becomes (or was to begin with) nearly parabolic at the present time, consistent with recent estimates of the Milky Way–Andromeda orbit \citep[see, e.g.,][] {vdM07}." + While the rest of this paper will primarily present. the results of one particular model. we will also show that all models. vield similar estimates for the eventual merger between the Milky Way and Andromeda.," While the rest of this paper will primarily present the results of one particular model, we will also show that all models yield similar estimates for the eventual merger between the Milky Way and Andromeda." + We will argue in refssee:time that this convergence results naturally from our assumed intragroup medium., We will argue in \\ref{ssec:time} that this convergence results naturally from our assumed intragroup medium. + The model we choose to focus upon begins with an initial separation of 1.3 Alpe. and initializes the Milky Way and Xndromeda on an eccentric orbit «€=0.494. with a distance at. perigalacticon of 450 κρο," The model we choose to focus upon begins with an initial separation of 1.3 Mpc, and initializes the Milky Way and Andromeda on an eccentric orbit $\epsilon=0.494$, with a distance at perigalacticon of 450 kpc." + With this orbit the initial angular velocity is 65 which could likely. originate from tical torques (??)..," With this orbit the initial angular velocity is 65, which could likely originate from tidal torques \citep{GT78,RLB89}." + This particular moce begins with the largest separation of all our moclels ai therefore may be the best representation of the evolution of the Local Group since its decoupling from the universa expansion., This particular model begins with the largest separation of all our models and therefore may be the best representation of the evolution of the Local Group since its decoupling from the universal expansion. + Since this model tracks the Local Group the farthest into the past. the intragroup medium. also has a significant amount of time to react to the two galaxies anc therefore is likely to be the most insensitive to its initia configuration.," Since this model tracks the Local Group the farthest into the past, the intragroup medium also has a significant amount of time to react to the two galaxies and therefore is likely to be the most insensitive to its initial configuration." + Jo simulate the evolution of our. Local Group and in particular the interaction between the Ην Was ando Ancromeda use the publically available N-bodyfhverodvnamic coce (?).., To simulate the evolution of our Local Group and in particular the interaction between the Milky Way and Andromeda use the publically available N-body/hydrodynamic code \citep{SpGad2}. + This. version of the code employs the “conservativeentropy formulation of Smoothee Particle Lvdrodyvnamics (SPLH.7) that conserves both energv and entropy (unlikeearlier.versionsofSPL:seec.g. 7).. while improving shock-capturing.," This version of the code employs the “conservative–entropy” formulation of Smoothed Particle Hydrodynamics \citep[SPH,][]{SHEnt} that conserves both energy and entropy \citep[unlike earlier versions of SPH; see +e.g.,][]{H93sph}, while improving shock-capturing." + We assume that the eas is of primordial composition. and include the ellects of radiative cooling.," We assume that the gas is of primordial composition, and include the effects of radiative cooling." + Star formation and its associated feedback: are. both included in a manner very similar to that clescribed in 2.., Star formation and its associated feedback are both included in a manner very similar to that described in \citet{Cox06}. + As is commonly assumed. stars are stochastically formed at a rate determined by the SPII eas density (sec.c.g.2???) with an ellicieney set to match. the observed: correlation oetween star formation and gas density (?)..," As is commonly assumed, stars are stochastically formed at a rate determined by the SPH gas density \citep[see, e.g.][]{Kz92,SH03,SdMH05, +Cox06} with an efficiency set to match the observed correlation between star formation and gas density \citep{Kenn98}." + Feedback from stellar winds and supernovae is treated in à very simplistic manner. namely the SPL particles that inve sullicient density to form stars are fixed to have an elective temperature of 107 Ix. This methodology is sinilar in principle to most of the currently. favored: models. for eedback (see.e.g..2222). and is easy to implement.," Feedback from stellar winds and supernovae is treated in a very simplistic manner, namely the SPH particles that have sufficient density to form stars are fixed to have an effective temperature of $10^5$ K. This methodology is similar in principle to most of the currently favored models for feedback \citep[see, e.g.,][]{Sp00,SH03, Stin06,Cox06}, and is easy to implement." + Since he focus of this work is the large.scale evolution of the Local Group and the generic dynamics of the collision between he Alilky Way and. Ancromeda. the detailed treatment of he interstellar medium does not influence our primary conclusions.," Since the focus of this work is the large–scale evolution of the Local Group and the generic dynamics of the collision between the Milky Way and Andromeda, the detailed treatment of the inter–stellar medium does not influence our primary conclusions." + Numerical resolution is a significant consideration or any computational problem., Numerical resolution is a significant consideration for any computational problem. + For our purposes here. we require sullicient resolution to reliably follow the interaction and merger of the Milky Way and Andromeda. while maintaining the ability to perform a number of simulations with the available computational resources.," For our purposes here, we require sufficient resolution to reliably follow the interaction and merger of the Milky Way and Andromeda, while maintaining the ability to perform a number of simulations with the available computational resources." + ‘These considerations motivated the particle number choices outlined in refsec:model.., These considerations motivated the particle number choices outlined in \\ref{sec:model}. + Given the large. number of components. in ese simulations (stellar disks. dark halos. and intragroup =jiedium) and the desire to reduce twobody. cllects. we required all particles to have an identical mass of 210 and we emploved a universal gravitational softening eneth of 150 pe.," Given the large number of components in these simulations (stellar disks, dark halos, and intragroup medium) and the desire to reduce two–body effects, we required all particles to have an identical mass of $2\times 10^{7}$ and we employed a universal gravitational softening length of 150 pc." + To test the sensitivity of the results to dese) parameter choices. we also ran a higher resolution Persion of one model with 30 times the barvonic disk mass resolution (and therefore number of particles) and 2 times 10 resolution of the dark matter and intragroup medium.," To test the sensitivity of the results to these parameter choices, we also ran a higher resolution version of one model with 30 times the baryonic disk mass resolution (and therefore number of particles) and 2 times the resolution of the dark matter and intragroup medium." + In lis case we also decreased the gravitational softening length X the barvons by a factor of 3. and increased that of the ark matter by a factor of 3.," In this case we also decreased the gravitational softening length of the baryons by a factor of 3, and increased that of the dark matter by a factor of 3." + While this test. vielded much »tter resolution of the stellar disks and in particular the idal material. the general merger dynamics were identical o the low resolution version.," While this test yielded much better resolution of the stellar disks and in particular the tidal material, the general merger dynamics were identical to the low resolution version." + In Figures 2. through 6 we present the basic propertics of he dynamical evolution of our Local Group. from 5 Car in he past and until 10 Gar into the future. bevond the merger ime between the Milky Way aid Andromeda.," In Figures \ref{fig:starimages}~ through \ref{fig:crelvel} we present the basic properties of the dynamical evolution of our Local Group, from 5 Gyr in the past and until 10 Gyr into the future, beyond the merger time between the Milky Way and Andromeda." + Most. of the eatures present in these figures are generic to binary galaxy interactions. and have been described in great detail by prior studies (see.e.g.27227).," Most of the features present in these figures are generic to binary galaxy interactions, and have been described in great detail by prior studies \citep[see, e.g.,][]{TT72,BH91, +BH92rev,MH96,Cox06}." + However. we will review some of he details that are particularly relevant to the Local Group. ancl subsequently highlight the unique status of our own Sun which will be a participant in this galaxy. interaction.," However, we will review some of the details that are particularly relevant to the Local Group, and subsequently highlight the unique status of our own Sun which will be a participant in this galaxy interaction." + The uture evolution of structures bevond the local group was simulated elsewhere (2??7)..," The future evolution of structures beyond the local group was simulated elsewhere \citep{NL03,NL04,Bus03,Bus05}." + ‘To begin. Figures 2. and 3. present the entire evolution of the Local Group from the point of view of a. distant observer.," To begin, Figures \ref{fig:starimages}~ and \ref{fig:gasimages} present the entire evolution of the Local Group from the point of view of a distant observer." +" These images begin at the start of our simulation. when the Milky Way anc Andromeda: are separated: by 1.3 Alpe. and include the present state of the Local Croup (labeled. ""Today) and the eventual merger of the Milly Way and Andromeda."," These images begin at the start of our simulation, when the Milky Way and Andromeda are separated by 1.3 Mpc, and include the present state of the Local Group (labeled “Today”) and the eventual merger of the Milky Way and Andromeda." + As a guide to the eve. each. panel includes the trajectory of both the Milkv Way and Andromeda.," As a guide to the eye, each panel includes the trajectory of both the Milky Way and Andromeda." + Shown in Ligure 2. is the evolution. of the stellar component. which in our simulation only has contributions from the Milkv Way anc Andromeda. as we ignore any structure smaller than the two largest galaxies in the Local Croup.," Shown in Figure \ref{fig:starimages} is the evolution of the stellar component, which in our simulation only has contributions from the Milky Way and Andromeda as we ignore any structure smaller than the two largest galaxies in the Local Group." + Figure 3. presents the projected gas distribution during the interaction. with panels shown at the same times as in Figure 2..," Figure \ref{fig:gasimages} presents the projected gas distribution during the interaction, with panels shown at the same times as in Figure \ref{fig:starimages}." + Here. the colorscale has been stretched to emphasize the abundant quantity of lowdensity gas that is spread. throughout the local group., Here the color–scale has been stretched to emphasize the abundant quantity of low–density gas that is spread throughout the local group. + The initial condition of our Local Group model assumes a uniform cistribution of warm eas. however the gas quickly responds to. the nonuniform potential.," The initial condition of our Local Group model assumes a uniform distribution of warm gas, however the gas quickly responds to the non–uniform potential." + In. particular gas is accreted and shocked to form a hvelrostatic halo of warm gas around the Alilky Wavy and Andromeda galaxies., In particular gas is accreted and shocked to form a hydrostatic halo of warm gas around the Milky Way and Andromeda galaxies. + The gas cistribution is also clearly allected by the interaction itself. as shocks," The gas distribution is also clearly affected by the interaction itself, as shocks" +drastically changed by a gas stream and depend strongly on the mass and its internal structure of the cloud. i.e. mainly on its binding energy.,"drastically changed by a gas stream and depend strongly on the mass and its internal structure of the cloud, i.e. mainly on its binding energy." + In general. the relative motion of a subsonically hot plasma stream stabilizes the clouds.," In general, the relative motion of a subsonically hot plasma stream stabilizes the clouds." + Without heat conduction. clouds with their initial states close to or inside the KH-unstable regime suffer from huge mass loss in the form of stripped-off cloudlets.," Without heat conduction, clouds with their initial states close to or inside the KH-unstable regime suffer from huge mass loss in the form of stripped-off cloudlets." +" While a small homogeneous cloud (nodel K) is stable for about 5 7,, and then strongly exposec to disruption into small gas packets. small dense clouds (model E) can avoid the transition into the KH-unstable state ard resist the violent hot plasma so that mass loss or even any strong deformation of the cloud does not occur."," While a small homogeneous cloud (model K) is stable for about 5 $\tau_{\mbox{\tiny dyn}}$ and then strongly exposed to disruption into small gas packets, small dense clouds (model E) can avoid the transition into the KH-unstable state and resist the violent hot plasma so that mass loss or even any strong deformation of the cloud does not occur." + Large massive clouds (model U) lose about of their mass within 5 nud may dissolve on larger timescales., Large massive clouds (model U) lose about of their mass within 5 $\tau_{\mbox{\tiny dyn}}$ and may dissolve on larger timescales. +detailed analysis of figure 2. where the core temperaturenumostv (1;L) relationship obtained iu this work solid. liue and in IHausen (1999) dotted line are shown in the upper paucl. whereas in the lower paucl hei relative differeuce is shown as a function of the core cluperature.,"detailed analysis of figure 2, where the core temperature--luminosity $T_{\rm c}-L$ ) relationship obtained in this work — solid line — and in Hansen (1999) — dotted line — are shown in the upper panel, whereas in the lower panel their relative difference is shown as a function of the core temperature." + As it can be seen there. for a given T; the uminositv is about lavecr dowutolos(L/L.)2 L5 and. thus. the model envelopes of Hansen (1999) are systematically more transparent than our envelopes for he same Z.. resulting iu a more efficient cooliug of the white dwarf interior.," As it can be seen there, for a given $T_{\rm c}$ the luminosity is about larger down to $\log(L/L_{\sun})\simeq -4.5$ and, thus, the model envelopes of Hansen (1999) are systematically more transparent than our envelopes for the same $T_{\rm c}$, resulting in a more efficient cooling of the white dwarf interior." + To be precise. let us quantify how this affects the cooling sequences.," To be precise, let us quantify how this affects the cooling sequences." + For Iuniuosities smaller thui Ly=10?L:; the contribution of thermal neutrinos aud unclear reactions are negligible aud. thus. oue cau sately asstune that the sole contribution to the cooling process is the release of binding energy.," For luminosities smaller than $L_0=10^{-2}L_{\sun}$ the contribution of thermal neutrinos and nuclear reactions are negligible and, thus, one can safely assume that the sole contribution to the cooling process is the release of binding energy." + Therefore we cau write: Accordingly. the difference in the cooling times between both cooling sequences can be easily estimated: where τν1ο) stands for the TZ.E relationship derived in this paper aud Zpgt(T.) is the oue derived by IHauseu 1999).," Therefore we can write: Accordingly, the difference in the cooling times between both cooling sequences can be easily estimated: where $L_{\rm TW}(T_{\rm c})$ stands for the $T_{\rm c}-L$ relationship derived in this paper and $L_{\rm BH}(T_{\rm c})$ is the one derived by Hansen (1999)." + We have independently computed a set of binding snereies with the same equation of state described iu 1ο previous section and used equation (2) to obtain an tinte of the difference introduced by the differences i je transparency of the cuvelope., We have independently computed a set of binding energies with the same equation of state described in the previous section and used equation (2) to obtain an estimate of the difference introduced by the differences in the transparency of the envelope. + At log(L/L.)=L5 we eot Afz2.1 Cyr. which is in good agreecinent with the value derived from the evolutionary code (1.8 Cr).," At $\log(L/L_{\sun})=-4.5$ we got $\Delta t\simeq 2.1$ Gyr, which is in good agreement with the value derived from the evolutionary code (1.8 Gyr)." + Thus. us difference can be mainly ascribed to the differences iu 1ο frauspareuceyv of the adopted model envelopes.," Thus, this difference can be mainly ascribed to the differences in the transparency of the adopted model envelopes." + Now the question is. why is there a difference in the nodel envelopes?," Now the question is, why is there a difference in the model envelopes?" + This question cannot be answered , This question cannot be answered categorically. +Iu fact. we are using the same thicknesses for the IT aud lle lavers. the same euvelope EOS aud the same OPAL (Z= 0) opacities for T>6000 IX. but not the same model atmospheres for the boundary conditions.," In fact, we are using the same thicknesses for the H and He layers, the same envelope EOS and the same OPAL $Z=0$ ) opacities for $T\geq6000$ K, but not the same model atmospheres for the boundary conditions." + However we do have indirect wavs of checking the consistency. of our results., However we do have indirect ways of checking the consistency of our results. + We recoimputed the cooling sequence of our 0.606 AL: white dwarf using a erev T(r) relation for deriving the boundary conditions., We recomputed the cooling sequence of our 0.606 $M_{\sun}$ white dwarf using a grey $T(\tau)$ relation for deriving the boundary conditions. + We found that the {ο£L relationship derived in this way was coincident. as loug as Tig=GOOQ Tk. with the one obtained using the model atiuosplieres boundary conditions. mn agreement with the fudines bv Tausen (1999).," We found that the $T_{\rm c}-L$ relationship derived in this way was coincident, as long as $T_{\rm eff}\geq 6000$ K, with the one obtained using the model atmospheres boundary conditions, in agreement with the findings by Hansen (1999)." + This allows us to directly compare our 7;L rolatioushipa (for τω=6000 IK) with the iudepenudoeut results of Althaus Beuvenuto (1998) for their 0.600 AL; white dwarf cooling track., This allows us to directly compare our $T_{\rm c}-L$ relationship (for $T_{\rm eff}\geq 6000$ K) with the independent results of Althaus Benvenuto (1998) for their 0.600 $M_{\sun}$ white dwarf cooling track. + This calculation adopts our sale imetallicitv aud thickness for the We and II lavers., This calculation adopts our same metallicity and thickness for the He and H layers. + Moreover. Althaus Benvenuto (1998) also used the same EOS in the envelope and the same OPAL opacities for T26000 Ik. The oulv differences of this calculation with respect to our calculation aud that of Hansen (1999) are threefold.," Moreover, Althaus Benvenuto (1998) also used the same EOS in the envelope and the same OPAL opacities for $T\geq 6000$ K. The only differences of this calculation with respect to our calculation and that of Hansen (1999) are threefold." + First. Althaus Deuvenuto (1998) used a exev P(r) relation for deriving the boundary conditious.," First, Althaus Benvenuto (1998) used a grey $T(\tau)$ relation for deriving the boundary conditions." + As we Lave shown. this procedure is well justified as long as Digg=6000 IX. Second. Althaus Benvenuto (1998) adopted a slightly differeut C/O profile for the core.," As we have shown, this procedure is well justified as long as $T_{\rm eff}\geq 6000$ K. Second, Althaus Benvenuto (1998) adopted a slightly different C/O profile for the core." +" Since the adopted internal C/O stratification docs not affect at all the derived 1.1, relationship. the slightly differcut C/O profile adopted by Althaus Benvenuto (1998) does not iuflueuce the result of the comparison."," Since the adopted internal C/O stratification does not affect at all the derived $T_{\rm c}-L$ relationship, the slightly different C/O profile adopted by Althaus Benvenuto (1998) does not influence the result of the comparison." + Third. they ciploved the full.spectra. turbulence theory of convection by Canuto. Goldiiau Mazztoelli (1996) instead of the mixing leugth theory. for the computation of the convective superadiabatie eracdicut the cuvelope.," Third, they employed the full–spectrum turbulence theory of convection by Canuto, Goldman Mazzitelli (1996) instead of the mixing length theory, for the computation of the convective superadiabatic gradient in the envelope." + However. the treatiieut of supcradiabatic categorically!convection does not affect the Το relationship.," However, the treatment of superadiabatic convection does not affect the $T_{\rm c}-L$ relationship." + Tn the upper panel of figure 2 we also show the core temperatureluninosity relationship derived by Althaus Benvenuto (1998) as a dasheddotted. line. whereas in the lower panel of this Segure the relative difference with respect to the present calculation is shown.," In the upper panel of figure 2 we also show the core temperature–luminosity relationship derived by Althaus Benvenuto (1998) as a dashed–dotted line, whereas in the lower panel of this figure the relative difference with respect to the present calculation is shown." + Our result closely follows that of Althaus Deuveuuto (1998) in the core temperature range when {μι=6000 EK. and therefore it is quite apparent from this feure that for some reason the model euvelopes of Hansen (1999) appear to be. at least in this temperature range. far more transparent than ours.," Our result closely follows that of Althaus Benvenuto (1998) in the core temperature range when $T_{\rm eff}\geq 6000$ K, and therefore it is quite apparent from this figure that for some reason the model envelopes of Hansen (1999) appear to be, at least in this temperature range, far more transparent than ours." + It is however remarkable that the calculation reported iu the present work and that of Hansen (1999) are parallel for almost the full rauge of Iuniunosities studied here., It is however remarkable that the calculation reported in the present work and that of Hansen (1999) are parallel for almost the full range of luminosities studied here. + Finally both our calculation and that of Tausen (1999) differ considerably at low 7; from the calculation of Althaus Benvenuto (1998). as is expected because of the improved atinospheric treatiueut at very low luminosities.," Finally both our calculation and that of Hansen (1999) differ considerably at low $T_{\rm c}$ from the calculation of Althaus Benvenuto (1998), as is expected because of the improved atmospheric treatment at very low luminosities." + For the sake of completcucss we also show the relationship obtained by Wood (1995) as a long dashed line (he also used a ervey T(r) relationship to derive the boundary conditions). although we refrain from doiug a detailed comparison with our results because this cooling sequence was computed using a differcut EOS for the white dwarf envelope.," For the sake of completeness we also show the relationship obtained by Wood (1995) as a long dashed line (he also used a grey $T(\tau)$ relationship to derive the boundary conditions), although we refrain from doing a detailed comparison with our results because this cooling sequence was computed using a different EOS for the white dwarf envelope." + Note. however. that at high," Note, however, that at high" +of disk is important to investigate the disk evolution. and fragmentation⋅ mlor /zz101 vvears.,of disk is important to investigate the disk evolution and fragmentation for $t\gtrsim 10^4$ years. + In this study. no model shows the formation of a star-λαοί system during the main aceretion phase because the secondary object continues to increase its mass and. finally exceeds the hyvdrogen-burning limit (AZ0.08 MM).," In this study, no model shows the formation of a star-planet system during the main accretion phase because the secondary object continues to increase its mass and finally exceeds the hydrogen-burning limit $M\gtrsim0.08$ $_\odot$ )." + On he other hand. Vorobvov&Basu(2010a) and. Machidaοἱal.(2010). showed the formation of a star-planct svsten during the main aceretion phase.," On the other hand, \citet{vorobyov_basu10a} and \citet{machidaetal10} showed the formation of a star-planet system during the main accretion phase." + The dilference is thought o be caused by treatment of the protostar and sink., The difference is thought to be caused by treatment of the protostar and sink. + In Vorobvov&Basu(2010a) and Machida (2010).. the protostar (or sink cell) is fixed at the center of the computational domain.," In \citet{vorobyov_basu10a} and \citet{machidaetal10}, the protostar (or sink cell) is fixed at the center of the computational domain." + Lt is expected. that. such reatment promotes fragmentation., It is expected that such treatment promotes fragmentation. + In reality. the density luctuation arising around the protostar can cancel out by movement of the protostar.," In reality, the density fluctuation arising around the protostar can cancel out by movement of the protostar." + Thus. fragmentation tends to occur when the protostar is fixed.," Thus, fragmentation tends to occur when the protostar is fixed." + In αστον. Vorobxov&Basu(2010a) ancl Machidaοἱal.(2010) did not impose the sink on fragments formed in the circumstellar disk.," In addition, \citet{vorobyov_basu10a} and \citet{machidaetal10} did not impose the sink on fragments formed in the circumstellar disk." + Instead. they suppressed. further collapse of fragments with adiabatie equation of state.," Instead, they suppressed further collapse of fragments with adiabatic equation of state." + Such treatment decreases the mass accretion onto fragments in some degree., Such treatment decreases the mass accretion onto fragments in some degree. + On the other hand. our sink treatment may overestimate the mass accretion onto fragments or protostar.," On the other hand, our sink treatment may overestimate the mass accretion onto fragments or protostar." + So far. few authors have investigated the evolution of circumstellar disk. from molecular cloud core.," So far, few authors have investigated the evolution of circumstellar disk from molecular cloud core." + With an isothermal equation of state. WKratterefaf(2010). showed that fragmentation occurs in the circumstellar disk with a wide parameter space during the carly stage in the main accretion phase and claimed that fragmentation Lrecqucnthy occurs when the disk-to-stellar mass ratio is greater than unity.," With an isothermal equation of state, \citet{ketal10} showed that fragmentation occurs in the circumstellar disk with a wide parameter space during the early stage in the main accretion phase and claimed that fragmentation frequently occurs when the disk-to-stellar mass ratio is greater than unity." +" However. their assumption of isothermality seenis not to be valid. for the disk evolution of the carly main accretion phase. because the gas becomes opaque and behaves adiabatically when the gas density exceeds. the critical density of p,=102$qpii&cm ο. 2010))."," However, their assumption of isothermality seems not to be valid for the disk evolution of the early main accretion phase, because the gas becomes opaque and behaves adiabatically when the gas density exceeds the critical density of $\rho_c \simeq 10^{-13}-10^{- 14} {\rm g~cm^{-3}}$ (e.g., )." + In. addition. the radiative cooling can allect the disk evolution ~10! vears after the protostar formation as described in refsec:cooling..," In addition, the radiative cooling can affect the disk evolution $\sim 10^4$ years after the protostar formation as described in \\ref{sec:cooling}." + Since the adiabatic equation. of. state stabilizes the circumstellar clisk. fragmentation barely occurs in our calculation even when the disk-to-stellar mass ratio exceeds unity.," Since the adiabatic equation of state stabilizes the circumstellar disk, fragmentation barely occurs in our calculation even when the disk-to-stellar mass ratio exceeds unity." + Thus. Ixrattere£a£.(2010) may overestimate the fragmentation condition. while our calculation may unclerestimate it because of lack of radiative cooling.," Thus, \citet{ketal10} may overestimate the fragmentation condition, while our calculation may underestimate it because of lack of radiative cooling." + Walchefa£.(2009) also stucied the circumstellar clisk formation with the aciabatic equation ofstate and radiative cooling., \citet{wetal09} also studied the circumstellar disk formation with the adiabatic equation of state and radiative cooling. + Vhey showed no fragmentation in the circumstellar disk. because the disk becomes very hot. during the early stage of main accretion. phase.," They showed no fragmentation in the circumstellar disk, because the disk becomes very hot during the early stage of main accretion phase." + Vheir spatial resolution is. iowever. somewhat coarse: the minimum smoothing length of their study is Z4=2 AU.," Their spatial resolution is, however, somewhat coarse; the minimum smoothing length of their study is $h_{\rm min}= 2$ AU." + On the other hand. P~3 AU in our simulations.," On the other hand, $h_{\rm min}\sim0.3$ AU in our simulations." + Lo addition. they restricted their initial conditions to rapidlv rotating cases 67>107) to investigate cisk evolution before the central density becomes ugh.," In addition, they restricted their initial conditions to rapidly rotating cases $\beta > 10^{-2}$ ) to investigate disk evolution before the central density becomes high." + The observation suggested that molecular cloud cores iie the rotational energy of 10.3<3«0.07 with a typical value of 3270.02 (Caselliefa£2002)., The observation suggested that molecular cloud cores have the rotational energy of $10^{-4}<\beta< 0.07$ with a typical value of $\beta \simeq 0.02$ \citep{cetal02}. +. Thus. they studied he cloud evolution in the limited parameter range.," Thus, they studied the cloud evolution in the limited parameter range." + We have carried out. hvdro-dvnamical. simulation to investigate the evolution of the circumstellar disk with two non-dimensional parameters representing the thermal anc rotational energy of the initial cloud., We have carried out hydro-dynamical simulation to investigate the evolution of the circumstellar disk with two non-dimensional parameters representing the thermal and rotational energy of the initial cloud. + Phe thermal energy a is related to the mass accretion rate onto the circumstellar disk as Mask=aUT+ (seo. Machidaefaf 2011).," The thermal energy $\alpha$ is related to the mass accretion rate onto the circumstellar disk as $\dot{M}_{\rm disk }= \alpha^{-3/2} c_s^3 G^{-1}$ (see, \citealt{machidaetal11}) )." + Thus. smaller a provides a high aceretion rate onto the circumstellar disk. ancl vice versa.," Thus, smaller $\alpha$ provides a high accretion rate onto the circumstellar disk and vice versa." + On the other hand. the initial rotational energy that is represented. by parameter dis related to the disk radius.," On the other hand, the initial rotational energy that is represented by parameter $\beta$ is related to the disk radius." + The centrifugal radius of theinitial cloud is related to 3 as regc=3402. where Ry is the initial cloud radius.," The centrifugal radius of theinitial cloud is related to $\beta$ as $r_{\rm cent} = 3 R_0 \beta$, where $R_0$ is the initial cloud radius." + Thus. with larger 2. the cloud forms a larger disk in the main accretion phase.," Thus, with larger $\beta$, the cloud forms a larger disk in the main accretion phase." + La other words. with larger 2. a large fraction of the in-falling matter accretes onto the disk. rather than directly onto the primary protostar.," In other words, with larger $\beta$, a large fraction of the in-falling matter accretes onto the disk, rather than directly onto the primary protostar." + As a result. smaller a and larger 3 increase disk surface density and makes a gravitationally unstable clisk.," As a result, smaller $\alpha$ and larger $\beta$ increase disk surface density and makes a gravitationally unstable disk." + On the other hand. the non-axisvmimetric structure arose in such unstable disk can stabilize the disk. because it can redistribute the angular momentum ancl promote mass accretion onto the protostar.," On the other hand, the non-axisymmetric structure arose in such unstable disk can stabilize the disk, because it can redistribute the angular momentum and promote mass accretion onto the protostar." + Thus. no fragmentation occurs when a strong non-axisvmuametricitv grows and transfers sullicient angular. momentum outward.," Thus, no fragmentation occurs when a strong non-axisymmetricity grows and transfers sufficient angular momentum outward." + By contrast. the disk. becomes highly eravitationally unstable ancl shows fragmentation when non-axisvmmetric structure does not erow sullicienth or when the growth timescale of the non-axisvmmetricitv is much longer than the disk growth timescale.," By contrast, the disk becomes highly gravitationally unstable and shows fragmentation when non-axisymmetric structure does not grow sufficiently or when the growth timescale of the non-axisymmetricity is much longer than the disk growth timescale." + “Phus. fragmentation condition depends also on the growth. of the non-axisvmmetriciv. which is closely related to parameters o. anc 3 because they determine the evolution of the mass and angular momentum of the disk.," Thus, fragmentation condition depends also on the growth of the non-axisymmetriciy, which is closely related to parameters $\alpha$ and $\beta$ because they determine the evolution of the mass and angular momentum of the disk." + With parameters a and. 2. we found that the disk evolution is qualitatively classified: into four naiocles: protostar dominant. massive disk. carly fragmentation and late fragmentation modes.," With parameters $\alpha$ and $\beta$ , we found that the disk evolution is qualitatively classified into four modes: protostar dominant, massive disk, early fragmentation and late fragmentation modes." + The schematic classification of, The schematic classification of +unique dependence. with the hope that observations of starbursts can be used to assess ECS kick velocities and progenitor mass ranges.,"unique dependence, with the hope that observations of starbursts can be used to assess ECS kick velocities and progenitor mass ranges." + We note that. iu the Simall Maegellenic Cloud (SAIC). dominated by 2£0 MMy-old stellar populations. a systematic overabundance of Be XRDs las been observed (?7) potentially making the SMC a unique laboratory for ECS NS formation.," We note that, in the Small Magellenic Cloud (SMC), dominated by $\simeq 40$ Myr-old stellar populations, a systematic overabundance of Be XRBs has been observed \citep{2000A&A...359..573H, 2004ApJ...609..133M} potentially making the SMC a unique laboratory for ECS NS formation." + For our modeling of IINKD. formation aud. evolution iu starbursts we onploy a sophisticated. population svuthesis code. StarTrack. described in extensive detail in 7.. which assumes that stellar dvuamical interactions are not significant compared to the effects of binary evolution for the star formation coucitious under consideration.," For our modeling of HMXB formation and evolution in starbursts we employ a sophisticated population synthesis code, $StarTrack$, described in extensive detail in \citet{2008ApJS..174..223B}, which assumes that stellar dynamical interactions are not significant compared to the effects of binary evolution for the star formation conditions under consideration." + We note that the paraimcter space of Alonte Carlo population svuthesis is very large. and thus a full exploration is not possible.," We note that the parameter space of Monte Carlo population synthesis is very large, and thus a full exploration is not possible." + Instead. we consider a default model (described in detail iu ?)) and we vary sole binary evolution aud EC'S-rclated parameters with the purpose of hiehliehtiug their effects ou the proposed ECS probe.," Instead, we consider a default model (described in detail in \citet{2008ApJS..174..223B}) ) and we vary some binary evolution and ECS-related parameters with the purpose of highlighting their effects on the proposed ECS probe." + Uere we briefly sununarize the lain assunrptious and paraueters relevant to tlis studs., Here we briefly summarize the main assumptions and parameters relevant to this study. + We enplov a delta function star formation episode at solu iictallicity adopting: (1) a Salpeter 7°) initial mass function with primary masses above { M. and secondary masses above 0.15 ADL: (2) a flat mass ratio distribution: (3) a distribution of initial binary separations that is flat in the logarithm with an upper ΠΠ of 10° Ro. and a lower Init such that the primary star initially fills at most half of its Roche Lobe (?).. and (1) a thermal distribution for initial eccentricities (?2)..," We employ a delta function star formation episode at solar metallicity adopting: (1) a Salpeter $^{-2.35}$ ) initial mass function with primary masses above 4 $_\odot$ and secondary masses above 0.15 $_\odot$; (2) a flat mass ratio distribution; (3) a distribution of initial binary separations that is flat in the logarithm with an upper limit of $^5$ $_\odot$ and a lower limit such that the primary star initially fills at most half of its Roche Lobe \citep{1983ARA&A..21..343A}, and (4) a thermal distribution for initial eccentricities \citep{1975MNRAS.173..729H}." +" We set the πακ NS mass at 2.5 M, and craw natal kicks for “standard” ICC-SN events from a single Maxwellian kick distribution with mean265 lans ? (?)..", We set the maximum NS mass at 2.5 $_\odot$ and draw natal kicks for “standard” ICC-SN events from a single Maxwellian kick distribution with mean265 km $^{-1}$ \citep{2005MNRAS.360..974H}. + Ilicks are potentially associated with BIT formation as well (see? for the strongest evidence at present for a DII kick)., Kicks are potentially associated with BH formation as well (see \citet{2009ApJ...697.1057F} for the strongest evidence at present for a BH kick). + For BUs formed through SNe explosions aud subsequent fallback of material we multiply the normal Maxwellian kick by the fraction of the SN ejecta which is ultimately lost from the system., For BHs formed through SNe explosions and subsequent fallback of material we multiply the normal Maxwellian kick by the fraction of the SN ejecta which is ultimately lost from the system. + Usually DIT formation at higher masses through direct collapse is assumed to be orfectle svaunetrie: here we adopt a simall kick of he NS kick). for reasons discussed in detail in Section L..," Usually BH formation at higher masses through direct collapse is assumed to be perfectly symmetric; here we adopt a small kick of the NS kick), for reasons discussed in detail in Section \ref{disc}." + To obtain statistically significant results. we sample at east LO® initial binaries for cach set of input parameters and we evolve the systems for MM.," To obtain statistically significant results, we sample at least $^6$ initial binaries for each set of input parameters and we evolve the systems for Myr." + However. we stress that the models and ΧΙΟ nmuubers preseuted rere are not normalized to match anv specific observed system. since we are purely interested duo examine herelatives ΑΟ nuubers as a function of starburst age.," However, we stress that the models and XRB numbers presented here are not normalized to match any specific observed system, since we are purely interested in examining the XRB numbers as a function of starburst age." + — Iu order to compare our results with observations. we must determine the X-rav luuainosity. Ly. based on the calculated mass-trauster rate for both wind-fed and Roche-lobe-overflow systems.," In order to compare our results with observations, we must determine the X-ray luminosity, $L_X$, based on the calculated mass-transfer rate for both wind-fed and Roche-lobe-overflow systems." + We apply iji estimated correction for the energy. baud as described aud justified in ? (Section 9.1)., We apply an estimated correction for the energy band as described and justified in \citet{ 2008ApJS..174..223B} (Section 9.1). + We ijidvze the IINEND. population with Ly in excess of 10° core il. appropriate for obsorvatious of nearby star-forming galaxies.," We analyze the HMXB population with $L_X$ in excess of $10^{32}$ erg $^{-1}$, appropriate for observations of nearby star-forming galaxies." + Au muportant problem in the population svuthesis of binary stars is the treatinent of conmnon envelope (CE) phases., An important problem in the population synthesis of binary stars is the treatment of common envelope (CE) phases. + Tu our smiulations. CE eveuts are treated using the usual energy. formatlisin described by ?orbits... for stars which have established a clear corc-cnvelope boundary.," In our simulations, CE events are treated using the usual energy formalism described by \citet{1984ApJ...277..355W}, for stars which have established a clear core-envelope boundary." + In this paper. we adopt a value for the CE efficiency of ac = IL.," In this paper, we adopt a value for the CE efficiency of $\alpha_{CE}$ = 1." + However. in our default models. we assume that a CE phase involving a donor star on the main sequence (MS) or hertzspruug eap (IG) leads to a binary merger (27?)..," However, in our default models, we assume that a CE phase involving a donor star on the main sequence (MS) or hertzsprung gap (HG) leads to a binary merger \citep{2008ApJS..174..223B, 2000ARA&A..38..113T}." +" Following ?.. massive stars are assumed to explode in ECS eveuts if the Πο core mass at the beginning of the asvinptotic giant brauch (ACB) is between 1.83-2.25 M, (see also ?))."," Following \citet{2000MNRAS.315..543H}, , massive stars are assumed to explode in ECS events if the He core mass at the beginning of the asymptotic giant branch (AGB) is between 1.83-2.25 $_\odot$ (see also \citet{2007arXiv0706.4096I}) )." + This choice. in effect. selects specific initial lnass ranges which depend on the binary evolution of the progenitors.," This choice, in effect, selects specific initial mass ranges which depend on the binary evolution of the progenitors." + Towever. given the uncertaiufies involved in selecting this mass range. we examine a nunber of Ile core mass ranges in what follows.," However, given the uncertainties involved in selecting this mass range, we examine a number of He core mass ranges in what follows." + We assume that ECS natal kicks follow a \laxwellian distribution with a sunaller mean than ICC-SN kicks. thus we linearly. scale down the “standard”.. ICC-SN AMaswellian distribution by varving factors.," We assume that ECS natal kicks follow a Maxwellian distribution with a smaller mean than ICC-SN kicks, thus we linearly scale down the “standard” ICC-SN Maxwellian distribution by varying factors." + The mass of ECS-formed NS is assumed equal to AMAL. (2??).. although we note that 7.. ? and ? find slishtlv higher cud masses for single star ECS events (1.358 - 1.1 M...," The mass of ECS-formed NS is assumed equal to $_\odot$ \citep{1987ApJ...322..206N, 2004ApJ...612.1044P, 2007arXiv0706.4096I}, although we note that \citet{2006ApJ...644.1063D}, \citet{2006A&A...450..345K} and \citet{2008ApJ...675..614P} find slightly higher end masses for single star ECS events (1.338 - 1.4 $_\odot$ )." + Exanuuuation of our simulation results in terms of the iuuber of IINEXNDs as a function of starburst age reveals an intriguing role of EC'S NS formation: ECS events cau dominate IINEND. formation between 20 and Αλία yost-starburst. creating a clearly ideutified “bump” iu he time evolution of TAENB nuiibers (sec Figure 1)).," Examination of our simulation results in terms of the number of HMXBs as a function of starburst age reveals an intriguing role of ECS NS formation: ECS events can dominate HMXB formation between 20 and Myr post-starburst, creating a clearly identified “bump” in the time evolution of HMXB numbers (see Figure \ref{ecsplot}) )." + At any eivennctallicity. the width aud relative height of this is primarily dependent on two parameters: the vpical ECS natal kick magnitude aud the massrauge of ECSprogeuitors.," At any given metallicity, the width and relative height of this is primarily dependent on two parameters: the typical ECS natal kick magnitude and the massrange of ECSprogenitors." + We first exinume the effect of ECS kicks (Figure 1.. top ucl).," We first examine the effect of ECS kicks (Figure \ref{ecsplot}, , top panel)." + We typically find two significant bursts of IINI, We typically find two significant bursts of HMXB + We typically find two significant bursts of IININ, We typically find two significant bursts of HMXB + We typically find two significant bursts of IININD, We typically find two significant bursts of HMXB +6.,. +" Therefore, we estimate this fraction as the ratio of the azimuthal angular frequency of the orbiting satellite to the angular frequency of the satellite’s mass shell."," Therefore, we estimate this fraction as the ratio of the azimuthal angular frequency of the orbiting satellite to the angular frequency of the satellite's mass shell." +" Consequently, the torque on the satellite mass shell becomes: 'This torque leads to expansion and the expansion rate can be estimated as This expansion reduces the satellite’s density as Ap "," Consequently, the torque on the satellite mass shell becomes: This torque leads to expansion and the expansion rate can be estimated as This expansion reduces the satellite's density as $\Delta \rho \propto +-\frac{\Delta r}{r^{4}}$ ." +We also use this relationship to compute the mass loss in At.Step (iv) of the algorithm above., We also use this relationship to compute the mass loss in Step (iv) of the algorithm above. +" 'The mass loss histories for the circular orbit simulation, the eccentric orbit simulation, and the inner orbit simulation are compared with the results of our mass-loss algorithm in Figs."," The mass loss histories for the circular orbit simulation, the eccentric orbit simulation, and the inner orbit simulation are compared with the results of our mass-loss algorithm in Figs." +" 22 — 24,, respectively."," \ref{fig:massloss.XC1} – \ref{fig:massloss.XK2}, respectively." +" For the circular orbit case, there are no gravitational shocks."," For the circular orbit case, there are no gravitational shocks." + Fig., Fig. + 22 shows two analytic estimates: andTorque.., \ref{fig:massloss.XC1} shows two analytic estimates: and. + The estimate only includes tidal truncation and predicts negligible mass loss., The estimate only includes tidal truncation and predicts negligible mass loss. + The estimate includes both the resonant torque approximation and tidal truncation., The estimate includes both the resonant torque approximation and tidal truncation. + Its mass loss history is much more similar to the simulation: more than of the original mass is lost., Its mass loss history is much more similar to the simulation: more than of the original mass is lost. + This suggests that mass loss for a satellite on a circular orbit mainly results from resonant torques and our algorithm for resonant torque provides a dramatically improved description., This suggests that mass loss for a satellite on a circular orbit mainly results from resonant torques and our algorithm for resonant torque provides a dramatically improved description. +" For the eccentric orbit and inner orbit simulation cases, the gravitational shock plays an important role in driving mass loss."," For the eccentric orbit and inner orbit simulation cases, the gravitational shock plays an important role in driving mass loss." + Figs., Figs. + 23 and 24 compares our mass loss algorithm to the simulations., \ref{fig:massloss.XE1} and \ref{fig:massloss.XK2} compares our mass loss algorithm to the simulations. +" Here, we include the model, the impulse approximation with the Spitzer correction [Shock(S)], the impulse approximation with the Weinberg correction [Shock(W)]], and the impulse approximation with Weinberg correction together with our resonant torque approximation Torque]]."," Here, we include the model, the impulse approximation with the Spitzer correction ], the impulse approximation with the Weinberg correction ], and the impulse approximation with Weinberg correction together with our resonant torque approximation ]." + All the estimates include tidal truncation., All the estimates include tidal truncation. + The model best represents the mass loss seen in the simulation while the with no resonant torque predicts less mass loss than that seen., The model best represents the mass loss seen in the simulation while the with no resonant torque predicts less mass loss than that seen. + The importance of the resonant torque is most obvious for the inner orbit simulation., The importance of the resonant torque is most obvious for the inner orbit simulation. +" Compared to the simulation, the estimate including the shock and the resonant torque [Shock(W)--Torque]] does significantly better estimating the mass loss in the simulation than that of the shock alone, which significantly underpredicts the mass loss."," Compared to the simulation, the estimate including the shock and the resonant torque ] does significantly better estimating the mass loss in the simulation than that of the shock alone, which significantly underpredicts the mass loss." + Tidal truncation alone Shock]| shows the worst agreement., Tidal truncation alone ] shows the worst agreement. +could not be well constrained by the PCA: we thus fixed the energy of the line to lie between ~ 6 keV and 7.5 keV. An additional line at 2 keV (due to calibration problems) was sometimes needed in XRT.,could not be well constrained by the PCA: we thus fixed the energy of the line to lie between $\sim$ 6 keV and 7.5 keV. An additional line at 2 keV (due to calibration problems) was sometimes needed in XRT. + Absorption was a combination of a fixed interstellar component (abundances fixed to ?)) plus a variable local component., Absorption was a combination of a fixed interstellar component (abundances fixed to \citealt{wilms00}) ) plus a variable local component. +" XRT found the total absorption to vary between 4.9-6.3 x 107! em"". taking into account the statistical uncertainties (0.07). and the dependence on the position of the source in the HID."," XRT found the total absorption to vary between 4.9–6.3 $\times$ $^{21}$ $^{-2}$, taking into account the statistical uncertainties $\pm$ 0.07), and the dependence on the position of the source in the HID." + The lower end (4.9 x 107! em?) is compatible. within the errors. with the average Galactic column density in the source direction estimated from ?u it is possible that. up to about L4 x 107! em- is intrinsic and variable (see ? for a detailed discussion of the variations of the absorption in this source: XRT data were not always available to do that in this work).," The lower end (4.9 $\times$ $^{21}$ $^{-2}$ ) is compatible, within the errors, with the average Galactic column density in the source direction estimated from \citet{kalberla05}; it is possible that, up to about 1.4 $\times$ $^{21}$ $^{-2}$ is intrinsic and variable (see \citet{cabanac} for a detailed discussion of the variations of the absorption in this source; XRT data were not always available to do that in this work)." + For the dise component. the model in (?) was used.," For the disc component, the model in \citep{Mitsuda:1984} was used." + We then replaced the phenomenological models. that first allowed us to easily compare the spectral parameters over the outburst. with à more physical one. the thermal Comptonisation model of ?..," We then replaced the phenomenological models, that first allowed us to easily compare the spectral parameters over the outburst, with a more physical one, the thermal Comptonisation model of \citet{Titarchuk:1994}." + We tested the best modelling by adding additional contributions and we carefully checked any improvement in the goodness of the fit., We tested the best modelling by adding additional contributions and we carefully checked any improvement in the goodness of the fit. + When a cut-off was needed. this provided a good fit to almost all our data (see Table 2 and 3. for details: otherwise. we used a simple power law model). although the temperature of the seed photons (tied to the disc temperature) was not always well constrained.," When a cut-off was needed, this provided a good fit to almost all our data (see Table \ref{tab:para} and \ref{tab:cutoffPL} for details; otherwise, we used a simple power law model), although the temperature of the seed photons (tied to the disc temperature) was not always well constrained." + The best-fit parameters are reported in Table 2:: Table 3 shows the phenomenological cut-off power law parameters., The best-fit parameters are reported in Table \ref{tab:para}; Table \ref{tab:cutoffPL} shows the phenomenological cut-off power law parameters. + In addition to providing a more physical interpretation to the data. this model also permits us to avoid the divergence of the power law flux towards low energy since Comptonisation," In addition to providing a more physical interpretation to the data, this model also permits us to avoid the divergence of the power law flux towards low energy since Comptonisation" +be discussed in the following sections that the estimation of CMB bispectra is similar and related to the case of lensing reconstruction of the CMB sky (Smith.Zahn&Dore2007).,be discussed in the following sections that the estimation of CMB bispectra is similar and related to the case of lensing reconstruction of the CMB sky \citep{SmZaDo00}. +. The problem of estimation of the skew spectrum is very similar to that of the primary CMB bispectrum., The problem of estimation of the skew spectrum is very similar to that of the primary CMB bispectrum. + There has been a recent surge in activity in this area. driven by the claim of detection of non-gaussianity in the WMAP data release (see Yadav&Wandelt (2007))).," There has been a recent surge in activity in this area, driven by the claim of detection of non-gaussianity in the WMAP data release (see \citet{YaWa08,Yadav08,YKW}) )." + Different techniques were developed which introduce various weighting schemes in the harmonie domain to make the method optimal (i.e. saturates the Cramer-Rao bound)., Different techniques were developed which introduce various weighting schemes in the harmonic domain to make the method optimal (i.e. saturates the Cramer-Rao bound). + Maps are constructed by weighting the observed CMB sky with /-dependent weights obtained from inflationary theoretical models., Maps are constructed by weighting the observed CMB sky with $l$ -dependent weights obtained from inflationary theoretical models. + These weighted maps are then used to compute one-point quantities which are generalisation of skewness and can be termed mixed skewness., These weighted maps are then used to compute one-point quantities which are generalisation of skewness and can be termed mixed skewness. + These mixed skewness measures are useful estimators of fv; parameters., These mixed skewness measures are useful estimators of $f_{NL}$ parameters. + A more general treatment was provided in Smith(2009) who took into account mode-mode coupling in an exact way with the use of proper inverse-covariance weighting of harmonie modes.," A more general treatment was provided in \cite{SmZa06,SmZaDo00,SmSeZa09} who took into account mode-mode coupling in an exact way with the use of proper inverse-covariance weighting of harmonic modes." + Recent work by Munshi&Heavens(2009). has improved the situation by focussing directly on the skew spectrum., Recent work by \cite{MuHe09} has improved the situation by focussing directly on the skew spectrum. + Their technique does not compress all the available information in the bispectrum into a single number but provides a power-spectrum which depends on the harmonic wavenumber /., Their technique does not compress all the available information in the bispectrum into a single number but provides a power-spectrum which depends on the harmonic wavenumber $l$. + This method has the advantage of being able to separate various contributions as they will have different dependence on /s. thus allowing an assessment of whether any non-gaussianity is primordial or not.," This method has the advantage of being able to separate various contributions as they will have different dependence on $l$ s, thus allowing an assessment of whether any non-gaussianity is primordial or not." + In this section we compute the contaminating secondary bispectrum contributions from lensing-secondary coupling., In this section we compute the contaminating secondary bispectrum contributions from lensing-secondary coupling. + The study of the bispectrum related to secondary anisotropy (see Cooray&Seth(2000) for more details and analytical modelling based on halo model which we use here) is arguably as important as that generated by the primary anisotropy.," The study of the bispectrum related to secondary anisotropy (see \cite{sethcoo} + for more details and analytical modelling based on halo model which we use here) is arguably as important as that generated by the primary anisotropy." + Primary non-Gaussianity in simpler inflationary models is vanishingly small (Salopek&Bond1990.1991:Falketal.1993:Gangui1994:Acquaviva2003:Maldacena2003): see &Riotto(2006) and references therein for more details.," Primary non-Gaussianity in simpler inflationary models is vanishingly small \citep{Salopek90,Salopek91,Falk93,Gangui94,Acq03,Mal03}; see \citet{Bartolo06} + and references therein for more details." + However. variants of simple inflationary models such as multiple scalar fields 2003).. features in the inflationary potential. non-adiabatie fluctuations. non-standard kinetic terms. warm inflation (Gupta.Berera&Heavens2002:MossXiong2007).. or deviations from Bunch-Davies vacuum can all lead to a much higher level of non-Gaussianity.," However, variants of simple inflationary models such as multiple scalar fields \citep{lindemukha,Lyth03}, features in the inflationary potential, non-adiabatic fluctuations, non-standard kinetic terms, warm inflation \citep{GuBeHea02,Moss}, or deviations from Bunch-Davies vacuum can all lead to a much higher level of non-Gaussianity." + Early observational work on the bispectrum from COBE (Komatsuetal.2002) and MAXIMA (Santosetal.2003) was followed by much more accurate analysis with WMAP (Komatsuetal.2003:Creminelli2007:Spergel2007).," Early observational work on the bispectrum from COBE \citep{Komatsu02} and MAXIMA \citep{Santos} was followed by much more accurate analysis with WMAP \citep{Komatsu03,Crem07a,Spergel07}." +. The primary bispectrum encodes information about inflationary dynamics and hence can constrain various inflationary scenarios. where as the secondary bispectrum will provide valuable information regarding the low-redshift universe and constrain structure formation scenarios.," The primary bispectrum encodes information about inflationary dynamics and hence can constrain various inflationary scenarios, where as the secondary bispectrum will provide valuable information regarding the low-redshift universe and constrain structure formation scenarios." + These bispectra are generated because of the cross-correlation effect of lensing due to various intervening materials and the secondary anisotropy such as the Sunyaev-Zeldovich effect due to inverse Compton scattering of CMB photons from hot gas in intervening clusters., These bispectra are generated because of the cross-correlation effect of lensing due to various intervening materials and the secondary anisotropy such as the Sunyaev-Zeldovich effect due to inverse Compton scattering of CMB photons from hot gas in intervening clusters. + The power spectrum C7 is the unlensed power spectrum of the CMB anisotropy., The power spectrum $\myC^S_l$ is the unlensed power spectrum of the CMB anisotropy. +" We have introduced the subscript 9 to distinguish it from the Cs that appear in the denominator which take contribution from the instrumental noise from signal to noise computation point of view (C;=€|IN/b(I)"". where JN is the instrumental noise and 6(/) is the beam function in multipole space)."," We have introduced the subscript $S$ to distinguish it from the $C_l$ s that appear in the denominator which take contribution from the instrumental noise from signal to noise computation point of view $C_l=C_l+N/b(l)^2$, where $N$ is the instrumental noise and $b(l)$ is the beam function in multipole space)." + We detine the different fields which are constructed from underlying harmonies and corresponding Cys. These will be useful for constructing an unbiased near optimal estimator., We define the different fields which are constructed from underlying harmonics and corresponding ${\cal C}_l$ s. These will be useful for constructing an unbiased near optimal estimator. +" The corresponding fields that we construct are 41(0)=22sYn, and in an analogous manner D and C."," The corresponding fields that we construct are $A^{(i)}(\hat \Omega) \equiv \sum_{lm}Y_{lm}(\hat\Omega)A^{(i)}_{lm}$, and in an analogous manner $B^{(i)}$ and $C^{(i)}$." + The optimised skew spectrum in the presence of all-sky coverage and homogeneous noise can now be (QA.written as: The cyclic terms that are considered here will have to constructed likewise from the corresponding terms in the expression for the reduced bispectrum discussed above 35.., The optimised skew spectrum in the presence of all-sky coverage and homogeneous noise can now be written as: The cyclic terms that are considered here will have to constructed likewise from the corresponding terms in the expression for the reduced bispectrum discussed above \ref{eq:bi_komatsu}. + The linear-order correction terms which needs to be included in the absence of spherical symmetry due to presence of cuts to avoid the galactic foreground and the inhomogeneous noise can be written as:, The linear-order correction terms which needs to be included in the absence of spherical symmetry due to presence of cuts to avoid the galactic foreground and the inhomogeneous noise can be written as: +"numerical simulations (??),, and given by p(r)= where r is the distance from the Galactic center and pp = 0.385 GeV cm? (??)..","numerical simulations \citep{1996ApJ...462..563N, 2008Natur.454..735D}, and given by $\rho(r) = \rho_0 \, (r/8.5 \, {\rm kpc})^{-1.25}$, where $r$ is the distance from the Galactic center and $\rho_0$ = 0.385 GeV $^{-3}$ \citep{2010JCAP...08..004C, 2011arXiv1105.4166L}." +" We also adopt a dark matter annihilation cross section of (συ)=3x10776 cm? s-!, which is the value predicted for a simple thermal relic."," We also adopt a dark matter annihilation cross section of $\langle\sigma v\rangle=3\times~10^{-26}$ $^3$ $^{-1}$, which is the value predicted for a simple thermal relic." +" Assuming approximate cylindrical symmetry for the filament geometry, the annihilation rate within a filament of length | and diameter w is given by: where r is the distance of the filament from the Galactic center."," Assuming approximate cylindrical symmetry for the filament geometry, the annihilation rate within a filament of length $l$ and diameter $w$ is given by: where $r$ is the distance of the filament from the Galactic center." +" We note that in many NRFs, the distance from the Galactic center changes considerably across the length of the filaments - we will discuss the effect of this when modeling specific filaments."," We note that in many NRFs, the distance from the Galactic center changes considerably across the length of the filaments - we will discuss the effect of this when modeling specific filaments." + The types and spectra of particles produced in dark matter annihilations depend on the details of the particle physics model., The types and spectra of particles produced in dark matter annihilations depend on the details of the particle physics model. +" In order to generate a bright flux of synchrotron emission with a spectrum peaking at 10 GHz, we will focus on dark matter which annihilates dominantly to charged leptons."," In order to generate a bright flux of synchrotron emission with a spectrum peaking at $\sim$ 10 GHz, we will focus on dark matter which annihilates dominantly to charged leptons." +" In particular, we will consider a democratic model which annihilates equally to e, u~, and 7- final states."," In particular, we will consider a democratic model which annihilates equally to $e^\pm$, $\mu^\pm$, and $\tau^\pm$ final states." +" The nearly instantaneous decays of the taus and muons produce lower energy electrons/positrons, as well as a prompt flux of 4-rays (as opposed to y-rays from the inverse-Compton scattering of energetic "," The nearly instantaneous decays of the taus and muons produce lower energy electrons/positrons, as well as a prompt flux of $\gamma$-rays (as opposed to $\gamma$ -rays from the inverse-Compton scattering of energetic electrons)." +It is this prompt flux of y-rays which ? find to be electrons).consistent with the excess observed in the Galactic center by Fermi-LAT., It is this prompt flux of $\gamma$ -rays which \citet{2011PhLB..697..412H} find to be consistent with the excess observed in the Galactic center by Fermi-LAT. + The spectrum of electrons and positrons produced through dark matter annihilations within a given NRF is calculated using the Pythia package (??). ," The spectrum of electrons and positrons produced through dark matter annihilations within a given NRF is calculated using the Pythia package \citep{2001CoPhC.135..238S, 2004JCAP...07..008G}." +"In the left frame of Fig. 2,,"," In the left frame of Fig. \ref{fig:leptonflux}," +" we show the injected electron spectrum per dark matter annihilation for our canonical case of a dark matter particle with a mass of 8 GeV, annihilating equally into e*e, uty and r*r-."," we show the injected electron spectrum per dark matter annihilation for our canonical case of a dark matter particle with a mass of 8 GeV, annihilating equally into $e^+ e^-$, $\mu^+ \mu^-$ and $\tau^+ \tau^-$." +" We note that the electron/positron spectrum is very hard, following a spectrum between 9? and E? between 100 MeV and 8 GeV, although we caution that this spectrum is not a continuous power law."," We note that the electron/positron spectrum is very hard, following a spectrum between $^{-0.5}$ and $^{0}$ between 100 MeV and 8 GeV, although we caution that this spectrum is not a continuous power law." + The majority (~2/3) of the electron energy is deposited in a delta function at 8 GeV following the dark matter annihilations directly into electrons., The majority $\sim$ 2/3) of the electron energy is deposited in a delta function at 8 GeV following the dark matter annihilations directly into electrons. +" These 8 GeV electrons will dominate the synchrotron spectrum from NRFs, in part due to their shorter synchrotron energy loss time."," These 8 GeV electrons will dominate the synchrotron spectrum from NRFs, in part due to their shorter synchrotron energy loss time." + We note that the positron spectrum is identical and lends another factor of two to the overall synchrotron flux., We note that the positron spectrum is identical and lends another factor of two to the overall synchrotron flux. +" In order to determine the synchrotron spectrum expected from dark matter annihilations, we must also model the diffusion of electrons throughout the NRFs."," In order to determine the synchrotron spectrum expected from dark matter annihilations, we must also model the diffusion of electrons throughout the NRFs." + Models of the filaments typically require an electron diffusion timescale similar to the energy loss time of the electron population in the NRF's magnetic field ," Models of the filaments typically require an electron diffusion timescale similar to the energy loss time of the electron population in the NRF's magnetic field \citep{1995ApJ...448..164G, 1999ApJ...526..727L}." +This has the effect of smearing out the electron (??)..energy distribution and softening the overall synchrotron spectrum., This has the effect of smearing out the electron energy distribution and softening the overall synchrotron spectrum. +" Through considerations of the electron gyroradius similar to those discussed in refsec:filamentaryarcs,, electrons created within the NRFs are constrained from effective diffusion perpendicular to the ordered magnetic field."," Through considerations of the electron gyroradius similar to those discussed in \\ref{sec:filamentaryarcs}, electrons created within the NRFs are constrained from effective diffusion perpendicular to the ordered magnetic field." +" In the case of an entirely ordered magnetic field, charged leptons would spiral freely along the magnetic field lines until exiting the filament."," In the case of an entirely ordered magnetic field, charged leptons would spiral freely along the magnetic field lines until exiting the filament." +" However, in the observed regime containing significant ordered and unordered fields, diffusion is expected to be significantly more complicated."," However, in the observed regime containing significant ordered and unordered fields, diffusion is expected to be significantly more complicated." +" In the case of very low turbulence levels, much work has been done within the perturbative framework of quasi-linear theory which seeks to calculate the parallel and perpendicular diffusion components as a function of the power in turbulent modes of the magnetic field with a wavenumber resonant with the inverse of the particles momentum (??).. "," In the case of very low turbulence levels, much work has been done within the perturbative framework of quasi-linear theory which seeks to calculate the parallel and perpendicular diffusion components as a function of the power in turbulent modes of the magnetic field with a wavenumber resonant with the inverse of the particles momentum \citep{1966ApJ...146..480J, 1971RvGSP...9...27J}." +"The amplitude of these modes, however, is poorly constrained in galactic simulations."," The amplitude of these modes, however, is poorly constrained in galactic simulations." +" More recently, numerical simulations have been used to analyze the parallel and perpendicular diffusion constants in regimes in which the ordered and unordered field are co-dominant."," More recently, numerical simulations have been used to analyze the parallel and perpendicular diffusion constants in regimes in which the ordered and unordered field are co-dominant." +" Notably, ? found that in the case of a magnetic field which is approximately ordered, the parallel diffusion constant exceeds the perpendicular diffusion constant by a factor of ~125."," Notably, \citet{2002PhRvD..65b3002C} found that in the case of a magnetic field which is approximately ordered, the parallel diffusion constant exceeds the perpendicular diffusion constant by a factor of $\sim$ 125." + Very similar results were later obtained for the case of more energetic cosmic rays (?).. , Very similar results were later obtained for the case of more energetic cosmic rays \citep{2007JCAP...06..027D}. . +"Since the length travelled by diffusive particles can be written as £ = V2Dt, where D is the assumed diffusion constant."," Since the length travelled by diffusive particles can be written as $\ell$ = $\sqrt{2Dt}$ , where D is the assumed diffusion constant." + This implies that perpendicular and parallel diffusion will remove particles from the filaments on equivalent, This implies that perpendicular and parallel diffusion will remove particles from the filaments on equivalent +which there is a great deal of evidence Arnett 1988. Pinto Woosley 1988. Shigevama. Nomoto Hashimoto 1988. Woosley 1988. Laas et al.,"which there is a great deal of evidence Arnett 1988, Pinto Woosley 1988, Shigeyama, Nomoto Hashimoto 1988, Woosley 1988, Haas et al." + 1990. Spvronulio. Meikle Allen 1990. Fassia Aleikle 1999).," 1990, Spyromilio, Meikle Allen 1990, Fassia Meikle 1999)." + Light elements (Hl. He) are mixed down to low velocities. and iron group elements are mixed. up to high velocities.," Light elements (H, He) are mixed down to low velocities, and iron group elements are mixed up to high velocities." + COT. dlxXLMOS. and. IxF98a.b. introduce. this mixing in dillerent wavs.," C97, dKLM98 and KF98a,b introduce this mixing in different ways." +" However. they. all invoke a macroscopically mixed “core” lving within ~2000 km/s. (ULMOS refer to the inwardly mixed. 11Πο zones as the ""inner envelope”.)"," However, they all invoke a macroscopically mixed “core” lying within $\sim$ 2000 km/s. (dKLM98 refer to the inwardly mixed H/He zones as the “inner envelope”.)" + The core thus contains zones that are L-rich. Le-rich. intermediate-element-rich.. ancl iron-group-rich. with the nebula being bathed in the radioactive decay energy.," The core thus contains zones that are H-rich, He-rich, intermediate-element-rich, and iron-group-rich, with the nebula being bathed in the radioactive decay energy." + The core is generally of mass 4:6 M..., The core is generally of mass 4–6 $_\odot$. + In addition. €C97 and IxE98a.b. include an outer. H-envelope. of mass 10. M. extending out to a velocity of 6000.7000 km/s. 1n general. the [raction. of the radioactive decay energy that does not. directly. escape from the nebula is injected into the nebular material via Coulomb interaction with the positrons ancl Compton-scattored electrons.," In addition, C97 and KF98a,b include an outer H-envelope of mass 10 $_\odot$ extending out to a velocity of 6000–7000 km/s. In general, the fraction of the radioactive decay energy that does not directly escape from the nebula is injected into the nebular material via Coulomb interaction with the positrons and Compton-scattered electrons." + The energy. of the resulting non-thermal high energy electrons then goes towards excitation. ionisation and heating of the nebula (IxE9582).," The energy of the resulting non-thermal high energy electrons then goes towards excitation, ionisation and heating of the nebula (KF98a)." + Three ellects play important roles in the evolution of the temperature ancl ionisation at the very late times considered here., Three effects play important roles in the evolution of the temperature and ionisation at the very late times considered here. +" These are the ionisation/thermal ""freeze-out” elfect. acliabatic cooling. and the ""Hi-catastrophe."," These are the ionisation/thermal ``freeze-out'' effect, adiabatic cooling, and the “IR-catastrophe”." + The first two are important in the HL/Le envelope. while the third plàvs an important role in the metal-rich core.," The first two are important in the H/He envelope, while the third plays an important role in the metal-rich core." + The ionisation [reeze-out effect. was suggested: originally. w Clavton. ct al. (, The ionisation freeze-out effect was suggested originally by Clayton et al. ( +1992) and bv Fransson Kozma (1993).,1992) and by Fransson Kozma (1993). + “These authors pointed out that as the SN evolves. here will eventually come a time when the recombination imescale exceeds the radioactive or expansion. timescale. so that the rate of change in the level of ionisation slows significantly.," These authors pointed out that as the SN evolves, there will eventually come a time when the recombination timescale exceeds the radioactive or expansion timescale, so that the rate of change in the level of ionisation slows significantly." + Once this phase is reached. the bolometric uninositv exceeds that of the instantaneous raclioactive decay deposition. since some of the luminosity results from recombination following ionisation at a significantly earlier epoch.," Once this phase is reached, the bolometric luminosity exceeds that of the instantaneous radioactive decay deposition, since some of the luminosity results from recombination following ionisation at a significantly earlier epoch." + In the model of KEOSa.b the ionisation [reeze-out phase begins at SOQ900 cays in most zones. but has a more pronounced effect on the luminosity in the L/Lle envelope.," In the model of KF98a,b the ionisation freeze-out phase begins at 800–900 days in most zones, but has a more pronounced effect on the luminosity in the H/He envelope." +" However. in their. ""inner-envelope"" model. ΟΗΕMOS finc that the freeze-out clocs not occur until much later than this."," However, in their “inner-envelope” model, dKLM98 find that the freeze-out does not occur until much later than this." +" Instead. they identify a ""thermal. [reeze-out” where the radiative cooling timescale exceeds that of the expansion timescale."," Instead, they identify a “thermal freeze-out'' where the radiative cooling timescale exceeds that of the expansion timescale." + In their model. this occurs before," In their model, this occurs before" +"The excess in the rms spectrum of NGC 3783 is similar in strength to the broad iron line in the time-averaged spectrum, so in the accretion disk model, the line and continuum vary together.","The excess in the rms spectrum of NGC 3783 is similar in strength to the broad iron line in the time-averaged spectrum, so in the accretion disk model, the line and continuum vary together." + ΝΟ7 found an ionized H-like line at 6.97 keV that is not seen to be variable in the rms spectrum., N07 found an ionized H-like line at 6.97 keV that is not seen to be variable in the rms spectrum. +" This offers support for the speculation of NO7 that this originates from hot gas filling the torus, which is not expected to be variable."," This offers support for the speculation of N07 that this originates from hot gas filling the torus, which is not expected to be variable." +" Turning to MCG-6-30-15, NO7 found a strong requirement for a blurred accretion disk component in the time averaged spectrum (as in several previous studies, e.g. Tanaka et al."," Turning to MCG-6-30-15, N07 found a strong requirement for a blurred accretion disk component in the time averaged spectrum (as in several previous studies, e.g. Tanaka et al." + 1995; Fabian et al., 1995; Fabian et al. + 2002)., 2002). +" The variability line profile matches well with the time-averaged line profile in the first of our observations, MCG-6-30-15(1), which follows the simple disk interpretation."," The variability line profile matches well with the time-averaged line profile in the first of our observations, MCG-6-30-15(1), which follows the simple disk interpretation." +" However, there is a large change between this and the variability profile for the second observation (see Section 3.5)."," However, there is a large change between this and the variability profile for the second observation (see Section 3.5)." +" NGC 3783 and MCG-6-30-15(1) are the only observations in our sample which both show clear evidence for broad line variations, and an amplitude consistent with the continuum, although there are others where the signal-to-noise ratio prevents definitive conclusions."," NGC 3783 and MCG-6-30-15(1) are the only observations in our sample which both show clear evidence for broad line variations, and an amplitude consistent with the continuum, although there are others where the signal-to-noise ratio prevents definitive conclusions." + There are four observations which show variability of the iron line redward of the core that exceeds that of the time averaged spectrum., There are four observations which show variability of the iron line redward of the core that exceeds that of the time averaged spectrum. +" NGC 3516(2) and NGC 5548(2) are the clearest cases, along with NGC 4151(2) and MCG-5-23-16(2) showing narrower or more marginal excesses."," NGC 3516(2) and NGC 5548(2) are the clearest cases, along with NGC 4151(2) and MCG-5-23-16(2) showing narrower or more marginal excesses." +" If the red wing is indeed more strongly variable than the continuum, it is a compelling indicator that relativistic effects are in play (Ponti et al."," If the red wing is indeed more strongly variable than the continuum, it is a compelling indicator that relativistic effects are in play (Ponti et al." + 2004; Miniutti Fabian 2004)., 2004; Miniutti Fabian 2004). +" Curiously, however, NO7 did not find evidence in either NGC 5548(2) or NGC 4151(2) for strong gravitational effects in the time averaged spectra."," Curiously, however, N07 did not find evidence in either NGC 5548(2) or NGC 4151(2) for strong gravitational effects in the time averaged spectra." +" NGC 5548(2) is the most puzzling case, with a non-relativistic iron line but a strong, broad variable excess that extends down to 5.0 keV, a much lower energy than the time- profile."," NGC 5548(2) is the most puzzling case, with a non-relativistic iron line but a strong, broad variable excess that extends down to 5.0 keV, a much lower energy than the time-averaged profile." +" MCG-5-23-16(2) and NGC 3516(2) are different in that they possess relativistically broad iron lines, as well as having strong variability excesses across the red wing."," MCG-5-23-16(2) and NGC 3516(2) are different in that they possess relativistically broad iron lines, as well as having strong variability excesses across the red wing." + This means that the iron line is more variable than the continuum and is likely to be explained by relativistic effects such as beaming or emission from iron moving with a large bulk velocity., This means that the iron line is more variable than the continuum and is likely to be explained by relativistic effects such as beaming or emission from iron moving with a large bulk velocity. +" While most of the excess variability is always seen in the red wings, in MCG-5-23-16(2) and NGC 5548(2) the variability also extends up to 7.0 keV. The second class of observations exhibit the majority of their variability blueward of the line core, and include Mrk 766(3), MCG-6-30-15(2), NGC 5506(1) and the more marginal cases of NGC 4051 and Ark 564."," While most of the excess variability is always seen in the red wings, in MCG-5-23-16(2) and NGC 5548(2) the variability also extends up to 7.0 keV. The second class of observations exhibit the majority of their variability blueward of the line core, and include Mrk 766(3), MCG-6-30-15(2), NGC 5506(1) and the more marginal cases of NGC 4051 and Ark 564." +" In Mrk 766(3), the variability excess in the 6.6-7.0 keV bin"," In Mrk 766(3), the variability excess in the 6.6-7.0 keV bin" +and In Eq.,and In Eq. + 35 and Eq., \ref{eq:delta_r_deq_ac} and Eq. + 36 the V is D is from ?.. and in Eq.," \ref{eq:delta_r_deq_bc} the $\nabla$ is $D$ is from \citet{1970SAOSR.309.....K}, , and in Eq." + 36. the Ho(v) is the radiative flux., \ref{eq:delta_r_deq_bc} the $H_0(\nu)$ is the radiative flux. + Solving Eq., Solving Eq. + 34. for om. using the coefficients in Eq. 35..," \ref{eq:delta_r_deq_sol} for $\delta m$, using the coefficients in Eq. \ref{eq:delta_r_deq_ac}," + Eq., Eq. + 36 and Eq. 37..," \ref{eq:delta_r_deq_bc} and Eq. \ref{eq:delta_r_deq_cc}," + the corresponding temperature change based on conserving the flux is uses two additional temperature corrections near the surface. where the flux error loses sensitivity.," the corresponding temperature change based on conserving the flux is uses two additional temperature corrections near the surface, where the flux error loses sensitivity." + One correction is based on the flux derivative., One correction is based on the flux derivative. + Because this correction applies high in the atmosphere where the gas Is quite transparent. radiation will carry almost all the energy. and it is a good approximation to ignore convective energy transport.," Because this correction applies high in the atmosphere where the gas is quite transparent, radiation will carry almost all the energy, and it is a good approximation to ignore convective energy transport." + The zeroth angular moment of the spherical radiative transfer equation (Eq. 10)), The zeroth angular moment of the spherical radiative transfer equation (Eq. \ref{eq:sph_rad_tran_m}) ) + is Replacing J(v) by A[Sέν). expanding the Planck function in S(v) in terms of T. integrating over frequency and retaining just the diagonal terms of the A operator. the resulting temperature correction becomes The term Agia IS approximated by the plane-parallel expression given in. 2.. assuming it has minimal dependence on the geometry.," is Replacing $J(\nu)$ by $\Lambda[S(\nu)]$, expanding the Planck function in $S(\nu)$ in terms of $T$, integrating over frequency and retaining just the diagonal terms of the $\Lambda$ operator, the resulting temperature correction becomes The term $\Lambda_{\mathrm{dia}}$ is approximated by the plane-parallel expression given in \citet{1970SAOSR.309.....K}, assuming it has minimal dependence on the geometry." +" A third temperature correction is used in the original. code to smooth the region of overlap between the first two corrections,", A third temperature correction is used in the original code to smooth the region of overlap between the first two corrections. + This is and this is retained here., This is and this is retained here. + The total temperature correction is therefore. One test of the validity of the spherical code is to compute a spherical solar atmosphere. which should be nearly identical to the plane-parallel model.," The total temperature correction is therefore, One test of the validity of the spherical code is to compute a spherical solar atmosphere, which should be nearly identical to the plane-parallel model." +" For both models we used the Kuruez file for the starting model and the file for the opacity distribution function,", For both models we used the Kurucz file for the starting model and the file for the opacity distribution function. +" To eliminate other possible sources of differences. we used the Bulirsch-Stoer solution to solve for the pressure structures and the Rybicki method for the radiative transfer in. the plane-parallel model as well as for the spherical calculations,"," To eliminate other possible sources of differences, we used the Bulirsch-Stoer solution to solve for the pressure structures and the Rybicki method for the radiative transfer in the plane-parallel model as well as for the spherical calculations." +" The spherical model used the atmospheric parameters 3.8458x10? ergs/s. Ma=1.9891x10? g. and Ro=6.95508x10"" em."," The spherical model used the atmospheric parameters $L_{\sun} = 3.8458 \times 10^{33}$ ergs/s, $M_{\sun} = 1.9891 \times 10^{33}$ g, and $R_{\sun} = 6.95508 \times 10^{10}$ cm." + These correspond to T;[u=5779.5 K and logg=4.43845. which are slightlydifferent from the canonical values used by Kuruez.," These correspond to $T_{\mathrm{eff}} = 5779.5$ K and $\log g = 4.43845$, which are slightlydifferent from the canonical values used by Kurucz." + Therefore. we computed the plane-parallel model with the consistent values of Tj and logg.," Therefore, we computed the plane-parallel model with the consistent values of $T_{\mathrm{eff}}$ and $\log g$." + The comparison is shown in Fig. 6.., The comparison is shown in Fig. \ref{fig:spsol_ppsol}. +" The |AT| is <0.25% until logy,Po<2. where the temperature of the spherical model begins to trend lower than the plane-parallel] model."," The $| \Delta T |$ is $\leq 0.25\%$ until $\log_{10} P_{\mathrm{gas}} < 2$, where the temperature of the spherical model begins to trend lower than the plane-parallel model." + The dip in the temperature difference down to —2.4% 1s due to the kink in the temperature structure of the model., The dip in the temperature difference down to $- 2.4\%$ is due to the kink in the temperature structure of the model. + This feature was discussed earlier in connection with Fig. 5.., This feature was discussed earlier in connection with Fig. \ref{fig:tp_ryb_josh}. + However. in this case the ? method is used to compute the radiative transfer in models. using the surface boundary condition in both codes.," However, in this case the \citet{1971JQSRT..11..589R} method is used to compute the radiative transfer in models, using the surface boundary condition in both codes." + Therefore. this difference cannot be due to a coding difference between the two routines.," Therefore, this difference cannot be due to a coding difference between the two routines." + This feature might be due to the number of rays used in the calculation of the radiative transfer., This feature might be due to the number of rays used in the calculation of the radiative transfer. + The Rybicki solution for the plane-parallel code uses three rays for each depth. whereas the same method in the spherical code uses =80 rays for the layers approaching the surface.," The Rybicki solution for the plane-parallel code uses three rays for each depth, whereas the same method in the spherical code uses $\approx 80$ rays for the layers approaching the surface." + Perhaps this finer griding produces a smoother temperature profile in these layers., Perhaps this finer griding produces a smoother temperature profile in these layers. + There is. however. no physical significance to the temperature differences nearthe surface because these layers are located in the solar chromosphere (?).. well above the temperature minimum. where other physics is completely dominant.," There is, however, no physical significance to the temperature differences nearthe surface because these layers are located in the solar chromosphere \citep{2006ApJ...639..441F}, , well above the temperature minimum, where other physics is completely dominant." + A test where larger differences are expected is. for the coolest model (Fay=3500 K. logg= 0.0)," A test where larger differences are expected is for the coolest model $T_{\mathrm{eff}} = 3500$ K, $\log g = 0.0$ )" +Alb these five sources are present in the £LRST catalogue (and in the FAST map as clearly. showed in Figure 21)).,All these five sources are present in the $FIRST$ catalogue (and in the $FIRST$ map as clearly showed in Figure \ref{vla_no_nvss}) ). + Their absence in the ΑΕSS catalogue is an indication of the incompleteness of the NVS survey near the Dux limit., Their absence in the $NVSS$ catalogue is an indication of the incompleteness of the $NVSS$ survey near the flux limit. + Using the restriction of an oll-axis value lower than 34 arcmin and a peak Lux density Sp ‘1.0 (the limit of the FIRST catalogue). we have 215 compact sources in common with the LYIST survey.," Using the restriction of an off-axis value lower than 34 arcmin and a peak flux density $_P>$ 1.0 (the limit of the $FIRST$ catalogue), we have 215 compact sources in common with the $FIRST$ survey." + In Figure 22 we show a comparison between our VLA and £LEST total Lux densities., In Figure \ref{ff_FIRST} we show a comparison between our VLA and $FIRST$ total flux densities. + Besicles these 215 common sources. there ΕΛ... sources that we did not detected in our survey and 29 sources present in our survey but not in the £LRST catalogue.," Besides these 215 common sources, there are 14 $FIRST$ sources that we did not detected in our survey and 29 sources present in our survey but not in the $FIRST$ catalogue." + A flux distribution and à contour maps of these last 20 sources are shown in Figure 23. and 24. while a contour maps of the 14. £LRST sources that we did. not. detect are shown in Figure 24.., A flux distribution and a contour maps of these last 29 sources are shown in Figure \ref{vla_no_first_histo} and \ref{vla_no_first} while a contour maps of the 14 $FIRST$ sources that we did not detect are shown in Figure \ref{first_no_vla}. + As shown in Figure 23. all the radio sources missing in the £LRST catalogue have a peak [ux density lower than 2 my., As shown in Figure \ref{vla_no_first_histo} all the radio sources missing in the $FIRST$ catalogue have a peak flux density lower than 2 mJy. + However. as shown in Fieure 24.. many of them appear on the ££LARST maps.," However, as shown in Figure \ref{vla_no_first}, many of them appear on the $FIRST$ maps." + This result. confirms the incompleteness of the FIRST survey below ~2 mJx. as already indicated by the cülferential source counts reported in Figure 5..," This result confirms the incompleteness of the $FIRST$ survey below $\sim$ 2 mJy, as already indicated by the differential source counts reported in Figure \ref{counts_tab}." + On the other hand. Figure 24. shows that many of the 14 £LARST sources missing in our survey probably are not real.," On the other hand, Figure \ref{first_no_vla} shows that many of the 14 $FIRST$ sources missing in our survey probably are not real." + Some of them may be uneleaned residual around strong sources (sec. for example. FELISTI61318|541607. ELISST163646|405442. FIRSTIG3S15|405840) or simply spurious sources in à not well cleaned. map (see. for example. the PIAST maps of ELItST161351|543258. ELIT163634|4213013 and ΓΗΤοτο|405125).," Some of them may be uncleaned residual around strong sources (see, for example, FIRST161318+541607, FIRST163646+405442, FIRST163815+405840) or simply spurious sources in a not well cleaned map (see, for example, the $FIRST$ maps of FIRST161351+543258, FIRST163634+413013 and FIRST163706+405125)." + As shown in Figure 19 and 22 the ux densities of our survey are in good agreement with the LLRST and VVSS Hux densities over two order of magnitude., As shown in Figure \ref{ff_NVSS} and \ref{ff_FIRST} the flux densities of our survey are in good agreement with the $FIRST$ and $NVSS$ flux densities over two order of magnitude. + Llowever. as xpected. the high resolution surveys tend to estimate lower flux than the lower resolution survey.," However, as expected, the high resolution surveys tend to estimate lower flux than the lower resolution survey." + This effect is evident in the lower panels of Figure 19. ancl 22: our VLA [lux densities are. in mean. lower than the INYSS [lux densities out higher than the £IST Dux densities.," This effect is evident in the lower panels of Figure \ref{ff_NVSS} and \ref{ff_FIRST} : our VLA flux densities are, in mean, lower than the $NVSS$ flux densities but higher than the $FIRST$ flux densities." + High resolution Lgurvevs. with their smaller svnthesized beam size. lose {lux ue to the resolution surface brightness elfect.," High resolution surveys, with their smaller synthesized beam size, lose flux due to the resolution surface brightness effect." + Llowever some consideration cam be made from Figure 19. ancl 22.., However some consideration cam be made from Figure \ref{ff_NVSS} and \ref{ff_FIRST}. +" In spite a factor of 3 in angular resolution between our VLA and ANMSS survev (157 vs. 45"" EWLIALD) the Lux ratio of the two survevs is always lower than 0.5 while the Lux ratio between our VLA and £2RST surveys reaches values of ~ 4. although the two surveys have still a factor of 3 in angular resolution differences (57 vs. 157 ENIM)."," In spite a factor of 3 in angular resolution between our VLA and $NVSS$ survey $^{\prime\prime}$ vs. $^{\prime\prime}$ FWHM) the flux ratio of the two surveys is always lower than 0.5 while the flux ratio between our VLA and $FIRST$ surveys reaches values of $\sim$ 4, although the two surveys have still a factor of 3 in angular resolution differences $^{\prime\prime}$ vs. $^{\prime\prime}$ FWHM)." + The missing Dux between the £442ST (VLA - D configuration) and our survey (VLA - € configuration) is greater than the missing [ux between our survey and the [NYSS survey (VLA - D configuration)., The missing flux between the $FIRST$ (VLA - B configuration) and our survey (VLA - C configuration) is greater than the missing flux between our survey and the $NVSS$ survey (VLA - D configuration). +" Therefore the € configuration of our survey with a svnthesized. beam: size of 15"". seems to be the better compromise between high (B configuration) and low (D configuration) resolution racio surveys.", Therefore the C configuration of our survey with a synthesized beam size of $^{\prime\prime}$ seems to be the better compromise between high (B configuration) and low (D configuration) resolution radio surveys. + Lt is less prone to surface brightness ellects than the B configuration without an excessive loss of Lux in comparison with the D configuration., It is less prone to surface brightness effects than the B configuration without an excessive loss of flux in comparison with the D configuration. + Using the Very. Large. Array (VLA) radio telescope. we observed at L4 Giz a total area of 4.222 deg? in the ISO/ELAIS regions NI N2 and N3.," Using the Very Large Array (VLA) radio telescope, we observed at 1.4 GHz a total area of 4.222 $^2$ in the ISO/ELAIS regions N1 N2 and N3." + The lower Ilux density limit reached by our observation is 0.135 mv. (at 5 0 level) on an area of 0.118 deg. while the bulk. of the observed regions are mapped with a flux density limit of 0.250 mJ. (5 7).," The lower flux density limit reached by our observation is 0.135 mJy (at 5 $\sigma$ level) on an area of 0.118 $^2$, while the bulk of the observed regions are mapped with a flux density limit of 0.250 mJy (5 $\sigma$ )." + The data were analyzed using the NILAO reduction package., The data were analyzed using the NRAO reduction package. + The source extraction has been carried out with the taskSAD., The source extraction has been carried out with the task. + The reliability ofSAD has been tested using the maps of the radio surveys LLRST and NVSS., The reliability of has been tested using the maps of the radio surveys $FIRST$ and $NVSS$. + Considering all the available observations. we detected a total of S67 sources at 5 c level. 44 of which have multiple components.," Considering all the available observations, we detected a total of 867 sources at 5 $\sigma$ level, 44 of which have multiple components." + These sources were used to calculate. the normalized dillerential source counts., These sources were used to calculate the normalized differential source counts. + They. provide a check on catalogue completeness ancl reliability. plus information about source evolution., They provide a check on catalogue completeness and reliability plus information about source evolution. + A comparison with other surveys shows a very good agreement. confirming the presence of the well-know flattening of the counts below 1 mv. the completeness of our catalogue ancl the reliability. of our procedure for the source extraction.," A comparison with other surveys shows a very good agreement, confirming the presence of the well-know flattening of the counts below 1 mJy, the completeness of our catalogue and the reliability of our procedure for the source extraction." + A comparison with the PAST and NVSS radio surveys has confirmed. the incompleteness of these two surveys near their [lux limits. while a flux comparison between the three surveys has shown that. our. survey with the VLA array in € configuration is the best compromise between high and low resolution radio surveys.," A comparison with the $FIRST$ and $NVSS$ radio surveys has confirmed the incompleteness of these two surveys near their flux limits, while a flux comparison between the three surveys has shown that our survey with the VLA array in C configuration is the best compromise between high and low resolution radio surveys." + The positional errors of the radio sources are ~ 2 aresec for the fainter sources (70.13 mJv) and ~ 0.6 aresec for the brighter sources (2 10 mv)., The positional errors of the radio sources are $\sim$ 2 arcsec for the fainter sources $\sim$ 0.13 mJy) and $\sim$ 0.6 arcsec for the brighter sources $>$ 10 mJy). + This small value will enable us to obtain an accurate and Fast optical/infrared identification of the racio sources., This small value will enable us to obtain an accurate and fast optical/infrared identification of the radio sources. +" This work was supported. by. the EC. PALR Network programme (EMIUN-C""E96-0068).", This work was supported by the EC TMR Network programme (FMRX-CT96-0068). +. GM. thanks the Roval Society for support., RGM thanks the Royal Society for support. + We thank Rick White for discussions on the optimal pointing grid and both Bob Becker and Jim Condon for discussion on the optimal observing strategy aud Bob Becker for the provision of a FIRST observe file., We thank Rick White for discussions on the optimal pointing grid and both Bob Becker and Jim Condon for discussion on the optimal observing strategy and Bob Becker for the provision of a FIRST observe file. +The svuibiotic nova RR Telis an extraordinary laboratory for spectroscopic studies of low-density astrophysical plasinas on account of the richness of its enission line spectrum that COVCTS a wide range du ionization and excitation stages.,The symbiotic nova RR Tel is an extraordinary laboratory for spectroscopic studies of low-density astrophysical plasmas on account of the richness of its emission line spectrum that covers a wide range in ionization and excitation stages. + Since the fundamental study by Thackeray (1977). new optical observations with higher spectral resolution and S/N ratio have have gradually luprovec the quality of the data aud have allowed the identification of weaker and blended spectral features (sce Me Kenna et al 1997. aud Crawford ct al.," Since the fundamental study by Thackeray (1977), new optical observations with higher spectral resolution and S/N ratio have have gradually improved the quality of the data and have allowed the identification of weaker and blended spectral features (see Mc Kenna et al 1997, and Crawford et al." + 1999)., 1999). + Also. the presence of a strict correlation between the FWIIM aud the ionization level of the enuüssion lines. as pointed out bv Thackerav (1977) ane confirmed by Peuston et al. (," Also, the presence of a strict correlation between the FWHM and the ionization level of the emission lines, as pointed out by Thackeray (1977) and confirmed by Penston et al. (" +1983). has provided a simple but powerful tool for the identification of spectral lines that las uot vet been fully exploited.,"1983), has provided a simple but powerful tool for the identification of spectral lines that has not yet been fully exploited." +" With this in mind. we have taken advantage of| very recent ligh resolution VETUVES observations of RR Tel to revisit the spectral features of the j0va and to perform, anénmitio ideutification of its chussion features."," With this in mind, we have taken advantage of very recent high resolution VLT–UVES observations of RR Tel to revisit the spectral features of the nova and to perform an identification of its emission features." + We present here some highlielts of these recen observations. deferring to a next paper a detailed. description of the spectral identifications aud nueasurenments.," We present here some highlights of these recent observations, deferring to a next paper a detailed description of the spectral identifications and measurements." + Details on the UVES spectrograph iux its performances may be found in D'Odorico et al (2000) as well as iu the UVES User Manual (D'Odorico Kaper. 2000).," Details on the UVES spectrograph and its performances may be found in D'Odorico et al (2000) as well as in the UVES User Manual (D'Odorico Kaper, 2000)." + The data we used consists of a spectrin obtained ou October l6th 1999 with the dichroic 1 and the standard setting centered at 3160 in the blue aria aud 5800 in the red anu. the exposure time was of 1200 s for both arms.," The data we used consists of a spectrum obtained on October 16th 1999 with the dichroic 1 and the standard setting centered at 3460 in the blue arm and 5800 in the red arm, the exposure time was of 1200 s for both arms." + The detector in the blue arm is an EEV CCD. while in the red it is a mosaic of one EEV Gdeutical to that used in the blue arm) aud oue MIT CCD.," The detector in the blue arm is an EEV CCD, while in the red it is a mosaic of one EEV (identical to that used in the blue arm) and one MIT CCD." + All CCDs are composed of £006015 square pixels of 15 jan side., All CCDs are composed of $4096\times 2048$ square pixels of 15 $\rm\mu m $ side. + The shit width was in the blue aud in the red., The slit width was in the blue and in the red. + The data was reduced using the coutext of aud. each CCD was treated iudepeudoeutlv: reduction meluded background subtraction. cosmic rav filteriue. flat ficldiug. extraction. waveleusth calibration and order imereine.," The data was reduced using the context of and each CCD was treated independently; reduction included background subtraction, cosmic ray filtering, flat fielding, extraction, wavelength calibration and order merging." + Since no arc spectra for waveleneth calibration with this setting are available for the date of observation. we used Cibration spectra acquired. ou different davs.," Since no arc spectra for wavelength calibration with this setting are available for the date of observation, we used calibration spectra acquired on different days." + From. our previous experience with UVES (Donifacio et al 2000). we expect the wavelength scale to be reproducible to within a shift of a few tenths of a κο]: suce we are nof interested in accurate radial velocities such a shift is of no consequence for our analysis.," From our previous experience with UVES (Bonifacio et al 2000), we expect the wavelength scale to be reproducible to within a shift of a few tenths of a pixel; since we are not interested in accurate radial velocities such a shift is of no consequence for our analysis." + The resolution. as ucasured from the Th lines of the calibration lup is z64000 for," The resolution, as measured from the Th lines of the calibration lamp is $\approx 65000$ for" +llalos are populated with a central galaxy wilh probabilitw ολ).,Halos are populated with a central galaxy with probability $N_{cen}(M)$. + Central galaxies are placed at the center of their host halos ancl assigned the peculiar velocity of their halos., Central galaxies are placed at the center of their host halos and assigned the peculiar velocity of their halos. +" llalos with a central galaxy are populated with Ny, galaxies. where Να,ANCM)) is drawn from a Poisson distribution."," Halos with a central galaxy are populated with $N_{sat}$ galaxies, where $P(N_{sat}|N(M))$ is drawn from a Poisson distribution." + Our parameter constraints are derived using SO halo catalogs., Our parameter constraints are derived using SO halo catalogs. + For those. (he position and velocity of the satellite galaxies are taken to be that of a randomly selected dark matter particle halo member.," For those, the position and velocity of the satellite galaxies are taken to be that of a randomly selected dark matter particle halo member." + For mock catalogs based on the FoF halos. the satellite galaxies ave independently distributed following an NEW prolile with concentration of the dark matter halo determined by Eqn. 6..," For mock catalogs based on the FoF halos, the satellite galaxies are independently distributed following an NFW profile with concentration of the dark matter halo determined by Eqn. \ref{conceqn}." + The peculiar velocity of a satellite galaxy is (he sum of the halo peculiar. velocity and a random velocity drawn [rom a Gaussian distribution determined by the virial velocity of the halo (?):: We assign comoving redshift space position s to an object in our mock catalogs using the conversion at τω=0.2: where typos is (he comoving distance along the line of sight in real The hypothesis underlying the Counts-In-Cdinders technique to constrain the LRG HOD is that 1-halo and 2-halo LRG pairs are separable based on their relative angular and redshift space positions., The peculiar velocity of a satellite galaxy is the sum of the halo peculiar velocity and a random velocity drawn from a Gaussian distribution determined by the virial velocity of the halo \citep{lokas/mamon:2001}: We assign comoving redshift space position $s$ to an object in our mock catalogs using the conversion at $z_{box} = 0.2$: where $x_{LOS}$ is the comoving distance along the line of sight in real The hypothesis underlying the Counts-In-Cylinders technique to constrain the LRG HOD is that 1-halo and 2-halo LRG pairs are separable based on their relative angular and redshift space positions. + In the regime of small separations where (he 1-halo term dominates. a cvlinder should be a good approximation to the density contours surrounding central ealaxies. as long as the satellite velocity is uncorrelated. with its distance from the halo center. and (he relative velocity dominates the separation of central ancl satellite objects in (he redshift direction.," In the regime of small separations where the 1-halo term dominates, a cylinder should be a good approximation to the density contours surrounding central galaxies, as long as the satellite velocity is uncorrelated with its distance from the halo center, and the relative velocity dominates the separation of central and satellite objects in the redshift direction." +" Based on our initial analvsis of completeness ancl contamination ol mock catalogs derived from. FoF halos. we set Arως=0.8 Mpe/h and Ate,=20 Mpe/h [or our z=0.2 catalogs."," Based on our initial analysis of completeness and contamination of mock catalogs derived from FoF halos, we set $\Delta r_{\perp,max} = 0.8$ $h$ and $\Delta z_{max} = 20$ $h$ for our $z=0.2$ catalogs." +" Arie, is set bv the typical comoving size of halos hosting salellite galaxies. and «σαν is set bv the amplitude of the velocity dispersion in halos massive enough to host satellite galaxies."," $\Delta r_{\perp,max}$ is set by the typical comoving size of halos hosting satellite galaxies, and $\Delta z_{max}$ is set by the amplitude of the velocity dispersion in halos massive enough to host satellite galaxies." + In later work we plan to improve the fidelity of our (ας eroup identification., In later work we plan to improve the fidelity of our CiC group identification. + ILowever. the choice made here is sullicient since we calibrate the," However, the choice made here is sufficient since we calibrate the" + , +the space of the gas ring toward the center.,the space of the gas ring toward the center. + As an alternative. they may be a surposition of the gas circulating inside the bar in elliptic streamings with that of the disc in circular motion.," As an alternative, they may be a surposition of the gas circulating inside the bar in elliptic streamings with that of the disc in circular motion." + But the map of the tontsed gas distribution appears quite irregular. so we preferred do not search solutions with warped dises. to avoid increasing the number of variables present in the model.," But the map of the ionised gas distribution appears quite irregular, so we preferred do not search solutions with warped discs, to avoid increasing the number of variables present in the model." + Taking into account the clear symmetry of the HI ring around NGC 4262. it is unlikely it comes from a primordial cloud of neutral hydrogen such that discussed in detail by Thilker et al. (," Taking into account the clear symmetry of the HI ring around NGC 4262, it is unlikely it comes from a primordial cloud of neutral hydrogen such that discussed in detail by Thilker et al. (" +2009).,2009). + On the contrary. Bekki et al. (," On the contrary, Bekki et al. (" +2005) do model the stripping of rings and ares of cold gas as due to interaction with other galaxies.,2005) do model the stripping of rings and arcs of cold gas as due to interaction with other galaxies. + In this context. a stream of gas pulled out of the disk of the galaxy (or contributed by a perturber) forms stars when it is compressed.," In this context, a stream of gas pulled out of the disk of the galaxy (or contributed by a perturber) forms stars when it is compressed." + Such an interaction scenario is supported also by a further hint. namely the observed inner decoupling of gas and stars velocity fields in NGC 4262 (Sarzi et al.," Such an interaction scenario is supported also by a further hint, namely the observed inner decoupling of gas and stars velocity fields in NGC 4262 (Sarzi et al." + 2006)., 2006). + In the specific case of GC 4262 the existence of a mutual interaction with the other Virgo galaxy NGC [254 has been proposed by Chyzy et al. (, In the specific case of NGC 4262 the existence of a mutual interaction with the other Virgo galaxy NGC 4254 has been proposed by Chyzy et al. ( +2007). while another example of such merger-induced. ringed lenticular galaxies could be NGC 404 (Thilker et al.,"2007), while another example of such merger-induced, ringed lenticular galaxies could be NGC 404 (Thilker et al." + 2010)., 2010). + As far as the UV- disk’s star formation is concerned. is likely occurring ndependently of the above possible (ring-forming) interaction event.," As far as the UV-detected, disk's star formation is concerned, is likely occurring independently of the above possible (ring-forming) interaction event." + Thanks to the UV-sensitive GALEX satellite we were able to detect an extended. UV-bright ring surrounding the otherwise normal SBO galaxy NGC 4262.," Thanks to the UV-sensitive GALEX satellite we were able to detect an extended, UV-bright ring surrounding the otherwise normal SB0 galaxy NGC 4262." + Such a feature (not recognizable in the optical) appears to host several knots. likely consisting of hot star clusters.," Such a feature (not recognizable in the optical) appears to host several knots, likely consisting of hot star clusters." + In this respect. NGC 4262—having clustered UV-bright sources 1n its outer parts—could be classified as a Type | extended ultraviolet disk (XUV).," In this respect, NGC 4262---having clustered UV-bright sources in its outer parts—could be classified as a Type 1 extended ultraviolet disk (XUV)." + About the origin of such a structure. one should be aware that theoretical models (e.g. Bekki 2005: Higdon Higdon 2010) ascribe the onset of rings and ares of cold gas as well as the formation of young star rings to the past interaction with other galaxies.," About the origin of such a structure, one should be aware that theoretical models (e.g. Bekki 2005; Higdon Higdon 2010) ascribe the onset of rings and arcs of cold gas as well as the formation of young star rings to the past interaction with other galaxies." + As a consequence. taking account also of the observed inner decoupling of gas and stars velocity fields (Sarzi et al.," As a consequence, taking account also of the observed inner decoupling of gas and stars velocity fields (Sarzi et al." + 2006). we are pretty confident that à past major interaction episode underwent by NGC 4262 is responsible of the onset of the UV-bright ring we see today.," 2006), we are pretty confident that a past major interaction episode underwent by NGC 4262 is responsible of the onset of the UV-bright ring we see today." +"‘Phe ""radio loudness' of an active galactic nucleus (AGN) is usually defined. as the ratio of its radio and optical Ilux densities or luminosities at two specific frequencies.",The `radio loudness' of an active galactic nucleus (AGN) is usually defined as the ratio of its radio and optical flux densities or luminosities at two specific frequencies. +" A possible bimodality in the radio loudness distribution. of the AGw population. the so-called: ""racio-Ioud/racdio-cquiet clichotomy. is an often-debated. somewhat contenious. and ongoing topic of study (c.g.Strittmatteretal.1980:SramekSingalοἱal. 2011)."," A possible bimodality in the radio loudness distribution of the AGN population, the so-called `radio-loud/radio-quiet dichotomy', is an often-debated, somewhat contentious, and ongoing topic of study \citep*[e.g.][]{strittmatter80,sramek80,condon81,kellermann89,miller90,miller93,xu99,white00,ivezic02,cirasuolo03a,cirasuolo03b,gopal08,zamfir08,singal11}." +. The resolution of this issue is crucial if fundamental questions relating to the physics of rlack ole (BIL) aceretion. jet formation and feedback are to be fully ackelressect.," The resolution of this issue is crucial if fundamental questions relating to the physics of black hole (BH) accretion, jet formation and feedback are to be fully addressed." +" One standard definition of radio loudness that has been used. particularly. in quasar studies is the ratio Sp./ S. where S,, and 5,, are the monochromatic 5 Cllz radio and nuclear 4400 ((D-band) Uux densities. respectively (Ixellermann.etal. 1989)."," One standard definition of radio loudness that has been used particularly in quasar studies is the ratio $S_{\nu_{5}}/S_{\nu_{B}}$ , where $S_{\nu_{5}}$ and $S_{\nu_{B}}$ are the monochromatic 5 GHz radio and nuclear 4400 $B$ -band) flux densities, respectively \citep[][]{kellermann89}." +". Raclio-loucl quasars were at. first. considered. to be hose with 5,4δρ210. while for most racdio-quiet quasars Kloπμσα. where Lua is the nuclear radiative bolometric luminosity and Lpgaa is the Ecclington lIuminositv).," However, in more recent times, BH mass have allowed a more sophisticated approach to be adopted when studying the radio loudnesses of AGN: the dependence of radio loudness on the Eddington ratio, $\lambda$ $\equiv L_{\rm bol}/L_{\rm Edd}$, where $L_{\rm bol}$ is the nuclear radiative bolometric luminosity and $L_{\rm Edd}$ is the Eddington luminosity)." + For example. Sikora.Stawarz&Lasota (2007).. henceforth referred to as SSLOT. investigated. the radioloudnesses of a total of 199 sources spread across five dilferent populations: broad-line racio," For example, \citet*[][]{sikora07}, henceforth referred to as SSL07, investigated the radioloudnesses of a total of 199 sources spread across five different populations: broad-line radio" +Correspondingly. we can express the angular momentum of the external gas as the following dimensionless ratio When .#>>|. we expect the flow to be viscously driven and to resemble an ADAF solution. whereas when. Z«|. the flow should be practically identical to the Bondi solution.,"Correspondingly, we can express the angular momentum of the external gas as the following dimensionless ratio When ${\cal L}\gg1$, we expect the flow to be viscously driven and to resemble an ADAF solution, whereas when ${\cal L}\ll1$, the flow should be practically identical to the Bondi solution." + These expectations are borne out by the numerical solutions described in refresults.., These expectations are borne out by the numerical solutions described in \\ref{results}. + For our choice of coup=10SOF =| corresponds to #—0.0037.," For our choice of $c_{\rm out} = 10^{-3}c$, ${\cal + L}=1$ corresponds to ${\cal R} = 0.0037$." + Since the viscous accretion equations tend to be very stiff. we use a relaxation method (Press et al.," Since the viscous accretion equations tend to be very stiff, we use a relaxation method (Press et al." + 1992) to solve Figure | shows sample solutions correspondingto @=0.1. y=5/3. Cou=105 and Pow=1 (the value of pau is arbitrary since we can rescale the density profile to any external density as needed. retbes)).," 1992) to solve Figure 1 shows sample solutions correspondingto $\alpha=0.1$, $\gamma=5/3$, $c_{\rm out} = 10^{-3}$ and $\rho_{\rm + out}=1$ (the value of $\rho_{\rm out}$ is arbitrary since we can rescale the density profile to any external density as needed, \\ref{bcs}) )." + Four solutions are shown. corresponding to Z7=85. 12. 1.8. O.LI. respectively (compare with Fig.," Four solutions are shown, corresponding to ${\cal L} = 85$, 12, 1.8, 0.11, respectively (compare with Fig." + | in Park 2009)., 1 in Park 2009). + Note that the rotation parameter .z is small for all the solutions. so these truly represent slowly-rotating flows.," Note that the rotation parameter ${\cal R}$ is small for all the solutions, so these truly represent slowly-rotating flows." + Even the most rapidly rotating solution 647— 0.31) has a centrifugal support of only of Keplerian at r—rp., Even the most rapidly rotating solution ${\cal R}=0.31$ ) has a centrifugal support of only of Keplerian at $r=r_{\rm B}$. + The solution with .Z=0.11 — the lowest curve in the panel of Fig., The solution with ${\cal L}=0.11$ – the lowest curve in the top-left panel of Fig. + | — is clearly in the Bondi regime since the gas has negligible outer specific angular momentum relative to hy., 1 – is clearly in the Bondi regime since the gas has negligible outer specific angular momentum relative to $l_{\rm ms}$. +" The sonic radius ry. shown by the black dot. is located at 317r,. which is almost exactly where a pure non-rotating Bondi flow has its sonic radius for our choice of P(r). Cou and y."," The sonic radius $r_s$, shown by the black dot, is located at $417r_g$, which is almost exactly where a pure non-rotating Bondi flow has its sonic radius for our choice of $\Phi(r)$, $c_{\rm out}$ and $\gamma$." + The two solutions with .Z=85 and 12 (the highest two curves) are definitely rotation-dominated., The two solutions with ${\cal L}= 85$ and 12 (the highest two curves) are definitely rotation-dominated. + The gas in these solutions has too much angular momentum to permit steady accretion in the absence of viscosity. so the accretion flow settles down to a viscously-driven ADAF solution.," The gas in these solutions has too much angular momentum to permit steady accretion in the absence of viscosity, so the accretion flow settles down to a viscously-driven ADAF solution." +" Correspondingly. the sonic radius is close to the marginally stable orbit. rj,=3r,."," Correspondingly, the sonic radius is close to the marginally stable orbit, $r_{\rm ms}=3r_g$." + The solution with .Zz=1.8 represents a transition state between the Bondi and ADAF regimes., The solution with ${\cal L}=1.8$ represents a transition state between the Bondi and ADAF regimes. + Its sonic radius is at an intermediate location. ry=|42re.," Its sonic radius is at an intermediate location, $r_s=142r_g$." + In Figure 2. the top-left panel shows how the sonic radius moves as we change .ZZ.," In Figure 2, the top-left panel shows how the sonic radius moves as we change ${\cal L}$." +" For all values of κI. ry is located at the position one would calculate for the non-rotating Bondi problem (upper dotted line). while for .Z greater than a few. ry is close to Tii, Cower dotted line)."," For all values of ${\cal L}<1$, $r_s$ is located at the position one would calculate for the non-rotating Bondi problem (upper dotted line), while for ${\cal L}$ greater than a few, $r_s$ is close to $r_{\rm ms}$ (lower dotted line)." + The transition between these two regimes is quite sudden. with most of the change happening over the range L5«Vx3.," The transition between these two regimes is quite sudden, with most of the change happening over the range $1.5 < {\cal L} < 2$." + The bottom two panels in Fig., The bottom two panels in Fig. + | show the profiles of density p and pressure p—pc; for the same four solutions as in the top left panel., 1 show the profiles of density $\rho$ and pressure $p=\rho c_s^2$ for the same four solutions as in the top left panel. + Even though the rotation profiles of these solutions are very different. and their sonic radii move around considerably. the profiles of p and p are nearly identical.," Even though the rotation profiles of these solutions are very different, and their sonic radii move around considerably, the profiles of $\rho$ and $p$ are nearly identical." + The insensitivity to the location of Ες is at least in part because we selected y=5/3. which is known to be a critical value of the adiabatic index both for the Bondi problem and for ADAFs.," The insensitivity to the location of $r_s$ is at least in part because we selected $\gamma=5/3$, which is known to be a critical value of the adiabatic index both for the Bondi problem and for ADAFs." + Nevertheless. it is clear that in many respects. an ADAF is very similar to a Bondi flow.," Nevertheless, it is clear that in many respects, an ADAF is very similar to a Bondi flow." + The top-right panel in Fig., The top-right panel in Fig. + | shows the radial velocity profiles of the four solutions., 1 shows the radial velocity profiles of the four solutions. + We see that the radial velocity is smaller for a rotating ADAF ¢the solutions with .#= 85. 12) compared to a slowly-rotating Bondi-like flow (27= 0.113.," We see that the radial velocity is smaller for a rotating ADAF (the solutions with ${\cal L}=85$ , 12) compared to a slowly-rotating Bondi-like flow ${\cal L}=0.11$ )." + Since the density profiles of both Kinds of solution are nearly the same. this means that the mass accretion rates are different.," Since the density profiles of both kinds of solution are nearly the same, this means that the mass accretion rates are different." + This is illustrated in the, This is illustrated in the +"and fy=bf"".",and $R_0=bl^p$. + Xs expected. we see that increasing / while ioleüng all other parameters fixed decreases the zero-signal racius.," As expected, we see that increasing $l$ while holding all other parameters fixed decreases the zero-signal radius." + Table 3. shows the best fit parameters for this power aw for the data shown in Figure 5.., Table \ref{tab:nfw_l} shows the best fit parameters for this power law for the data shown in Figure \ref{fg:nfw_l}. +" Finally. we consider the behaviour of the peak FAM, signal and the zero-signal radius for an NEW. profile. of ixed mass. with fixed aperture parameters A and /. as a ""unction of concentration parameter e."," Finally, we consider the behaviour of the peak $\fmap$ signal and the zero-signal radius for an NFW profile of fixed mass, with fixed aperture parameters $R$ and $l$ , as a function of concentration parameter $c$." + Phe data have a strong dependence on halo mass. therefore Figure 6. shows he behaviour of the peak signal and. zero-signal contours for various combinations of/ ane 2 for both a halo of mass OthM. and 1075.TAL...," The data have a strong dependence on halo mass, therefore Figure \ref{fg:nfw_c} shows the behaviour of the peak signal and zero-signal contours for various combinations of $l$ and $R$ for both a halo of mass $10^{11}h^{-1}\,M_\odot$ and $10^{15}h^{-1}\,M_\odot$." +" Llere. again. the behaviour of cach appears to be a power law of the form men,=ae” and fy=be""."," Here, again, the behaviour of each appears to be a power law of the form $m_{peak}=ac^n$ and $R_0=bc^p$." + “Table 40 shows the best fit parameters for these power laws for the data shown in Figure 6.., Table \ref{tab:nfw_c} shows the best fit parameters for these power laws for the data shown in Figure \ref{fg:nfw_c}. +" The behaviour of the peak PAZ, signal from the NEW. profile dillers ereathy from. that of the SES model as the aperture radius and filter polynomial order are changed.", The behaviour of the peak $\fmap$ signal from the NFW profile differs greatly from that of the SIS model as the aperture radius and filter polynomial order are changed. + Moreover. the behaviour changes with halo mass and concentration parameter in a non-trivial way.," Moreover, the behaviour changes with halo mass and concentration parameter in a non-trivial way." + A similar trend. is seen when considering the behaviour of the zero-signal radius. where the slope of the power law behaviour changes based on aperture size. filter shape. virial mass and concentration parameter.," A similar trend is seen when considering the behaviour of the zero-signal radius, where the slope of the power law behaviour changes based on aperture size, filter shape, virial mass and concentration parameter." + Again. it is not. possible to model this behaviour simply and arrive at à general analytic expression for the zero-signal radius that simultaneously describes its behaviour as a function of all the parameters one might vary.," Again, it is not possible to model this behaviour simply and arrive at a general analytic expression for the zero-signal radius that simultaneously describes its behaviour as a function of all the parameters one might vary." + This vastly dilfering behaviour implies that if one were to consider several llexion aperture mass reconstructions of a lens field using dilferent aperture radii and filter polynomial order. one might be able to distinguish not only between an SIS model anc an NEW. model. but. between NEW models with dillerent masses and concentration parameters.," This vastly differing behaviour implies that if one were to consider several flexion aperture mass reconstructions of a lens field using different aperture radii and filter polynomial order, one might be able to distinguish not only between an SIS model and an NFW model, but between NFW models with different masses and concentration parameters." + Moreover. considering the behaviour exhibited in. Figures 4 and 5. it appears that a change in aperture radius shows a greater change inthe overall peak signal than a change in polynomial order. and thus might provide a better," Moreover, considering the behaviour exhibited in Figures \ref{fg:nfw_r} and \ref{fg:nfw_l}, it appears that a change in aperture radius shows a greater change inthe overall peak signal than a change in polynomial order, and thus might provide a better" +AT V streneth aud A3 V wines... example of two normal parent spectra producing a peculiar composite”.,"A7 V strength and A3 V wings... example of two normal parent spectra producing a peculiar composite""." + The effect of voiliug in the spectrum of a binary with components nof very dissimilar from one another (M—2 and 1.4 solar masses) has been investigated iu detail by Lyubiniukoy (1992)., The effect of veiling in the spectrum of a binary with components not very dissimilar from one another (M=2 and 1.4 solar masses) has been investigated in detail by Lyubimkov (1992). + Most of lis analysis. devoted to Am stars. refers to courposi| spectra (computed for Lb sclected evolutionary phases) obtained by combining two spectra for which solar abundances are adopted ouly for clemeuts lighter than Ti.," Most of his analysis, devoted to Am stars, refers to composite spectra (computed for 4 selected evolutionary phases) obtained by combining two spectra for which solar abundances are adopted only for elements lighter than Ti." + A ecneral apparcut uuderabunudauce of these elements is derived by his computatious when the original duplicity is ucelected. in agreement with the weak metal lines obtained by our example plotted im Fig.," A general apparent underabundance of these elements is derived by his computations when the original duplicity is neglected, in agreement with the weak metal lines obtained by our example plotted in Fig." +" {,", 4. + AccordingC» to the data collected in the previous sectionis. 1l stars of our origiualOo sample are doubles with an angular separation smaller than 1.2 arcsec. 3 stars are SD2 iux | are probably non-imgle. according to the Iipparcos data.," According to the data collected in the previous sections, 11 stars of our original sample are doubles with an angular separation smaller than 1.2 arcsec, 3 stars are SB2 and 4 are probably non-single, according to the Hipparcos data." + In couchision. for 18/89 20 '4 of our siuuple stars duplicitv mmus be exaimiued in further detail before determuning atmospheric abunuidanuces.," In conclusion, for 18/89= 20 $ \%$ of our sample stars duplicity must be examined in further detail before determining atmospheric abundances." + Cremer et al. (, Grenier et al. ( +1999) in them radial velocity study of a sample of D to F stars. included in the Tipparcos catalogue. obtained spectra for 16 stars of our sample.,"1999) in their radial velocity study of a sample of B to F stars, included in the Hipparcos catalogue, obtained spectra for 16 stars of our sample." + Of these 12 are suspected. probable or established binarics. ouly lofthese are amoug the 18 known binaries previously meutioned.," Of these 12 are suspected, probable or established binaries, only 4 of these are among the 18 known binaries previously mentioned." + If all of them will be confined to be binaries the percentage will raise to., If all of them will be confirmed to be binaries the percentage will raise to. + We note also that 11 of these stars are in conunou with the € list aud 8 are classified as POL by hun., We note also that 11 of these stars are in common with the G list and 8 are classified as PHL by him. + If we apply the preseut knowledge to the 15 stars analyzed by St93. we see that 2 of them are SB2 (IID 9δ19. ane the atinospherie parameters. derived frou the combined photometric iudices. require the hypothesis that the two stars are strictly the same so that the same 2nd ee can be adopted.," If we apply the present knowledge to the 15 stars analyzed by St93, we see that 2 of them are SB2 (HD 38545 and HD 111786), for HD 198160 and HD 198161 the atmospheric parameters, derived from the combined photometric indices, require the hypothesis that the two stars are strictly the same so that the same and g can be adopted." + The duplicity of these stars requires to be further examined in order to determine accurate suele clemeuts abuudances., The duplicity of these stars requires to be further examined in order to determine accurate single elements abundances. + Furthermore. the variability of the 5 variable stars niust be examined to assess that its amplitude docs not affect the photometrically derived atimospheric parameters.," Furthermore, the variability of the 5 variable stars must be examined to assess that its amplitude does not affect the photometrically derived atmospheric parameters." + Ileh S/N spectroscopic data of spectral resions iu which not severely blended features are present are necessary ο discriminate between velius (spectral ines when they retain the breadth of their temperature ype. but are shallower than normal (Corbally 1987}) which indicates a composite spectrum and normal xofiles with weak intensities. which are sign of real uetal uuderabuudauces.," High S/N spectroscopic data of spectral regions in which not severely blended features are present are necessary to discriminate between ""veiling"" (spectral lines when they retain the breadth of their temperature type, but are shallower than normal (Corbally 1987)) which indicates a composite spectrum and normal profiles with weak intensities, which are sign of real metal underabundances." + Such discrimination. however. )ocomies extremely difficult when the observed. spectrum is characterized by broad aud weak metal lines as in most candidates.," Such discrimination, however, becomes extremely difficult when the observed spectrum is characterized by broad and weak metal lines as in most candidates." + What we can expect in a composite spectrum of two similar A-type stars ive Balmer lines broader than those of the sinele commponcuts by an amount which depends on the relative RV of the commponcuts. so simulating a star with a higher eecee value when compared to computed spectra or intrinsically very hieh for an carly A-type star as it iav be the case of ΠΟ 291255 (the parameters derived bx AID programs are Z;4g42110370 Is oooge=50).," What we can expect in a composite spectrum of two similar A-type stars are Balmer lines broader than those of the single components by an amount which depends on the relative RV of the components, so simulating a star with a higher g value when compared to computed spectra or intrinsically very high for an early A-type star as it may be the case of HD 294253 (the parameters derived by MD programs are 10370 K g=4.50)." + Moreover. the composite Balmer line profile will present a flat iuner core which depends on the differeuce of the two radial velocities as well as a global profile which uav be different from what is expected from the douinatiug broadenings: Doppler core aud linear Stark wines.," Moreover, the composite Balmer line profile will present a flat inner core which depends on the difference of the two radial velocities as well as a global profile which may be different from what is expected from the dominating broadenings: Doppler core and linear Stark wings." + For the stars recognized to be double by speckle observations. and not observed by the Iipparcos satellite. the extraction of luminosity ratios from speckle data will be frndamental ο better define the character of the two componcuts.," For the stars recognized to be double by speckle observations, and not observed by the Hipparcos satellite, the extraction of luminosity ratios from speckle data will be fundamental to better define the character of the two components." + Algorithms to extract luminosity ratios from 4.oeckle data have been developed. but these tecliuiques are still limited (Sowell Wilson 1993).," Algorithms to extract luminosity ratios from speckle data have been developed, but these techniques are still limited (Sowell Wilson 1993)." + If the luminosity of the companion is large enoueh (of the order of of the total huninosity). the veiling may not be neglected: iu fact the metallic lines will appear weaker. thus leading to zu underestimate of the metallicity.," If the luminosity of the companion is large enough (of the order of of the total luminosity), the veiling may not be neglected; in fact the metallic lines will appear weaker, thus leading to an underestimate of the metallicity." + The IR colows could also prove to be powerful diagnostic tool for the presence of cooler companious., The IR colours could also prove to be powerful diagnostic tool for the presence of cooler companions. + A cool companion of ΠΟ 111786 was predicted Dy its photometry in the JAD and Io bands by Cerbaldi (1990) ou the basis of the discrepancy with the (B-V) value aud was ascribed to a probable cool companion.," A cool companion of HD 111786 was predicted by its photometry in the J,H and K bands by Gerbaldi (1990) on the basis of the discrepancy with the (B-V) value and was ascribed to a probable cool companion." + The foregone discussion leads us tfo formulate he hypothesis hat a considerable fraction of candidates are du fact ynarics., The foregoing discussion leads us to formulate the hypothesis that a considerable fraction of candidates are in fact binaries. + This is supported by he large fraction of binaries recently discovered along stars ether through the speckle techuique or w the Tipparcos experiment., This is supported by the large fraction of binaries recently discovered among stars either through the speckle technique or by the Hipparcos experiment. + Also the lieh nuuboer of stars with a υπο colour excess supports that our μπατν hvpothesis is at the origin of distorted energy distributions aud of not colerent uvby.? indices of several candidates.," Also the high number of stars with a ""blue"" colour excess supports that our binarity hypothesis is at the origin of distorted energy distributions and of not coherent $\beta$ indices of several candidates." + The PHL phenomenon cannot be easilv explained if the stars are single. however its explanation becomes trivial if the stars are binary as has Όσσα demonstrated in the case of the stars IID 38515 aud ID 111756. classified PIIL by Cray (1988. 1998). which iade turned out to be binaries.," The PHL phenomenon cannot be easily explained if the stars are single, however its explanation becomes trivial if the stars are binary, as has been demonstrated in the case of the stars HD 38545 and HD 111786, classified PHL by Gray (1988, 1998), which indeed turned out to be binaries." + The appareutlv erratic abundance patterus pose serious problems to the accretion hypothesis. but again it nav be casily reconciled iu the case of binary stars.," The apparently erratic abundance patterns pose serious problems to the accretion hypothesis, but again it may be easily reconciled in the case of binary stars." + The fact that some of the stars are binaries does uot exclude the possibility that chemical peculiarities are actually present in their atmospheres., The fact that some of the stars are binaries does not exclude the possibility that chemical peculiarities are actually present in their atmospheres. + However their quantification requires that the binaritv is properly accounted for., However their quantification requires that the binarity is properly accounted for. + We have shown that each author has his own definition and list of A Doo caudidates and these lists only partly overlap., We have shown that each author has his own definition and list of $\lambda$ Boo candidates and these lists only partly overlap. + Until all the classification schemes converge into, Until all the classification schemes converge into +"(and gen; /n)), the integral in equation (20)) becomes: The column density through a smoothing volume (for any impact parameter and any distance into the sphere) can now be calculated; multiplying by an opacity then provides an optical depth.","(and _f = ), the integral in equation \ref{eq:sigma}) ) becomes: The column density through a smoothing volume (for any impact parameter and any distance into the sphere) can now be calculated; multiplying by an opacity then provides an optical depth." +" Typically, )isconstructedusingcubicsplines(?).."," Typically, is constructed using cubic splines \citep{Monaghan_92}." +" T hekernelusedinthisworkis This provides compact support (i.e. it reduces to zero outside the smoothing volume), and is simple to integrate."," The kernel used in this work is This provides compact support (i.e. it reduces to zero outside the smoothing volume), and is simple to integrate." +" With a prescription for calculating optical depth for a single sphere in place, a scheme for calculating ray/sphere intersections must be constructed."," With a prescription for calculating optical depth for a single sphere in place, a scheme for calculating ray/sphere intersections must be constructed." +" To this end, the code creates a data object called araylist,, which stores (in order of intersection) all particles that the ray (given its origin and direction vector) will intersect."," To this end, the code creates a data object called a, which stores (in order of intersection) all particles that the ray (given its origin and direction vector) will intersect." +" Once the list is created, the optical depth can be calculated quickly using equation (18))."," Once the list is created, the optical depth can be calculated quickly using equation \ref{eq:scatter}) )." + The construction of the raylist must be computationally efficient for the code to be effective., The construction of the raylist must be computationally efficient for the code to be effective. + The procedure is similar to that implemented by ? inSPHRAY; the code constructs an octree to spatially index the particles efficiently (as there may be density changes over several orders of magnitude)., The procedure is similar to that implemented by \citet{SPHRAY} in; the code constructs an octree to spatially index the particles efficiently (as there may be density changes over several orders of magnitude). +" The cells either contain child cells, or particles (the cells))."," The cells either contain child cells, or particles (the )." + The tree is constrained to have a maximum number of particles in each leaf., The tree is constrained to have a maximum number of particles in each leaf. +" All cells have an associated Axis Aligned Bounding Box (AABB), which is the minimum box size, aligned to the three cartesian axes, to contain all the smoothing volumes of the particles in the cell (see Figure 4))."," All cells have an associated Axis Aligned Bounding Box (AABB), which is the minimum box size, aligned to the three cartesian axes, to contain all the smoothing volumes of the particles in the cell (see Figure \ref{fig:aabb}) )." +" These AABBs are necessary as tree nodes may contain a particle, but not its entire smoothing volume This allows the determination of intersections between the ray and the cells (or more correctly, their AABBs)."," These AABBs are necessary as tree nodes may contain a particle, but not its entire smoothing volume This allows the determination of intersections between the ray and the cells (or more correctly, their AABBs)." +" Starting with the root cell, each child cell is tested for intersection, constituting a walk through the tree."," Starting with the root cell, each child cell is tested for intersection, constituting a walk through the tree." +" If a leaf cell is intersected by the ray, then the particles in the leaf are tested for intersection (by calculating their impact parameters)."," If a leaf cell is intersected by the ray, then the particles in the leaf are tested for intersection (by calculating their impact parameters)." + This ensures that only a minimum fraction of the particles in the system need testing for intersection., This ensures that only a minimum fraction of the particles in the system need testing for intersection. +" This illustrates the necessity of AABBs; tree nodes may contain a particle, but not its entire smoothing volume."," This illustrates the necessity of AABBs; tree nodes may contain a particle, but not its entire smoothing volume." +" Thus, calculating intersections between a ray and tree nodes may miss contributions to the density field from smoothing volumes that cross node intersections."," Thus, calculating intersections between a ray and tree nodes may miss contributions to the density field from smoothing volumes that cross node intersections." +" Tests for intersections between rays and AABBs are carried out using the ray slopes algorithm (?),, which has been shown to be faster than other commonly used methods, such as using Plüccker coordinates (?).."," Tests for intersections between rays and AABBs are carried out using the ray slopes algorithm \citep{rayslope}, which has been shown to be faster than other commonly used methods, such as using Plüccker coordinates \citep{plucker}." + An important facet of an MCRT code is the determination of the scattering location of the photon., An important facet of an MCRT code is the determination of the scattering location of the photon. +" In general, the scattering location will occur inside a smoothing volume, and possibly at a location where the density depends on the contributions from several particles."," In general, the scattering location will occur inside a smoothing volume, and possibly at a location where the density depends on the contributions from several particles." +" Therefore, when attempting to determine the scattering location, it is important to define four classes of particle: The classes are illustrated in Figure 5.."," Therefore, when attempting to determine the scattering location, it is important to define four classes of particle: The classes are illustrated in Figure \ref{fig:classes}." + Particles of class (i) obviously do not affect the calculation - particles of class (ii) are accounted for simply., Particles of class (i) obviously do not affect the calculation - particles of class (ii) are accounted for simply. +" Particles of classes (iii) and (iv) will have differing effects on the optical depth calculation, and will require separate treatments."," Particles of classes (iii) and (iv) will have differing effects on the optical depth calculation, and will require separate treatments." +" The scattering location is determined by iteration: firstly, the optical depth is calculated particle by particle using the raylist until the optical depth exceeds the randomly selected optical depth at particlekk."," The scattering location is determined by iteration: firstly, the optical depth is calculated particle by particle using the raylist until the optical depth exceeds the randomly selected optical depth at particle." +". Then, the optical depth is calculated from the beginning of the sphere for particle (ensuring that all potential contributors before and after this location are accounted for), iterating over distance until the answer converges ontaU."," Then, the optical depth is calculated from the beginning of the sphere for particle (ensuring that all potential contributors before and after this location are accounted for), iterating over distance until the answer converges on." +",catter-- AS the optical depth always increases with distance, convergence can be achieved with simple algorithms and relatively litle computation."," As the optical depth always increases with distance, convergence can be achieved with simple algorithms and relatively little computation." + This code uses a recursive bisector algorithm to perform the iteration., This code uses a recursive bisector algorithm to perform the iteration. +" Starting from the path length between the beginning of sphere (k—1) to the end of sphere k, this value is halved recursively until the correct optical depth is obtained (to within some tolerance) or until the path length reaches a minimum value (defined as a fraction of the smallest smoothing length in the simulation)."," Starting from the path length between the beginning of sphere $(k-1)$ to the end of sphere $k$, this value is halved recursively until the correct optical depth is obtained (to within some tolerance) or until the path length reaches a minimum value (defined as a fraction of the smallest smoothing length in the simulation)." +are much more sparsely populated.,are much more sparsely populated. +" We obtained reliable photometry for only 168 aud 692 stars for S2 and $3. respectively,"," We obtained reliable photometry for only 468 and 692 stars for S2 and S3, respectively." + The fal CMDs for the fields ave shown iu Figures 2 and 3.., The final CMDs for the fields are shown in Figures \ref{cmds} and \ref{outer_cmds}. + We measured the star formation rate and metallicity as a function of stellar age using the software package AMIATCTID2002)., We measured the star formation rate and metallicity as a function of stellar age using the software package MATCH. +.. We £ft the observed CMDs @vith magnitude cuts set to limits provided in Table 1)) by populating the stellar evolution models of with a initial mass function (IME) for a erid of asstuned distance and foreground extinction values o allow for systematic differences iu stellar evolution uodels and/or systematic plotometiic crror., We fit the observed CMDs (with magnitude cuts set to limits provided in Table \ref{table}) ) by populating the stellar evolution models of with a initial mass function (IMF) for a grid of assumed distance and foreground extinction values to allow for systematic differences in stellar evolution models and/or systematic photometric errors. + The choices of software and models used for the ANGST xoject are discussed in detail in and stummarizecd i(2009)., The choices of software and models used for the ANGST project are discussed in detail in and summarized in. +. The best fits provide the combination of ages and uctallicities that are contained in the observed field., The best fits provide the combination of ages and metallicities that are contained in the observed field. + We attempted to fit the data with a spread in the model photometry alone the reddeuiug line to account for the effects of differential reddening., We attempted to fit the data with a spread in the model photometry along the reddening line to account for the effects of differential reddening. +" Ποπονα, applying a spread in reddening of A:=0.5 to the models degraded he quality of the CAID fits. showing that differcutial reddening docs not significantly affect our iieasurements in NGC 101."," However, applying a spread in reddening of $A_V=0.5$ to the models degraded the quality of the CMD fits, showing that differential reddening does not significantly affect our measurements in NGC 404." + The data from the deep field were best fit wa sinele foreground reddening y-=0.140.06 aud i5 1840.09 (see Fieure 1)., The data from the deep field were best fit by a single foreground reddening $A_V$ $\pm$ 0.06 and $m-M_0$ $\pm$ 0.09 (see Figure \ref{residuals}) ). + This distance modulus is Afyp=27.consistent with. but larger than. the value measured wo the ANGST suvev2009).," This distance modulus is consistent with, but larger than, the value measured by the ANGST survey." +. The best fit values compensate for auv svsteiuatic differences between the data aud overall nodel isochrones. whereas the survey value i50lated the well-detemmined location of the tip of the red elaut xanch iu order to measure the best distance.," The best fit values compensate for any systematic differences between the data and overall model isochrones, whereas the survey value isolated the well-determined location of the tip of the red giant branch in order to measure the best distance." + Since hese distance and extinction values provided the best overall fit of the models to the data. we performed our fits to the data of every region asstming these values.," Since these distance and extinction values provided the best overall fit of the models to the data, we performed our fits to the data of every region assuming these values." + Our uncertaintics in star formation rate account for changes in the SEIT measured if the assumed value. for i6 distance modulus was £0.15 mag away from the chosen value aud if the extinction value was +0.1 mae away from the chosen value., Our uncertainties in star formation rate account for changes in the SFH measured if the assumed value for the distance modulus was $\pm$ 0.15 mag away from the chosen value and if the extinction value was $\pm$ 0.1 mag away from the chosen value. + We note that in Figure 3 1ο apparent maguitude of the tip of the RGB appears zdnter than iu our more populous CMDs., We note that in Figure \ref{outer_cmds} the apparent magnitude of the tip of the RGB appears fainter than in our more populous CMDs. + Our fits to rese CAIDs (Figure 5)) were not significantly improved w allowing a erecater distance modulus. indicating that jo ΜΗ uunubers of stars iu these fields cause the tip of ιο RGB to be under-populated.," Our fits to these CMDs (Figure \ref{s3_fit}) ) were not significantly improved by allowing a greater distance modulus, indicating that the small numbers of stars in these fields cause the tip of the RGB to be under-populated." +" Ou the other απ, the SEIIs of these fields could be significantly different than 1ο iuner fields."," On the other hand, the SFHs of these fields could be significantly different than the inner fields." + The shallow depth aud low uwmubers of stars du these fields limits our ability to constrain the ec, The shallow depth and low numbers of stars in these fields limits our ability to constrain the age. +", Our fits show only that of the stars are older ian 1.6 Cr.", Our fits show only that of the stars are older than 1.6 Gyr. + Thus. it is possible that most of these stars are onlv a few Gyr old. which could produce a ziuter TRGB.," Thus, it is possible that most of these stars are only a few Gyr old, which could produce a fainter TRGB." + Uufortunately. there is not chough data to constrain whether the cause is undersampling or age.," Unfortunately, there is not enough data to constrain whether the cause is undersampling or age." + The CMD can be fitted equivalently well by either possibility., The CMD can be fitted equivalently well by either possibility. + Systematic errors are determiued bv the MATCII package by comparing the results of SEIIs frou fits to the data with different values for the distance aud foreeround reddening to the feld., Systematic errors are determined by the MATCH package by comparing the results of SFHs from fits to the data with different values for the distance and foreground reddening to the field. + These errors are then added in quadrature to the random errors governed bv our siuupling of the CAID., These errors are then added in quadrature to the random errors governed by our sampling of the CMD. + The random errors are determined by randomly drawing from the observed CMD to produce Tess diagrams that vary due to the Poisson statistics of our photometric sample., The random errors are determined by randomly drawing from the observed CMD to produce Hess diagrams that vary due to the Poisson statistics of our photometric sample. + By producing and fitting 100 of these Monte Carlo CAIDs. we are able to determine he xu of the residuals between SFIs from these fits and those from the fits to the original data.," By producing and fitting 100 of these Monte Carlo CMDs, we are able to determine the rms of the residuals between SFHs from these fits and those from the fits to the original data." +" The conibined le error measurements therefore account for he uncertainties in the distauce to the galaxy. the orcerouud reddening. anv systematic shifts between he model colors aud magnitudes and our measured photometry, as well as the uuuber of stars aud features xeseut in our CMD."," The combined $\sigma$ error measurements therefore account for the uncertainties in the distance to the galaxy, the foreground reddening, any systematic shifts between the model colors and magnitudes and our measured photometry, as well as the number of stars and features present in our CMD." + Our Monte Carlo tests are also used to determine our ine sensitivitvtechnique)., Our Monte Carlo tests are also used to determine our time sensitivity. +. Briefly. we calculate he standard deviation of the 1iaxiumun likelihood value Toni our LOO runs.," Briefly, we calculate the standard deviation of the maximum likelihood value from our 100 runs." + We asstune that anv fit to the data more than one standard deviation away frou the vest fit is unacceptable., We assume that any fit to the data more than one standard deviation away from the best fit is unacceptable. + We then rerun our fits while suppressing star formation iu various time bius., We then rerun our fits while suppressing star formation in various time bins. + If the fit quality does uot change significantly (by more than one standard deviation). we continue to expaud the lenetl of these removed tine bins until the software can no longer find an acceptable fit.," If the fit quality does not change significantly (by more than one standard deviation), we continue to expand the length of these removed time bins until the software can no longer find an acceptable fit." + At this time resolution. we can be coufident that our data provide meaningful constraints ou the SFU.," At this time resolution, we can be confident that our data provide meaningful constraints on the SFH." + The final time bius are all sensitive enough that their removal from the SEIT results in an unacceptable CMD fit., The final time bins are all sensitive enough that their removal from the SFH results in an unacceptable CMD fit. + Photometric depth determines the precision with which we can recover the SEIT of a region., Photometric depth determines the precision with which we can recover the SFH of a region. + The effects of age aud ietallicity are more difficult to distinguish with shallow photometry than with deep photometry., The effects of age and metallicity are more difficult to distinguish with shallow photometry than with deep photometry. + Qur deepest photometry comes from our deep feld aud reaches the red chump iu the least crowded region., Our deepest photometry comes from our deep field and reaches the red clump in the least crowded region. + This photometry therefore provides the most leverage for breaking the degeneracy between the age aud metallicity of the old populations., This photometry therefore provides the most leverage for breaking the degeneracy between the age and metallicity of the old populations. + In coutrast. the data from our 2 shallow fields provide the least of this leverage.," In contrast, the data from our 2 shallow fields provide the least of this leverage." + However. since the stellar populations should be well mixed at ages m1 Cyr. we used the metallicity distribution for the old stars (2 Cr) as determunmed from the fit to our full deep field to limit the range of allowed metallicities at cach age in the fits to the shallower data.," However, since the stellar populations should be well mixed at ages $\gg$ 1 Gyr, we used the metallicity distribution for the old stars $>$ 2 Gyr) as determined from the fit to our full deep field to limit the range of allowed metallicities at each age in the fits to the shallower data." + When the free xuanmeters used to fit the shallower data were limited. we found the resulting age distribution of the ancicut xopulatious of the shallower fields to be cousisteut with hose of the deep data. aud the quality of the fit remained. in the acceptable range (within 1 standard deviation of he value obtained when the full exid of free parameters was allowed).," When the free parameters used to fit the shallower data were limited, we found the resulting age distribution of the ancient populations of the shallower fields to be consistent with those of the deep data, and the quality of the fit remained in the acceptable range (within 1 standard deviation of the value obtained when the full grid of free parameters was allowed)." + In what follows. the full-field SFIIs for he shallower fields are the best fits possible with the restriction that the ancient population (72 (αντ) contain oulv the metallicities at cach age that contributed to the vest fit of the deep full-field data.," In what follows, the full-field SFHs for the shallower fields are the best fits possible with the restriction that the ancient population $>$ 2 Gyr) contain only the metallicities at each age that contributed to the best fit of the deep full-field data." +where pj is the DII mass. M and 22 the mass and radius of the companion star. respectively.,"where $\mbh$ is the BH mass, $M$ and $R$ the mass and radius of the companion star, respectively." + The above equation implies that the stellar radius is roughly. half of its radius. ie.. the orbital periods of the incipient binaries are around 2—4 davs.," The above equation implies that the stellar radius is roughly half of its Roche-lobe radius, i.e., the orbital periods of the incipient binaries are around $2-4$ days." + We have followed the evolution of the binary svstems containing an IMDBILI and a massive donor star for the initial parameters given in last section. using an updated version of the evolution code developed by Egeleton(1971).," We have followed the evolution of the binary systems containing an IMBH and a massive donor star for the initial parameters given in last section, using an updated version of the evolution code developed by \citet{e71}." +. The opacities in (he code are from Rogers& (1992).. and [rom Alexander&Ferguson(1994) [or temperatures below 1055 Ix. For the donor star we assumed a solar chemical composition (.X=0.7. Y=0.28. Z=0.02) and a mixing length parameter a=2.," The opacities in the code are from \citet{ri92}, and from \citet{af94} for temperatures below $10^{3.8}$ K. For the donor star we assumed a solar chemical composition $X=0.7$, $Y=0.28$, $Z=0.02$ ) and a mixing length parameter $\alpha=2$." + To follow the details of mass (ransler process. we included losses of orbital angular momentum due (to mass loss and gravitational wave radiation.," To follow the details of mass transfer process, we included losses of orbital angular momentum due to mass loss and gravitational wave radiation." + We limited ihe mass aceretion rate of the black hole to its Exdington limit rate. and let the excess mass be lost from the svstem will (he specific orbital angular momentum of the black hole.," We limited the mass accretion rate of the black hole to its Eddington limit rate, and let the excess mass be lost from the system with the specific orbital angular momentum of the black hole." + We also assumed that the companion stars are on zero-age main-sequence when they have been captured aud settled in a circular orbit., We also assumed that the companion stars are on zero-age main-sequence when they have been captured and settled in a circular orbit. + This means that the time lorcircular IMDII binary formation is much less than the stellar main-sequence lifetime., This means that the time for IMBH binary formation is much less than the stellar main-sequence lifetime. + This may nol be (rue lor (he companion stus more massive (han e15M.. since the Formation history of IMBIL binaries could be as long as 10* vrs (PortegiesZwartetal.2004).," This may not be true for the companion stars more massive than $\sim 15\,\ms$, since the formation history of IMBH binaries could be as long as $\sim 10^7$ yrs \citep{pz04}." +. So our results for stars of A215AL. should be regarded as the most optimistic cases.," So our results for stars of $M\gsim 15\,\ms$ should be regarded as the most optimistic cases." + Fieurel shows (wo examples of mass (transfer sequences for a binary containing a 1000M. DII with a 5 and 15 M. donor star. respectively [changing the BIL masses (sav. to 100 A.) does not alter the results considerably].," Figure1 shows two examples of mass transfer sequences for a binary containing a $1000\,\ms$ BH with a 5 and 15 $\ms$ donor star, respectively [changing the BH masses (say, to $100\,\ms$ ) does not alter the results considerably]." + In the figure the mass transfer rates have been converted into X-ray. Iuminosities to be compared wilh observations., In the figure the mass transfer rates have been converted into X-ray luminosities to be compared with observations. + The X-ray luminosities were calculated according to the slim disk model by Ohsugaetal.(2002).. in which photon trapping effect. wasincluded!.," The X-ray luminosities were calculated according to the slim disk model by \citet{o02}, in which photon trapping effect was." +. The solid and dashed curves correspond respectively (o stable and unstable mass transfer in the accretion disk. according to the criterion given in Dubusetal.(1999).," The solid and dashed curves correspond respectively to stable and unstable mass transfer in the accretion disk, according to the criterion given in \citet{d99}." +. since the initial binary orbit is (oo wide for the companion star to fill its Roche lobe. ihe mass (ransler through. Roche-lobe overflow begins until the star evolves and expands alter a time labelled below the time-axis in the figure.," Since the initial binary orbit is too wide for the companion star to fill its Roche lobe, the mass transfer through Roche-lobe overflow begins until the star evolves and expands after a time labelled below the time-axis in the figure." + The N-rav. luminosities are generally around LOeres1 |. comparable with those of the most luminous ULXs.," The X-ray luminosities are generally around $10^{40}\,\ergs$ , comparable with those of the most luminous ULXs." + However. the stable," However, the stable" +"In the special case of circular orbits (the majority of short-period exoplanets, for good reason), there are many useful analytic approximations that we can make to simplify the problem.","In the special case of circular orbits (the majority of short-period exoplanets, for good reason), there are many useful analytic approximations that we can make to simplify the problem." +" Furthermore, the simpler circular case offers intuition into the behavior of our model."," Furthermore, the simpler circular case offers intuition into the behavior of our model." +" In the circular limit, Equation 6 can be rewritten as: where €=TradWady is a dimensionless constant quantifying the planet’s energy recirculation efficiency?,, and ®=wat."," In the circular limit, Equation \ref{dimensionless} can be rewritten as: where $\epsilon = \tau_{\rm rad}\omega_{\rm adv}$ is a dimensionless constant quantifying the planet's energy recirculation , and $\Phi = \omega_{\rm adv} t$." + A day in the life of a parcel of gas proceeds as shown in Figure 1.., A day in the life of a parcel of gas proceeds as shown in Figure \ref{heating}. +" Note that we have included the sin’/4@ factor in the y-axis, so that we may plot on the same figure the heating curves for parcels at different latitudes."," Note that we have included the $\sin^{1/4}\theta$ factor in the y-axis, so that we may plot on the same figure the heating curves for parcels at different latitudes." +" The two effects of a high ε are 1) a delay in the time of maximum temperature, and 2) higher night-time temperature."," The two effects of a high $\epsilon$ are 1) a delay in the time of maximum temperature, and 2) higher night-time temperature." +" Although the observed light curve depends on both the radiative and advective timescales, the heating pattern of a parcel of gas depends only on their ratio, ε."," Although the observed light curve depends on both the radiative and advective timescales, the heating pattern of a parcel of gas depends only on their ratio, $\epsilon$ ." +" The night-time temperature islargely independent of latitude, 0, but depends sensitively on ε."," The night-time temperature islargely independent of latitude, $\theta$, but depends sensitively on $\epsilon$." +" The maximum temperature reached by a parcel, on the other hand, depends sensitively on its latitude but only weakly on ε."," The maximum temperature reached by a parcel, on the other hand, depends sensitively on its latitude but only weakly on $\epsilon$." +" Because of the equivalency of latitude and albedo, the the dashed lines in Figure 1 can be thought of as the heating curves for equatorial parcels of gas, but with A=30%:: albedo has a more important impact on the day-side heating pattern than on the night-side cooling."," Because of the equivalency of latitude and albedo, the the dashed lines in Figure \ref{heating} can be thought of as the heating curves for equatorial parcels of gas, but with $A \approx 30$: albedo has a more important impact on the day-side heating pattern than on the night-side cooling." +" Finally, the delay between a parcel passing through the sub-stellar longitude and reaching its maximum temperature, ®max, depends more sensitively on e than does the maximum temperature reached, Tinax-"," Finally, the delay between a parcel passing through the sub-stellar longitude and reaching its maximum temperature, $\Phi_{\rm max}$ , depends more sensitively on $\epsilon$ than does the maximum temperature reached, $\tilde{T}_{\rm max}$." +" In the €>oo limit, T'sin!/=(1/z)!/4, as one would expect from Equation 6.."," In the $\epsilon \to \infty$ limit, $\tilde{T} \sin^{1/4}\theta = (1/\pi)^{1/4}$, as one would expect from Equation \ref{dimensionless}." + The diurnal heating patterns shown in Figure 1 are similar to those measured at the surface of Earth., The diurnal heating patterns shown in Figure \ref{heating} are similar to those measured at the surface of Earth. +" In both cases parcels of gas move in and out of the sunlight: on Earth this motion is entirely due to the planet's rotation (wind velocities are small compared to rotational velocity), while on a gaseous planet this motion is due to a combination of rotation and zonal winds."," In both cases parcels of gas move in and out of the sunlight: on Earth this motion is entirely due to the planet's rotation (wind velocities are small compared to rotational velocity), while on a gaseous planet this motion is due to a combination of rotation and zonal winds." +" Indeed, our model may also be relevant to a rocky planet with a thin atmosphere and rapid rotation, provided that the rotational period is shorter than the lateral heat conduction timescale."," Indeed, our model may also be relevant to a rocky planet with a thin atmosphere and rapid rotation, provided that the rotational period is shorter than the lateral heat conduction timescale." +" For a planet on a circular orbit, we can use the fact that the temperature extrema for a particle of gas occur when it reaches its equilibrium temperature."," For a planet on a circular orbit, we can use the fact that the temperature extrema for a particle of gas occur when it reaches its equilibrium temperature." +" The temperature extrema are therefore related to their location on the planet by: and where $,;, and $44, are the angles between the sub-stellar meridian and temperature minimum and maximum, respectively."," The temperature extrema are therefore related to their location on the planet by: and where $\Phi_{\rm min}$ and $\Phi_{\rm max}$ are the angles between the sub-stellar meridian and temperature minimum and maximum, respectively." +" Since Tii, is typically much less than unity, ®min&—7/2 in most situations (see Figure 2)), while Ti is close to unity so small differences in this maximum temperature correspond to significant changes in the phase offset of the maximum, as shown in Figure 3.."," Since $\tilde{T}_{\rm min}$ is typically much less than unity, $\Phi_{\rm min}\approx -\pi/2$ in most situations (see Figure \ref{phi_min}) ), while $\tilde{T}_{\rm max}$ is close to unity so small differences in this maximum temperature correspond to significant changes in the phase offset of the maximum, as shown in Figure \ref{phi_max}." +" Note that the the diurnal heating pattern has a longitudinal asymmetry: parcels of gas are heated faster than they cool, so parcels East of the hot-spot tend to be warmer than those West of the hot-spot."," Note that the the diurnal heating pattern has a longitudinal asymmetry: parcels of gas are heated faster than they cool, so parcels East of the hot-spot tend to be warmer than those West of the hot-spot." +" This asymmetry manifests itself in the disc-integrated thermal phase curve of the planet: the offset in the peak of the lightcurve tends to be larger than ,,4..", This asymmetry manifests itself in the disc-integrated thermal phase curve of the planet: the offset in the peak of the lightcurve tends to be larger than $\Phi_{\rm max}$. +" In the Appendix we develop analytic approximations in thecircular regime for Tax, Tausk and Taawn maximum temperature reachedby a parcel, its temperature(the at the dusk terminator, and at the dawn terminator)."," In the Appendix we develop analytic approximations in thecircular regime for $T_{\rm max}$, $T_{\rm dusk}$ and $T_{\rm dawn}$ (the maximum temperature reachedby a parcel, its temperature at the dusk terminator, and at the dawn terminator)." + Those analytic approximations are, Those analytic approximations are +keV by a [actor of 1 since 1995 or by the difficulty in carrying out backgrouud subtraction [or the syectva stemming [rom the large (—1'.5) point spread [uuction.,keV by a factor of $\sim$ 4 since 1995 or by the difficulty in carrying out background subtraction for the spectra stemming from the large $\sim$ $'$ .5) point spread function. + Indeed. the fit to the spectra suggests the presence of a harder componeut that was not statistically significant.," Indeed, the fit to the spectra suggests the presence of a harder component that was not statistically significant." + We believe a [actor of L is tc0 large to be ascribed to difficulties with background subtraction., We believe a factor of 4 is too large to be ascribed to difficulties with background subtraction. + We tlie explored a variety of models., We then explored a variety of models. + We do not include a long discussion of those moclels tliat Failed. but iustead focus ou the more successful oues.," We do not include a long discussion of those models that failed, but instead focus on the more successful ones." + Most of the moclels failed by inissiug fIux 1[un the 0.8-1.0 keV band. a regiou kuown to contain the potential for considerable liue emission.," Most of the models failed by missing flux in the 0.8-1.0 keV band, a region known to contain the potential for considerable line emission." +" Table includes"" a .listing of+ the models ranked by increasing. y-/v.Jg", Table \ref{specfit} includes a listing of the models ranked by increasing ${\chi}^2/{\nu}$. +" The ""dual brems”E aud *bretms+imulti- models yield. adequate fits but leave systematic residuals.", The `dual brems' and `brems+multi-gauss' models yield adequate fits but leave systematic residuals. +" The uou-equilibrium iouizatic[un uodel (in ""xspec' lingo. 1vel: Borkowski.Lyerly.&Revuolds2001 and. references therein). the jxlane-parallel shock model (*pshock’: Borkowski.Lyerly.&Revuolds 2001)) as well as other shock nodels also. provided adequate fits. jit didiH not achieveH the lowest 4> values."," The non-equilibrium ionization model (in `xspec' lingo, `nei'; \citealt{Bork01} and references therein), the plane-parallel shock model (`pshock'; \citealt{Bork01}) ) as well as other shock models also provided adequate fits, but did not achieve the lowest ${\chi}^2$ values." + The iouizationH equililium collisional plasma moclel (equilib) yielded a very poor fit., The ionization equilibrium collisional plasma model (`equilib') yielded a very poor fit. + The single component power aw. bremsstrahluug. aud Ravinoud-Siith iuodels were included for direct comparison with the ustorical resuts from ROSATaud (e.g.. 599. Petreetal.199 [)).," The single component power law, bremsstrahlung, and Raymond-Smith models were included for direct comparison with the historical results from and (e.g., S99, \citealt{Petre94}) )." + The best-it 1nocel was an absorbed. two-temperature. optically thin thermal plasma imocel (he variable Mekal model ‘vinelxV in xspec lingo that uses the line caleulatious of Mewe.Cirouenschild. (1985)... Mewe.Lemeu.&vaudeuOord (1986).. and Ixaastra(1992). plus the Fe L enhancements of Liedahl.Osterheld.&Golds," The best-fit model was an absorbed, two-temperature, optically thin thermal plasma model (the variable Mekal model `vmekal' in xspec lingo that uses the line calculations of \cite{Mewe1}, \cite{Mewe2}, and \cite{Kaastra92} plus the Fe L enhancements of \cite{Lied95}) )." +tein (1995))). Figure 2 shows the fitted spectrum., Figure \ref{fig-dvmek} shows the fitted spectrum. + Thebest-[it temperatures are 0.ius and ULLο keV; and are shown as the upper set of contour plots in Figure 3.) (the lower set of contours in each figure will be discussed shortly)., The best-fit temperatures are $^{+0.04}_{-0.05}$ and $^{+0.44}_{-0.42}$ keV and are shown as the set of contour plots in Figure \ref{cont_dvmek} (the lower set of contours in each figure will be discussed shortly). + The fluxes are isted⋅ in⋅ Table i2. aud generally [all. in⋅ the range of⋅ −⋅↽x10 13 erys 1 Do.cin the 0.5-2 keV band aud —3-1x10.13| erg |1 em7 in the 2-10 keV band with the low ΠΠους COLESpounding to the absorbed flux aud the high to the unabsorbed., The model-derived fluxes are listed in Table \ref{fluxval} and generally fall in the range of $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$ in the 0.5-2 keV band and $\sim$ $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$ in the 2-10 keV band with the low numbers corresponding to the absorbed flux and the high to the unabsorbed. +" These fluxes correspoud to a 0.5-2 keV luminosiy of S7.5-1LL« 109 ere Land a 2-10 keV luminosity of —6-7.5x 10 erg 1 The best-fit. column. —2.3x aqu107! »? and shown in. FigureEN .)3.. lies. about a [actor. ofaos 8-10 above the measured column in: the direction: of ""NTNGC1 pepe1313. ~3.7* —-o440910°"" 27 1905).."," These fluxes correspond to a 0.5-2 keV luminosity of $\sim$ $\times$ $^{38}$ erg $^{-1}$ and a 2-10 keV luminosity of $\sim$ $\times$ $^{38}$ erg $^{-1}$ The best-fit column, $\sim$ $\times$ $^{21}$ $^{-2}$ and shown in Figure \ref{cont_dvmek}, lies about a factor of 8–10 above the measured column in the direction of NGC 1313, $\sim$ $\times$ $^{20}$ $^{-2}$ \citep{SFD98}." +" However. it does correspoud to within with the Ejy value of 0.31 measured [rom optical spectra (Ryderοἱal.1993). and using the Ny-Ep,y conversion of (1995): Ny 95.3x107* Epv."," However, it does correspond to within with the $_{\rm B-V}$ value of 0.31 measured from optical spectra \citep{Ryder93} and using the $_{\rm +H}$ $_{\rm B-V}$ conversion of \cite{PS95}: $_{\rm H}$ $\sim$ $\times$ $^{21}$ $_{\rm B-V}$." + The vinekal model periMts varving the abundauces of astroplivsically-iportant elemeuts., The vmekal model permits varying the abundances of astrophysically-important elements. + We varlec the abundauces of eac‘h element iu turn but forced the correspouding abundances of the soft and hard components to va‘y slinultaneously but iudepeudently., We varied the abundances of each element in turn but forced the corresponding abundances of the soft and hard components to vary simultaneously but independently. + This approach eusured the most robus cletection of specific liue features as well as ciffereuces between the soft aud bard coupouents., This approach ensured the most robust detection of specific line features as well as differences between the soft and hard components. + The only abundauce incousintent with solar is that of Si for the soft component., The only abundance inconsistent with solar is that of Si for the soft component. + Figure 1. slows the ucertainty contours. [ο “the abundance of Si., Figure \ref{cont_si} shows the uncertainty contours for the abundance of Si. + The soft component abundauce is 3.20 which Is slg€»ülicantly different [rou solar at the confidence level., The soft component abundance is 3.20 which is significantly different from solar at the confidence level. + The Si abundance for the hard component is consistent wit1 solar., The Si abundance for the hard component is consistent with solar. +The fluxes foreach component are listed separately tu Table 2..,The fluxes foreach component are listed separately in Table \ref{fluxval}. . + Civen the time-scales associated with stellar formation (~10 vvr for low-mass stars). very voung clusters are expected to contain a population of PAIS stars (c.g. Bonatto&Biea2010b.. and references therein).," Given the time-scales associated with stellar formation $\sim10^7$ yr for low-mass stars), very young clusters are expected to contain a population of PMS stars (e.g. \citealt{vdB92}, and references therein)." + Thus. he assumption that the red and. faint stars belong to the PNIS is consistent with the ~5 MMyr of age of the ECS in the complex (Sect. 5)).," Thus, the assumption that the red and faint stars belong to the PMS is consistent with the $\sim5$ Myr of age of the ECs in the complex (Sect. \ref{N2175}) )." + Internal. cillerential reddening is implied. by the colour distribution at faint. magnitudes (J2 14). which is wider than the spread. predicted. purely o» PALS models.," Internal differential reddening is implied by the colour distribution at faint magnitudes $\jj\ga14$ ), which is wider than the spread predicted purely by PMS models." + A comparison with the reddening vector (lor Ay=0to 10) shows cdillerent. degrees of cillerential reddening. being lower for NGC22175s ancl 1136. and uigher for the remaining cases.," A comparison with the reddening vector (for $\aV=0~{\rm to}~10$ ) shows different degrees of differential reddening, being lower for 2175s and 136, and higher for the remaining cases." + I£ most of the colour spread is due to non-uniform reddening - and not to systematic differences in the stellar content - the upper limitto the cilferential reddening would be Xy.=6 mimae., If most of the colour spread is due to non-uniform reddening - and not to systematic differences in the stellar content - the upper limitto the differential reddening would be $\Delta\aV\la6$ mag. + As discussed, As discussed +Collisionless shocks iu space aud other astroplivsical environments are efficient accelerators of energetic chareed-particles.,Collisionless shocks in space and other astrophysical environments are efficient accelerators of energetic charged-particles. + Diffusive shock acceleration (hereinafterDSA:Isrvinsky1977:Axfordctal.1977:Bell1978:Blauctford&Ostriker LOTS).. is the uost popular theory for chareed-particle acceleration.," Diffusive shock acceleration \citep[hereinafter +DSA;][]{Krymsky1977,Axford1977,Bell1978a,Blandford1978}, is the most popular theory for charged-particle acceleration." + It naturally predicts a universal power-law distribution αρ with 5~LO for stroug shocks. where f is the phase-space> distribution function. close to what observed oe1 cosnic ravs in many cifferent regions of space.," It naturally predicts a universal power-law distribution $f \varpropto p^{-\gamma}$ with $\gamma \sim 4.0$ for strong shocks, where $f$ is the phase-space distribution function, close to what observed in cosmic rays in many different regions of space." + The asic conclusions of DSA can be drawn from the Parker ransport equation (Parker1965) bv consideriug the shock to be a compressive discontinuity iu au infinite one-dimensional aud time steady svstem., The basic conclusions of DSA can be drawn from the Parker transport equation \citep{Parker1965} by considering the shock to be a compressive discontinuity in an infinite one-dimensional and time steady system. + DSA is thought o be the mechanisin that accelerates anomalous Cosmic ravs (ACRs) in the IHeliospherie termination shock aud also ealactic cosmic raves (GCRs) with energy up to at east LOY eV in supernova blast waves., DSA is thought to be the mechanism that accelerates anomalous cosmic rays (ACRs) in the Heliospheric termination shock and also galactic cosmic rays (GCRs) with energy up to at least $10^{15}$ eV in supernova blast waves. + However. recent observations iu the termination shock aud the Ucliosheath by 1 (Stonectal.2005). found he intensity of ACRs is not peaked at the termination shock and the cuerey spectrum is still unfolding after entering the ILleliosheath. which stronely imdicates the simple planar shock ποσο] is inadequate to interpret the acceleration of AC'Rs.," However, recent observations in the termination shock and the Heliosheath by $1$ \citep{Stone2005} found the intensity of ACRs is not peaked at the termination shock and the energy spectrum is still unfolding after entering the Heliosheath, which strongly indicates the simple planar shock model is inadequate to interpret the acceleration of ACRs." + Nuuerical and analytical studies sugeest the possible solution cau be made by considers the temporary and/or spatial variation (Floriuski&2008:Kota&JokipiSchwadronetal. 2008)..," Numerical and analytical studies suggest the possible solution can be made by considering the temporary and/or spatial variation \citep{Florinski2006GeoRL,McComas2006,Jokipii2008AIP,Kota2008AIP,Schwadron2008ApJ}." + Iu xurtieular. MeConmas&Sceliiwadrou(2006). discussed the imuportauce of the magnetic ecometiy of à bluut shock onu particle acceleration.," In particular, \citet{McComas2006} discussed the importance of the magnetic geometry of a blunt shock on particle acceleration." + They argued that the missing ACRs at the nose of the IIeliospherie termination shock is due to particle enereization occuring prinuiuilv back along the flauks of the shock where magnetic feld lues have had a longer comnection tine aud higher injection effüciency., They argued that the missing ACRs at the nose of the Heliospheric termination shock is due to particle energization occuring primarily back along the flanks of the shock where magnetic field lines have had a longer connection time and higher injection efficiency. + Ἱνόία&Jokrpi(2008) presenteda inore sophisticated simulation which gives results stuular to that described by MeCoimas&Sclavadrou (2006)., \citet{Kota2008AIP} presenteda more sophisticated simulation which gives results similar to that described by \citet{McComas2006}. +. Sclavadronetal.(2008). also developed a 3-D analytic model for particle acceleration iu a blunt shock. including perpendicular diffusion aud drift motion due to large-scale shock structure.," \citet{Schwadron2008ApJ} also developed a 3-D analytic model for particle acceleration in a blunt shock, including perpendicular diffusion and drift motion due to large-scale shock structure." + Large-sceale dgmnagnetie field) line mneandering is ubiquitous in the heliosphere aud other astrophlivsical euvironnients (Jokipiü1966:Jokipü&Parker1969:Parker 1979).," Large-scale magnetic field line meandering is ubiquitous in the heliosphere and other astrophysical environments \citep{Jokipii1966,Jokipii1969,Parker1979}." + The acceleration of charged-particles in colliiouless shocks has been shown to be stronely affected by inagnetic-field. turbulence at different scales (άσσος2005a.b:Caacalone&Neugebauer2008:Guo&Caacalone 2010).," The acceleration of charged-particles in collisionless shocks has been shown to be strongly affected by magnetic-field turbulence at different scales \citep{Giacalone2005a,Giacalone2005b,Giacalone2008,Guo2010}." +.. The large-scale magnetic field variation will have iuportaut effects ou the shock acceleration since the trausport of charged particles is different in the direction parallel aud. perpendicular to the iuagnetic field. as shown in carly work (Jokipii1982. 1987)..," The large-scale magnetic field variation will have important effects on the shock acceleration since the transport of charged particles is different in the direction parallel and perpendicular to the magnetic field, as shown in early work \citep{Jokipii1982ApJ,Jokipii1987ApJ}. ." + The bluut shocks aud shocks with fluctuating frout (Li&Zank2006) which have the similar, The blunt shocks and shocks with fluctuating front \citep{Li2006AIP} which have the similar +and E-scaling is irrelevant (and where even a hefty error in a more relevant and uncertain parameter — distance — does not change matters significantly).,"and ${\dot +E}^{1/2}$ -scaling is irrelevant (and where even a hefty error in a more relevant and uncertain parameter — distance — does not change matters significantly)." + In all these discarded cases. in addition. the efficiencies required would be ηὃν10004. making the potential associations utterly unphysical.," In all these discarded cases, in addition, the efficiencies required would be $\eta \gg 1000\%$, making the potential associations utterly unphysical." + Finally. in evaluating possible associations. we compare the photon indices of known pulsars (Table 1) with those of the EGRET sources (see. e.g.. Merck et al.," Finally, in evaluating possible associations, we compare the photon indices of known pulsars (Table 1) with those of the EGRET sources (see, e.g., Merck et al." + 1996; Zhang Cheng 1998: Cheng Zhang 1998)., 1996; Zhang Cheng 1998; Cheng Zhang 1998). + We have also quantified the chance probability for obtaining these associations. adapting the numerical code described by Romero et al. (," We have also quantified the chance probability for obtaining these associations, adapting the numerical code described by Romero et al. (" +19993. b): there is a probability of having 8 chance coincidences between different unidentified 3EG sources and Parkes pulsars. as in Table Camilo et al. (,"1999a, b): there is a probability of having 8 chance coincidences between different unidentified 3EG sources and Parkes pulsars, as in Table Camilo et al. (" +2001) proposed the possible physical association #11. with required efficiency of (Table 2).,"2001) proposed the possible physical association 1, with required efficiency of (Table 2)." + This pulsar appears to be located just outside the SNR G284.3-1.8. which itself is interacting with an adjacent— molecular cloud (Ruiz May 1986).," This pulsar appears to be located just outside the SNR $-$ 1.8, which itself is interacting with an adjacent molecular cloud (Ruiz May 1986)." +" Another Parkes pulsar. PSR J1013—5934 (#22 in Table 2). is coineident with 3EG 1013-5915. but it is an old pulsar (7=12 MMyr) with low £22.5«IO"" eeresss! and cannot be a significant 7-ray contributor."," Another Parkes pulsar, PSR $-$ 5934 2 in Table 2), is coincident with 3EG $-$ 5915, but it is an old pulsar $\tau=12$ Myr) with low $\dot E = 2.5\times +10^{32}$ $^{-1}$ and cannot be a significant $\gamma$ -ray contributor." + D'Amico et al. (, D'Amico et al. ( +2001) have studied cases #66 and 14 (efficiencies: jj=2% and7%.. respectively).,"2001) have studied cases 6 and 14 (efficiencies: $\eta = 2$ and, respectively)." + Both are plausible candidates to generate the respective EGRET source fluxes., Both are plausible candidates to generate the respective EGRET source fluxes. + PSR 11837-0559. is also coincident with 3EG J1837-0606 (113). but its E/d is 80 times smaller than for PSR 71837-00604. and it cannot contribute significantly to the 7-ray source.," PSR $-$ 0559, is also coincident with 3EG $-$ 0606 13), but its $\dot E/d^2$ is 80 times smaller than for PSR $-$ 0604, and it cannot contribute significantly to the $\gamma$ -ray source." + The pulsars in pairs #88 and 9 have far too low a spin-down luminosity at too large a distance (Table 2) to explain their coincident 7-ray sources., The pulsars in pairs 8 and 9 have far too low a spin-down luminosity at too large a distance (Table 2) to explain their coincident $\gamma$ -ray sources. + They are also both old. with 7~ 4MMvyr.," They are also both old, with $\tau \sim 4$ Myr." + Cases #110 and ΕΙ are discussed elsewhere in connection with a proposal for a SNR shock origin of the bulk of the z-rays resulting from 3EG J1714—3857 (Butt et al., Cases 10 and 11 are discussed elsewhere in connection with a proposal for a SNR shock origin of the bulk of the $\gamma$ -rays resulting from 3EG $-$ 3857 (Butt et al. + 2001): neither of these pulsars is energetic enough to contribute significant amounts of high-energy flux., 2001); neither of these pulsars is energetic enough to contribute significant amounts of high-energy flux. + We now discuss the remaining four EGRET sources positionally superposed with five newly discovered pulsars., We now discuss the remaining four EGRET sources positionally superposed with five newly discovered pulsars. + We provide observational data on the apparent associations in Tables 3 and 4., We provide observational data on the apparent associations in Tables 3 and 4. + Cases #33-5. 7 and 12 all contain Vela-like pulsars. with relatively short periods. low characteristic ages. and high spin-down luminosities (E>10° ss! ).," Cases 3–5, 7 and 12 all contain Vela-like pulsars, with relatively short periods, low characteristic ages, and high spin-down luminosities $(\dot E \ga 10^{35}$ $^{-1}$ )." + The pulsar in case #33 would require an efficiency #=5% at its nominal distance to explain the luminosity of the corresponding 3EG source. which has photon index 2.23 (see Table 4).," The pulsar in case 3 would require an efficiency $\eta = 5\%$ at its nominal distance to explain the luminosity of the corresponding 3EG source, which has photon index 2.23 (see Table 4)." + This spectrum is softer than that of the Crab. although it is consistent with it within the uncertainties.," This spectrum is softer than that of the Crab, although it is consistent with it within the uncertainties." + It is also consistent with the index of 3EG 2227+6122. for which PSR J2229+6114 has been proposed as the likely source (Halpern et al.," It is also consistent with the index of 3EG 2227+6122, for which PSR J2229+6114 has been proposed as the likely source (Halpern et al." + 2001)., 2001). + The 5-ray source in case #33 is not variable (Tompkins 1999; Torres et al., The $\gamma$ -ray source in case 3 is not variable (Tompkins 1999; Torres et al. +" 20019). as expected from direct pulsar or pulsar wind nebula/SNR shock emission,"," 2001c), as expected from direct pulsar or pulsar wind nebula/SNR shock emission." + PSR J10135-3719 has 7=39 kkyr and E28.2«I0? ss! (Table 3).," PSR $-$ 5719 has $\tau=39$ kyr and $\dot E = 8.2\times +10^{35}$ $^{-1}$ (Table 3)." + While no cataloged SNR is superposed with the 3EG source (Torres et al., While no cataloged SNR is superposed with the 3EG source (Torres et al. + 2001b). this absence does not mean that one does not exist. and further sensitive searches may prove fruitful.," 2001b), this absence does not mean that one does not exist, and further sensitive searches may prove fruitful." + Thus the connection between 3EG J1014—5705 and PSR J1015—5719 appears plausible and is worth additional study., Thus the connection between 3EG $-$ 5705 and PSR $-$ 5719 appears plausible and is worth additional study. + The pulsars in pairs #44 and 5 require unreasonably high efficiencies at their nominal distances to explain the 7-ray flux from the corresponding EGRET source ()=100%.. Table 4).," The pulsars in pairs 4 and 5 require unreasonably high efficiencies at their nominal distances to explain the $\gamma$ -ray flux from the corresponding EGRET source $\eta \ga +100$, Table 4)." + However. both pulsars are located in the direction of the Centaurus arm. and it is known that in such directions the electron density/distance model of Taylor Cordes (1993) can be unreliable. sometimes overestimating the distances by factors of up to ~4 (see discussion in Camilo et al.," However, both pulsars are located in the direction of the Centaurus arm, and it is known that in such directions the electron density/distance model of Taylor Cordes (1993) can be unreliable, sometimes overestimating the distances by factors of up to $\sim 4$ (see discussion in Camilo et al." + 2001)., 2001). + Both pulsars are located (at least in projection) well within the boundaries of the incomplete shell SNR G312.4—0.4 (Caswell Barnes 1985). to which Yadigaroglu Romani (1997) estimate a X—D distance of 1.9kkpe.," Both pulsars are located (at least in projection) well within the boundaries of the incomplete shell SNR $-$ 0.4 (Caswell Barnes 1985), to which Yadigaroglu Romani (1997) estimate a $\Sigma-D$ distance of kpc." + At this distance the required efficiencies for the pulsars in cases #44 and 5 would be and3%.. respectively. which would make them considerably more plausible sources of the observed high energy emission.," At this distance the required efficiencies for the pulsars in cases 4 and 5 would be and, respectively, which would make them considerably more plausible sources of the observed high energy emission." + Furthermore. 3EG J1410—6147 has a photon index comparable to that of the Crab. and is not variable (Tables 1. 2 and 4).," Furthermore, 3EG $-$ 6147 has a photon index comparable to that of the Crab, and is not variable (Tables 1, 2 and 4)." + Pairs #44 and 5 therefore appear intriguing., Pairs 4 and 5 therefore appear intriguing. + However it should be noted that X—D distances are notoriously unreliable (e.g.. for this very SNR. Caswell Barnes 1985 and Case Bhattacharya 1999 infer values in substantial disagreement both with each other and with that determined by Yadigaroglu Romani 1997).," However it should be noted that $\Sigma-D$ distances are notoriously unreliable (e.g., for this very SNR, Caswell Barnes 1985 and Case Bhattacharya 1999 infer values in substantial disagreement both with each other and with that determined by Yadigaroglu Romani 1997)." + Ideally. further observations of SNR G312.4-0.4 may indicate whether it shows signs of interaction with PSRs J1412-6145 or JI413-6141. and possibly constrain their distances.," Ideally, further observations of SNR $-$ 0.4 may indicate whether it shows signs of interaction with PSRs $-$ 6145 or $-$ 6141, and possibly constrain their distances." + Depending on the actual distances. the >-ray emission from 3EG JI410-6147 may conceivably arise from à combination of PSRs J1412—6145. J1413-6141. and/or SNR G312.4—0.4.," Depending on the actual distances, the $\gamma$ -ray emission from 3EG $-$ 6147 may conceivably arise from a combination of PSRs $-$ 6145, $-$ 6141, and/or SNR $-$ 0.4." + The efficiency required to explain the EGRET flux in case #77 is 4)=12%. which seems possible.," The efficiency required to explain the EGRET flux in case 7 is $\eta = 12\%$, which seems possible." + However. the spectral index of 2.50 is larger than those of known +-ray pulsars.," However, the spectral index of 2.50 is larger than those of known $\gamma$ -ray pulsars." + One of the SNRs coincident with the EGRET source. G337.8-0.1. harbors a maser (Koralesky et al.," One of the SNRs coincident with the EGRET source, $-$ 0.1, harbors a maser (Koralesky et al." + 1998). which is indicative of interaction between the SNR shock and the ambient medium.," 1998), which is indicative of interaction between the SNR shock and the ambient medium." + Thus. were a sufficiently massive molecular cloud located nearby. it could help produce the high energy radiation as a result of hadronie interaction (Aharonian. Drury. ΝΟΚ 1994: Aharonian Atoyan 1996).," Thus, were a sufficiently massive molecular cloud located nearby, it could help produce the high energy radiation as a result of hadronic interaction (Aharonian, Drury, Völlk 1994; Aharonian Atoyan 1996)." + Part of the EGRET flux could plausibly come from PSR J1637—4642 and part from pion ~-decay via SNR G337.8—0.1’s interaction with the putative cloud., Part of the EGRET flux could plausibly come from PSR $-$ 4642 and part from pion $\gamma$ -decay via SNR $-$ 0.1's interaction with the putative cloud. + Inthis case. the photon index would reflect a weighted average value.," Inthis case, the photon index would reflect a weighted average value." + Both possible mechanisms for the high energy emission would produce a non-variable source. as is the case for 3EG J1639—4702.," Both possible mechanisms for the high energy emission would produce a non-variable source, as is the case for 3EG $-$ 4702." + Lastly we consider case £112. for which the required efficiency 1s high at the nominal pulsar distance and upper limit flux value. ;j=55%.," Lastly we consider case 12, for which the required efficiency is high at the nominal pulsar distance and upper limit flux value, $\eta = 55$." +. The pulsar is located. in projection. Just outside the plerionic SNR G27.8+0.6. for which the distance is ~ 2kkpe (Reich et al.," The pulsar is located, in projection, just outside the plerionic SNR G27.8+0.6, for which the distance is $\sim +2$ kpc (Reich et al." + 1984)., 1984). + Although the estimated ages are comparable (7=52 kkyr for the pulsar and 45 kkyr for the SNR). it seems unlikely that both objects are physically associated. given the offset between the centrally peaked SNR component and the pulsar (see Reich et al.," Although the estimated ages are comparable $\tau = 52$ kyr for the pulsar and $\sim 45$ kyr for the SNR), it seems unlikely that both objects are physically associated, given the offset between the centrally peaked SNR component and the pulsar (see Reich et al." + 1984)., 1984). + Whatever the possible relation between pulsar and SNR. the 3EG source in case #112 is variable (Table 2). arguing against a pulsar origin.," Whatever the possible relation between pulsar and SNR, the 3EG source in case 12 is variable (Table 2), arguing against a pulsar origin." + Examination of X-ray archives via HEASARC has revealed no compelling counterpart sources to any of the pulsars in Table 3. (, Examination of X-ray archives via HEASARC has revealed no compelling counterpart sources to any of the pulsars in Table 3. ( +A possible X-ray source at the edge of an,A possible X-ray source at the edge of an +The aim of the present paper is to investigate the potential cosmological signatures of a very general dark enerev component. which is characterize by an equation of state. sound. speed and. anisotropic stress.,"The aim of the present paper is to investigate the potential cosmological signatures of a very general dark energy component, which is characterize by an equation of state, sound speed and anisotropic stress." + In section 2. we review the parameterization of a &eneralized: cosmologica fluid and comment its relation to some recent studies of anisotropies dark energy., In section \ref{para} we review the parameterization of a generalized cosmological fluid and comment its relation to some recent studies of anisotropies dark energy. + The parameerization will then be subjected to the most detailed and most extensive scrutiny this far., The parameterization will then be subjected to the most detailed and most extensive scrutiny this far. + Ehe data ancl method utilized for this are describe in section 3.., The data and method utilized for this are described in section \ref{data}. + In the section d. we use the most recen cosmological data to constrain the properties of dark energy., In the section \ref{cons1} we use the most recent cosmological data to constrain the properties of dark energy. + Section 5. is devoted to investigate how much the future data could be able to improve the constraints., Section \ref{cons2} is devoted to investigate how much the future data could be able to improve the constraints. + We conclude by stating the fundamental uncertainty in the properties of dark energy but also mention some cases where a positive detection could be established., We conclude by stating the fundamental uncertainty in the properties of dark energy but also mention some cases where a positive detection could be established. +" Consider a general [uid with the energy momentum tensor |pn, | where sy is the four-velocity of the uid. and the projection tensor Pj, is delined as Pye—gueμμ."," Consider a general fluid with the energy momentum tensor }= + + where $u_\mu$ is the four-velocity of the fluid, and the projection tensor $h_{\mu\nu}$ is defined as $h_{\mu\nu} \equiv g_{\mu\nu} + u_\mu u_\nu$." +" llere YX,, can include only spatial inhomogeneity.", Here $\Sigma_{\mu\nu}$ can include only spatial inhomogeneity. + At the background level. the evolution of the Iuid is determined by the continuity equation.," At the background level, the evolution of the fluid is determined by the continuity equation, + = 0." + The effects. to the overall expansion are. therefore determined. by the equation of state i alone., The effects to the overall expansion are therefore determined by the equation of state $w$ alone. +" We define aperfect UWuied by the condition My,=0.", We define a fluid by the condition $\Sigma_{\mu\nu}=0$. + The condition for theadiabalicili of a Iuid is p=p(p). which implies that the evolution of the sound speed is determined by the equation olstate alone.," The condition for the of a fluid is $p=p(\rho)$, which implies that the evolution of the sound speed is determined by the equation of state alone." + Generally. however. the sound speed is defined as the ratio of pressure and. density. perturbations in the frame comoving with the dark energy ιά (7?)..pp," Generally, however, the sound speed is defined as the ratio of pressure and density perturbations in the frame comoving with the dark energy fluid \citep{Weller:2003hw},." + In the adiabatic situation one has €2anαρdpPolonuSHiL[i . but in general the sound. speed is an independent:p variable.," In the adiabatic situation one has $\clam = d p/d\rho = \frac{\dot{p}}{\dot{\rho}} = w - \frac{\dot{w}}{3H(1+w)}$ , but in general the sound speed is an independent variable." + In. the following we will consider a constant. equation of state for simplicity., In the following we will consider a constant equation of state for simplicity. + ‘Taking these considerations into account. the evolution equations for the dark energy.density. perturbation ὁ and velocity. potential @ in the synchronous gauge (7).. can be written as c= | .”..- Fa... where Ph ijs the trace of the synchronous metric perturbation.," Taking these considerations into account, the evolution equations for the dark energydensity perturbation $\delta$ and velocity potential $\theta$ in the synchronous gauge \citep{Ma:1995ey}, can be written as = + - , = , where $h$ is the trace of the synchronous metric perturbation." + Llere e is the anisotropic stress of dark energy. related to notation. of IEq.(1)) by (p1ple=(il20;JN.," Here $\sigma$ is the anisotropic stress of dark energy, related to notation of \ref{fluid}) ) by $(\rho + p)\sigma \equiv +-(\hat{k}_i\hat{k}_j-\frac{1}{3}\delta_{ij})\Sigma^{ij}$ ." +" From the above equations it is then clear that. while w and ¢7,,, determine respectively the background ancl perturbative pressure of the Duid that is rotationally invariant. c quantifies how much the pressure of the Iuid varies with clirection."," From the above equations it is then clear that, while $w$ and $\clam$ determine respectively the background and perturbative pressure of the fluid that is rotationally invariant, $\sigma$ quantifies how much the pressure of the fluid varies with direction." + To close the system of equations. we describe the evolution of the anisotropic stress with an equation adopted from Iu (?).. Bi).," To close the system of equations, we describe the evolution of the anisotropic stress with an equation adopted from Hu \citep{Hu:1998kj}, = )." + This parameterization leads to reasonable results arn approximates the evolution of any Πα present in the standard: cosmological mocdel. in. particular neutrinos anc photons which have a non-zero anisotropic stress (?)..," This parameterization leads to reasonable results and approximates the evolution of any fluid present in the standard cosmological model, in particular neutrinos and photons which have a non-zero anisotropic stress \citep{Hu:1998tj}. ." + More specifically. for those relativistic components. the correc choice Lor the viscous paramicter 1s c7vis=1/3.," More specifically, for those relativistic components, the correct choice for the viscous parameter is $\cvis=1/3$ ." + X perfec ια (vanishing shear viscosity) should have ο=0., A perfect fluid (vanishing shear viscosity) should have $\cvis=0$. + Εναοί]. one can describe the physical properties of =o by introducing5 the rescaled Iparameter oí;=οτεLs{1|ee).," Equivalently, one can describe the physical properties of $\sigma$ by introducing the rescaled parameter $\avis = \cvis/(1+w)$." +" While ον, is somehow physically analogous to sound spec squared. the aes. is the quantity directly. multiplying the source term of the stress (see. RIS of eq. (9)))."," While $\cvis$ is somehow physically analogous to sound speed squared, the $\avis$ is the quantity directly multiplying the source term of the stress (see RHS of eq. \ref{sigmaevol}) ))." + In. this study we will use both the e7;;vis and ays. parameterizations., In this study we will use both the $\cvis$ and $\avis$ parameterizations. + Since tw is constrained near w=1. where the relation between these parameters is divergent. using one or the other might. lead to different results ancl interpretations.," Since $w$ is constrained near $w=-1$, where the relation between these parameters is divergent, using one or the other might lead to different results and interpretations." + The statistical details also depend on which parameter one assumes a uniform distribution. and it is useful to test how robust ones conclusions are to such assumptions.," The statistical details also depend on which parameter one assumes a uniform distribution, and it is useful to test how robust ones conclusions are to such assumptions." + Usually. a dark energy Εις with nonzero γι generates shear stress which tends to smoothen its. distribution.," Usually, a dark energy fluid with nonzero $\avis$ generates shear stress which tends to smoothen its distribution." + ]lowever. the consequences to phantom: dark energy are qualitatively different and for such a fDuid. with a,,: a low value amp—5 and ahigh value 7,,5—μωροΕν for the thick and thin lines. respectively."," Here we used two extreme values of $\gamma_m$: a low value $\gamma_{m, l} = \gamma$ and a high value $\gamma_{m, +h} = 1 + \mu_e m_p (\gamma - 1) / m_e$ for the thick and thin lines, respectively." + The former corresponds to a case that the electron minimum energy simply reflects the velocity of the shock. while the latter to a case that the kinetic energy of tons ts efficiently transfered to electrons.," The former corresponds to a case that the electron minimum energy simply reflects the velocity of the shock, while the latter to a case that the kinetic energy of ions is efficiently transfered to electrons." + We also used three values of p=2.2.2.5. and 2.8.," We also used three values of $p = 2.2, 2.5$ and 2.8." +" The characteristic synchrotron frequency (7) corresponding to 7,4. the SSA frequeney (4,4). and the FPA frequency (7455) at the day 7 in these results are given in Fig. 6.."," The characteristic synchrotron frequency $\nu_m$ ) corresponding to $\gamma_m$, the SSA frequency $\nu_{\rm ssa}$ ), and the FFA frequency $\nu_{\rm ffa}$ ) at the day 7 in these results are given in Fig. \ref{fig:nu}," + but only for the p22.2 case.," but only for the $p = +2.2$ case." + The 4 degree of freedom Is fy=24—321. and the minimum reduced X=ο is less than the unity. i.e.. an acceptable fit.," The $\chi^2$ degree of freedom is $n_{\rm dof} = 24 - 3 = 21$, and the minimum reduced $\tilde{\chi}^2 \equiv \chi^2/n_{\rm dof} $ is less than the unity, i.e., an acceptable fit." + The confidence limit projected on the parameter 5 can be estimated by à region where AA. i.e.. difference of 47 from the minimum. is smaller than a certain value; AV7«0.19 and 0.32 for 95.4 and C.L.. respectively. assuming a pure Gaussian statistics (e.g.. Press et al.," The confidence limit projected on the parameter $b$ can be estimated by a region where $\Delta \chi^2$, i.e., difference of $\chi^2$ from the minimum, is smaller than a certain value; $\Delta \tilde{\chi}^2 < 0.19$ and 0.32 for 95.4 and C.L., respectively, assuming a pure Gaussian statistics (e.g., Press et al." + 1992)., 1992). + Therefore. we conclude that a mild beaming b—0.1 1s marginally allowed and stronger beaming is excluded for the possibility (1).," Therefore, we conclude that a mild beaming $b \sim 0.1$ is marginally allowed and stronger beaming is excluded for the possibility (i)." + The flux evolution and comparison with observed data are shown in Fig. 7..," The flux evolution and comparison with observed data are shown in Fig. \ref{fig:flux_early}," + for the best-fit models with 620.1 and 1., for the best-fit models with $b = 0.1$ and 1. + The result in the isotropic case (5= 1) is similar to that of BKCO2. as it should be.," The result in the isotropic case $b = 1$ ) is similar to that of BKC02, as it should be." + A general trend seen in Fig., A general trend seen in Fig. + 2 can be understood as follows., \ref{fig:eps_B_Mwind} can be understood as follows. + When jet is more strongly collimated. the amount of CSM swept-up by the jet becomes smaller. and hence higher mass loss rate is required to compensate this.," When jet is more strongly collimated, the amount of CSM swept-up by the jet becomes smaller, and hence higher mass loss rate is required to compensate this." + However. the observed spectral feature is mostly explained by SSA. and hence magnetic field must become smaller to keep SSA frequency at the observed value.," However, the observed spectral feature is mostly explained by SSA, and hence magnetic field must become smaller to keep SSA frequency at the observed value." + This explains behaviors 5= 0.1-1., This explains behaviors between $b = $ 0.1--1. + However. FFA becomes significant when M. betweenbecomes very large at 5< 0.1.," However, FFA becomes significant when $\dot{M}_w$ becomes very large at $b \lesssim +0.1$ ." + The observed data are not fitted well only by spectral break by FFA. because the early rise of radio flux due to decreasing optical depth is more rapid than SSA (see Weiler et al.," The observed data are not fitted well only by spectral break by FFA, because the early rise of radio flux due to decreasing optical depth is more rapid than SSA (see Weiler et al." + 1986 for radio supernovae showing this feature). and it does not fit the observed slow rise of radio flux at 1.43GHz.," 1986 for radio supernovae showing this feature), and it does not fit the observed slow rise of radio flux at 1.43GHz." +" As a result. M,. cannot increase significantly with decreasing b at b= 0.1.and SSA frequency is always higher than FFA for the best fit models(see Fig. 6))."," As a result, $\dot{M}_w$ cannot increase significantly with decreasing $b$ at $b \lesssim 0.1$ ,and SSA frequency is always higher than FFA for the best fit models(see Fig. \ref{fig:nu}) )." + Because of this constraint.," Because of this constraint," +"At tree level. there are two cliagrais: oue is re. from the sinele-W,, contribution: aud the other is the two-W,, term with fi»=0 for the secoud term of (611)). At one-loop level. five diagrams are nonzero.","At tree level, there are two diagrams: one is $\Gamma^{(2)}_{\delta}$, from the $\psid$ contribution; and the other is the $\psid$ term with $t_{12}=0$ for the second term of \ref{eqn:G2_n_detail}) ), At one-loop level, five diagrams are nonzero." +" where Tu ((15)). Ay and A. are two-W,, contributious from the first and second terms of ((10)) respectively. Ky and AC) are contributions. aud ACs is the four-W,, contribution."," where In \ref{eqn:G2_1loop_ker}) ), $\mK_1$ and $\mK_2$ are $\psid$ contributions from the first and second terms of \ref{eqn:G2_n}) ) respectively, $\mK_3$ and $\mK_4$ are $\psid$ contributions, and $\mK_5$ is the $\psid$ contribution." +" At last. the thice-W,,nou-linear power spectra of the log-transformed field 6, can be expressed as m his section. we slow our nuuerical results."," At last, the non-linear power spectrum of the log-transformed field $\phid$ can be expressed as In this section, we show our numerical results." + To siniplifv t1ο calculation. we adop the approximation ((26)). which has been shown to be accurate enough in Bernardeaneta].(2008).," To simplify the calculation, we adopt the approximation \ref{eqn:gammpsi_apprx}) ), which has been shown to be accurate enough in \cite{BCS08}." +. For the trec-kvel propagator. we only include the feistest-erowing mode. Le. the sandard perturbation kernel FY.," For the tree-level propagator, we only include the fastest-growing mode, i.e. the standard perturbation kernel $F^{(n)}$." + Since the non-incarη quantity: D;Und. is involved throiehout our formulac. all the calculation 1s done miuerically," Since the non-linear quantity $\Gamma^{(n)}_{\delta}$ is involved throughout our formulae, all the calculation is done numerically." +" All results asstme the fiducial concordance ACDM cosmologv of simulation 0 of the Covote Univorse suite (Heituiumetal.2010.2009:Lawrence2010).. with (0,772. Ql? Lig. Ut Os. hi) = (0.1296. 0.0 221.0.97 2-1. 0.8. 0.72)."," All results assume the fiducial concordance $\Lambda$ CDM cosmology of simulation 0 of the Coyote Universe suite \citep{cu1,cu2,cu3}, with $\Omega_m h^2$, $\Omega_b h^2$, $n_s$, $w$, $\sigma_8$, $h$ ) = (0.1296, 0.0224, 0.97, -1, 0.8, 0.72)." + We use these parameters becase we conpare our perturbative md sto dmeasurements frou thi SS]uula1011., We use these parameters because we compare our perturbative results to measurements from this simulation. + The linear power spectruni is calculated with the public Doltzuiuum code (Lewisctal.2000).. and tl10 nnnier‘ical inteeration is poronued with the multi-dineusional iutegratiou -—10.," The linear power spectrum is calculated with the public Boltzmann code \citep{camb}, and the numerical integration is performed with the multi-dimensional integration routine." + Iu Fie.(7)). we show the two-polunt prooeator P(1){On) up to two-loop order.," In \ref{fig:gamma_phi}) ), we show the two-point propagator $\Gamma^{(1)}_A(k)$ up to two-loop order." + As expected from the analysis of SPT. the propagator of the A field apxoachles a coustaut aless than one at large scales.," As expected from the analysis of SPT, the propagator of the $A$ field approaches a constant less than one at large scales." +" The value of this large-scale bias, which also encodes the statistical information o the density fluctuation (Eq.22 )). strongly depends ou the smoothing process adopted before the transformlon."," The value of this large-scale bias, which also encodes the statistical information of the density fluctuation \ref{eqn:SPT_bias}) ), strongly depends on the smoothing process adopted before the transformation." +" For he ziioothiung radius R>x. effectively uo loop integration contributes to D,[1th). therefore] the bias. approaches to 1 from the tree-level result. (38))."," For the smoothing radius $R \to \infty$, effectively no loop integration contributes to $\Gamma_A^{(1)}(k)$, therefore the bias approaches to $1$ from the tree-level result, \ref{eqn:GA1_tree}) )." + When the sincothing radius goes malle since. Cee} that appears in the loop iutegration also decays at large fk. the effect of the smoothing becomes less and less iaportautD) until fie bias freezes at some value. where higher-loop coutributious are significant.," When the smoothing radius goes smaller, since $\Gamma_{\delta}^{(n)}(k)$ that appears in the loop integration also decays at large $k$, the effect of the smoothing becomes less and less important until the bias freezes at some value, where higher-loop contributions are significant." + Inthis sense. the presence of DU) heps to regulate the convergence of the perturbative series.," Inthis sense, the presence of $\Gamma_{\delta}^{(n)}(k)$ helps to regulate the convergence of the perturbative series." + At small scales. ri(k) is daupened both by nonlinearities anc by smoothiug. while TC) has no additional sinoothliue imposed.," At small scales, $\Gamma_A^{(1)}(k)$ is dampened both by nonlinearities and by smoothing, while $\Gamma_{\delta}^{(1)}(k)$ has no additional smoothing imposed." + This is why Dk) decay sat larger scales than D;(1)(k) for large smoothing scales., This is why $\Gamma_A^{(1)}(k)$ decays at larger scales than $\Gamma_{\delta}^{(1)}(k)$ for large smoothing scales. + The top solid line shows rU) with a smooting scale R=20hMpec.. which reduces to 0.5 around &~0.17," The top solid line shows $\Gamma^{(1)}_A(k)$ with a smoothing scale $R=20$, which reduces to 0.5 around $k\sim 0.1$." + As the 31u000fing radius becomes sialler. the curve approaches I;(1)(k) at buge &.," As the smoothing radius becomes smaller, the curve approaches $\Gamma_{\delta}^{(1)}(k)$ at large $k$." + For 25h. (the bottoni solid lino). the dauipiug of boostingrith) is. similar. to that of. (1)," For $R=5$ (the bottom solid line), the damping of $\Gamma_A^{(1)}(k)$ is similar to that of $\Gamma_\delta^{(1)}(k)$." + Tf the large-scale bias is divide out. he A propagators to line up Dd).for siidll &. the A propagator may slightly exceed the 6 propagator on smal scales. if the ssinootlingscale is suticicutly small.," If the large-scale bias is divided out, boosting the $A$ propagators to line up for small $k$, the $A$ propagator may slightly exceed the $\delta$ propagator on small scales, if the smoothingscale is sufficiently small." + We have found this to be the case in preliminary siniulation nieastrvelncuts., We have found this to be the case in preliminary simulation measurements. + Disappointingly. this nuplies that the logarithmic transform bv itself docs uot help appreciably to recoustinct mnode-by-uxkde initial phases aud amplitudes.," Disappointingly, this implies that the logarithmic transform by itself does not help appreciably to reconstruct mode-by-mode initial phases and amplitudes." + But the similarity in damping is not surprising. eiven that blilk displacements roni the initial conditions affect both fields.," But the similarity in damping is not surprising, given that bulk displacements from the initial conditions affect both fields." + Iu SJ). we illustrate the non-linear power spectra of both P4(k) and ο) at à=0.7 aud a=1.," In \ref{fig:pk_1}) ), we illustrate the non-linear power spectra of both $P_A(k)$ and $P_{\delta}(k)$ at $a=0.7$ and $a=1$." + The squares and triangles are the 0 and A power spectra measured from Covote Universe simulation 0. which µας I particles iu a cubic 1300 Mpc (~Lh Cipe3) box.," The squares and triangles are the $\delta$ and $A$ power spectra measured from Coyote Universe simulation 0, which has $^3$ particles in a cubic 1300 Mpc $\sim1$ ) box." + Its resoluion is high enough that the power spectrum is accurate to sub-percenut level down to ., Its resolution is high enough that the power spectrum is accurate to sub-percent level down to . + We imeasure both power spectra ou 1287 -cell exids. using nearest-erid-poiut (NCP) deusity assigninent.," We measure both power spectra on $128^3$ -cell grids, using nearest-grid-point (NGP) density assignment." + Even for the.1 field. the shot noise is neelieilde at this cell size (Nevrincketal. 2011)..," Even for the $A$ field, the shot noise is negligible at this cell size \citep{NSS11}. ." + We do not correct, We do not correct +shows that the influence of the composition is not too high because increasing 10 times the numerical densitv only generates a multiplication of 0.3 of the magnetic field.,shows that the influence of the composition is not too high because increasing 10 times the numerical density only generates a multiplication of 0.3 of the magnetic field. + Even though the composition of the nuclei of the several planets could be very different. its numerical densities couldn't variate enough to change the order of magnitude of the generated fields.," Even though the composition of the nuclei of the several planets could be very different, its numerical densities couldn't variate enough to change the order of magnitude of the generated fields." + The model could be generalized to other objects in the Universe like (he main sequence stars and the neutron stars. objects where the gravitational effects are higher than in the planets.," The model could be generalized to other objects in the Universe like the main sequence stars and the neutron stars, objects where the gravitational effects are higher than in the planets." + Even though these objects are surely not metallic in its core. chareecl particles could be [ound like electrons that could. behave like the electrons in the model.," Even though these objects are surely not metallic in its core, charged particles could be found like electrons that could behave like the electrons in the model." + In objects like neulron stars. geocdvnamo is surely less probable due to the ultra hieh densitv of the entire object.," In objects like neutron stars, geodynamo is surely less probable due to the ultra high density of the entire object." + In conclusion. the theory achieves wilh a thermodynamic model a scaling law that agrees with the values of the Solar Svstem magnetic fields.," In conclusion, the theory achieves with a thermodynamic model a scaling law that agrees with the values of the Solar System magnetic fields." + Even though the accepted theory Lor the generation of the magnetic fields is the geodvnamo. this thermodynamic model could be used to explain the order of magnitude ancl the scaling of the actual fields. Fact that couldn't be explained with the current theory.," Even though the accepted theory for the generation of the magnetic fields is the geodynamo, this thermodynamic model could be used to explain the order of magnitude and the scaling of the actual fields, fact that couldn't be explained with the current theory." +acceessed with the Hanle effect.,essed with the Hanle effect. +Requiring that jb satisly jb<1 allows constraints to be placed on &. ancl (his indicates whieh models can account for the characteristics of these svstems.,"Requiring that $jb$ satisfy $jb \leq 1$ allows constraints to be placed on $\kappa$, and this indicates which models can account for the characteristics of these systems." + The method is applied to the samples of 19 very powerful ΕΠΗ radio galaxies (relerred to as ERIIb sources) and 29 central dominant galaxies (CDGs) studied by Daly (2009)., The method is applied to the samples of 19 very powerful FRII radio galaxies (referred to as FRIIb sources) and 29 central dominant galaxies (CDGs) studied by Daly (2009). + The FRIIb sources have radio powers at least a factor of ten above the classical FRI/FRIL transition (Fanarolf Riley 1974)., The FRIIb sources have radio powers at least a factor of ten above the classical FRI/FRII transition (Fanaroff Riley 1974). + Black hole masses aud beam powers are available for all of these sources: the masses are listed in Tables 1 and 2 of Daly (2009)., Black hole masses and beam powers are available for all of these sources; the masses are listed in Tables 1 and 2 of Daly (2009). + Deam powers for the powerful classical double radio galaxies are obtained from Guerra et al. (, Beam powers for the powerful classical double radio galaxies are obtained from Guerra et al. ( +2000). Wan. Daly. Guerra (2000). and O'Dea οἱ al. (,"2000), Wan, Daly, Guerra (2000), and O'Dea et al. (" +2009): note that these beam powers are independent of olfsets of the extended radio source [rom minimum energy conditions (ODea οἱ al.,2009); note that these beam powers are independent of offsets of the extended radio source from minimum energy conditions (O'Dea et al. + 2009)., 2009). + Deam powers for the CDGs are obtained from Rallerty et al. (, Beam powers for the CDGs are obtained from Rafferty et al. ( +2006). and also are independent of offsets from mininuun energy conditions.,"2006), and also are independent of offsets from minimum energy conditions." + Almost all of the radio sources associated with CDGs have FRI radio source structure or amorphous radio structure. wilh a few exceptions such as Cvgnus A (Dirzan et al.," Almost all of the radio sources associated with CDGs have FRI radio source structure or amorphous radio structure, with a few exceptions such as Cygnus A (Birzan et al." + 2008)., 2008). + The name. redshift. total beam power. black hole mass. and Eddington magnetic field strength are listed [or each source in Tables 1 and 2 for the ΕΤΤΗ and CDG sources. respectively.," The name, redshift, total beam power, black hole mass, and Eddington magnetic field strength are listed for each source in Tables 1 and 2 for the FRIIb and CDG sources, respectively." + The beam powers and black hole masses were combined to solve for joey using equation (2) and are listed in Tables 1 and 2., The beam powers and black hole masses were combined to solve for $jb_{BZ}$ using equation (2) and are listed in Tables 1 and 2. + Values of jba; were obtained explicitly for the ERIIb sources using &(M)25 so jba;7[δομήv/(5). and are included in Table 1.," Values of $jb_{M}$ were obtained explicitly for the FRIIb sources using $\kappa(M) \approx 5$ so $jb_M \approx jb_{BZ}/\sqrt(5)$, and are included in Table 1." + The value of VIELTTN is listed in the final column of Tables 1 and 2. and is discussed below.," The value of $\sqrt(jb_{BZ})$ is listed in the final column of Tables 1 and 2, and is discussed below." + For simplicity. (he average values of asvinmnetric error bars was used.," For simplicity, the average values of asymmetric error bars was used." + The parameter jbj5z is shown as a function of black hole mass in Figure 1., The parameter $jb_{BZ}$ is shown as a function of black hole mass in Figure 1. + Analyzing the (wo samples separately. there is no indication of a dependence of jopy on black hole niass (see Figure 1).," Analyzing the two samples separately, there is no indication of a dependence of $jb_{BZ}$ on black hole mass (see Figure 1)." + Since jhyy. and δ��. ave proportional to /L;/Ly (see eq.," Since $jb_{BZ}$, and $jb_{M}$, are proportional to $\sqrt{L_j/L_{E}}$ (see eq." + 2). this is equivalent to finding no dependence of L;/Lj; on black hole mass.," 2), this is equivalent to finding no dependence of $L_j/L_E$ on black hole mass." +" The parameter joy, is shown as a function of redshilt in Figure 2.", The parameter $jb_{BZ}$ is shown as a function of redshift in Figure 2. + Each sample clearly exhibits a dependence of jo on redshilt (see Figure 2)., Each sample clearly exhibits a dependence of $jb$ on redshift (see Figure 2). + The sample of 19 powerlul ERIIb sources has the dependence Log(jbsz)=(0.9220.24)Log(l+2)—(0.324250.06).," The sample of 19 powerful FRIIb sources has the dependence $Log(jb_{BZ}) = +(0.92 \pm 0.24)~Log(1+z)~-(0.34 \pm 0.06)$." + Given that these are the most powerful radio sources al each redshift and that they are drawn from a complete sample of sources. (his represents the envelope of the distribution of jb values as a function of redshift.," Given that these are the most powerful radio sources at each redshift and that they are drawn from a complete sample of sources, this represents the envelope of the distribution of $jb$ values as a function of redshift." +" Thus. (his redshift dependence can be interpreted as (he evolution of (he maximum value of jb as a function of redshift. ancl is obtained in the context of the BZ moclel,"," Thus, this redshift dependence can be interpreted as the evolution of the maximum value of $jb$ as a function of redshift, and is obtained in the context of the BZ model." + The normalization of jb decreases by a factor of about 1/v/(5) if the Meier model is, The normalization of $jb$ decreases by a factor of about $1/\sqrt(5)$ if the Meier model is +for any trends and/or transition in properties from cluster-like to field-like environments.,for any trends and/or transition in properties from cluster-like to field-like environments. + For each of the luminosity bins we compute a composite galaxy LE. following the method described by Colless(1989).," For each of the luminosity bins we compute a composite galaxy LF, following the method described by \cite{colless89}." +. In. addition to the LEs derived for the entire sample we also creale LFs for red. (quiescent) and blue (stu-Iorming) galaxies separately. adopting a color of b;—rp=1.07 at which to divide the two samples (Coleetal.2005).," In addition to the LFs derived for the entire sample we also create LFs for red (quiescent) and blue (star-forming) galaxies separately, adopting a color of $b_j-r_F=1.07$ at which to divide the two samples \citep{cole05}." +. Table I shows the derived values of (he LF parameters. together with marginal lo errors.," Table 1 shows the derived values of the LF parameters, together with marginal $\sigma$ errors." + Most of the ehanges in M and a appear to occur in (he six lowest luminosity bins. which we will focus on in our discussion.," Most of the changes in $M^*$ and $\alpha$ appear to occur in the six lowest luminosity bins, which we will focus on in our discussion." + We plot the LFs for these six bins (lor all. blue ancl red sanmiples) in Figures | (all). 2 (blue galaxies) and 3 (red galaxies) aud the related error ellipses in Figure 4.," We plot the LFs for these six bins (for all, blue and red samples) in Figures 1 (all), 2 (blue galaxies) and 3 (red galaxies) and the related error ellipses in Figure 4." + Fieure 5 summarizes (he variation in LF parameters with group Iuminosity for each of {he samples we consider., Figure 5 summarizes the variation in LF parameters with group luminosity for each of the samples we consider. + As in Ekeetal.(20046) we find two noticeable trends in the data as a whole. viz.," As in \cite{eke04b} we find two noticeable trends in the data as a whole, viz." + thal A brightens and a steepens wilh increasing group mass., that $M^*$ brightens and $\alpha$ steepens with increasing group mass. + With the finer resolution we adopt. we are able to see that. in fact. the LF parameter values appear to reach approximately constant levels. comparable to those seen in rich clusters 2003).. for groups brighter than Mjc—22.5.," With the finer resolution we adopt, we are able to see that, in fact, the LF parameter values appear to reach approximately constant levels, comparable to those seen in rich clusters \citep{depropris03}, for groups brighter than $M^G_{b_J} +\simeq -22.5$." +" This is similar to the behaviour reported bv Domínguezοἱal.(2002) ancl Martinezetal.(2002) from their analvsis of groups in the 2dEGIS LOOW galaxy release (wilh a different grouping algoritim) ancl is presumably related to the observation that galaxy. properties appear to change at some ""threshold. density in ihe neighborhood of clusters (xoclamaetal.2001:Lewis2002:Tanaka2005)."," This is similar to the behaviour reported by \cite{dominguez02} and \cite{martinez02} from their analysis of groups in the 2dFGRS 100K galaxy release (with a different grouping algorithm) and is presumably related to the observation that galaxy properties appear to change at some `threshold' density in the neighborhood of clusters \citep{kodama01,lewis02,tanaka05}." +. Ol course. once we reach (hese asymptotic values. (he group Iumninosity. which we use as a diseriminator will directly mirror the richness of the group.," Of course, once we reach these asymptotic values, the group luminosity which we use as a discriminator will directly mirror the richness of the group." + Consider each of these trends in turn., Consider each of these trends in turn. + As noted above. the characteristic magnitude A/* levels off (or may even go fainter again) for groups with magnitudes brighter (han A~—22 (~10h.2L. ).," As noted above, the characteristic magnitude $M^*$ levels off (or may even go fainter again) for groups with magnitudes brighter than $M^G_{b_J} \simeq -22$ $\simeq 10^{11} h^{-2} L_{\odot}$ )." +" The value seen for these more luminous groups is similar to that seen in rich clusters. even though thev start from only moderate mass eroups: assuming =0.7 and a corresponding average universal M/L ratio of 300 in solar units (e.g. Dahcalletal. 2000). thev have group (halo) masses M,~6xLOM to 3x101144..."," The value seen for these more luminous groups is similar to that seen in rich clusters, even though they start from only moderate mass groups; assuming $h=0.7$ and a corresponding average universal ${\cal M}/L$ ratio of 300 in solar units (e.g. \citealt{bahcall00}) ), they have group (halo) masses ${\cal M}_h \simeq 6 \times 10^{13}$ to $3 \times 10^{14} +{\cal M}_{\odot}$." +" We obtain a similar value [or the mass at the ""turnover! point. M,~LOM. if we use Eke et al."," We obtain a similar value for the mass at the `turnover' point, ${\cal M}_h \simeq 10^{13.6}$, if we use Eke et al." +'s (2004b) luminosity dependent mass-to-light ratios.,'s (2004b) luminosity dependent mass-to-light ratios. + Amonge the less luminous exgroups. there is a clear fainteninge of A/* as one egoes from intermediate to low Lhuninositv.," Among the less luminous groups, there is a clear faintening of $M^*$ as one goes from intermediate to low luminosity." + The dinuming is seen in each left hand. panel of Figure 3.," The dimming is seen in each left hand panel of Figure 3," +to calculate the contribution of each cell of the AMI erie to either the emission or absorption in a given data cube pixel.,to calculate the contribution of each cell of the AMR grid to either the emission or absorption in a given data cube pixel. + Εις feature is used to decompose spectral features into separate enission and absorption Components. as part oL our investigation of LLESAX in spiral arms.," This feature is used to decompose spectral features into separate emission and absorption components, as part of our investigation of HISA in spiral arms." + These cillerences are critical when we extend the creation of single spectra to making Cully three-dimensional catacubes of simulated.LEE emission., These differences are critical when we extend the creation of single spectra to making fully three-dimensional datacubes of simulated emission. + The cubes are discussed in the next section., The cubes are discussed in the next section. +" Figure 1. shows an spectrum. measured. from a position within the SPILL galaxy. corresponding roughly to the Earth's position in our Galaxy. toward a. direction corresponding to Galactic longitude £z135.5"" and Iatitude bzo(037."," Figure \ref{figsp1} shows an spectrum measured from a position within the SPH galaxy, corresponding roughly to the Earth's position in our Galaxy, toward a direction corresponding to Galactic longitude $\ell \approx 135.5^\circ$ and latitude $b \approx -0.3^\circ$." +" We see ""local spiral arm gas in a radialvelocity rango 20«re,«UO kms and an outer arm bevond . loc ∣⇁∣≈⇀∫≻↖∖↓∡⊔↓⊳∖⊳∐↕⋖⋅⋯∐∢⋅"," We see “local"" spiral arm gas in a radialvelocity range $-20 < v_r < 0$ km $^{-1}$, and an outer arm beyond $v_r \approx -38$ km $^{-1}$." +↓⋅⋜⊔⋅⊔↓⊳∖↓↕∪∖∖⋎⊳∖⊳∖∪⊔↓⋖⋅⋖⋅∖⇁⊔⇂∢⋅⊔≼∼⋖⋅∪⇂↓↓ . ⋜↧∣⋡≱∖∪↓⋅↓≻↥⊲↓∪⊔⊳∖∖⋰↓↿↓↕⋜↧↓↥⋜↧↓⋅↓⋅∢≱∖∖⋎∠⇂↕↓≻↕↓↕⊻⊽∕↾⋜↧↓≻↓≻∢⊾⋜⊔⋰↓⊔⋏∙≟⊔⋖⋅∥↓⋅∣⇁∣∶⋉↓ kms L©.," The outer arm shows some evidence of absorption, witha narrow dip in $T_b$ appearing near $v_r = -41$ km $^{-1}$." + ο.Phis LIISA1 signature. is+ common in+ svnthetic+ spectra all across our region of interest., This HISA signature is common in synthetic spectra all across our region of interest. + Since LUISA is a main focus of our investigation into molecular cloud formation. the code was modified so that in addition to total brightness temperature cubes. we create separate clatacubes where only positive or negative intensity contributions (d) for a given erid cell are mapped.," Since HISA is a main focus of our investigation into molecular cloud formation, the code was modified so that in addition to total brightness temperature cubes, we create separate datacubes where only positive or negative intensity contributions $dI$ ) for a given grid cell are mapped." + For this paper. the simulated galaxy has reached. a time of 250 Myr.," For this paper, the simulated galaxy has reached a time of 250 Myr." + At this age the distribution of gas in different phases. and the fraction of molecular gas. have reached a roughly steady state.," At this age the distribution of gas in different phases, and the fraction of molecular gas, have reached a roughly steady state." + While tracing the evolution of specific ISM. structures using many timesteps from an SPILL simulation is the subject of. future investigations. the present work concentrates on deriving properties from a single epoch. as is the case with most Calactic radio observations.," While tracing the evolution of specific ISM structures using many timesteps from an SPH simulation is the subject of future investigations, the present work concentrates on deriving properties from a single epoch, as is the case with most Galactic radio observations." + As mentioned previously. the models are restricted to Galactocentric radii of 5 to LO κρο," As mentioned previously, the models are restricted to Galactocentric radii of 5 to 10 kpc." + For this reason it is reasonable to aimi to reproduce observations of the Outer Galaxy. toward its Anticenter (6= 180°).," For this reason it is reasonable to aim to reproduce observations of the Outer Galaxy, toward its Anticenter $\ell = 180^\circ$ )." + In this paper. we survey the entire. second. quadrant of our SPL ealaxy. covering longitudes between (=90° and ἐξ1807.," In this paper, we survey the entire second quadrant of our SPH galaxy, covering longitudes between $\ell = 90^\circ$ and $\ell = 180^\circ$." +" For the Galactic point of view. we construct 7,(f.b.ον) cubes with angular coordinates corresponding το 7CGalactic"" coordinates[rom the position of the observer."," For the Galactic point of view, we construct $T_b(\ell,b,v_r)$ cubes with angular coordinates corresponding to “Galactic"" coordinatesfrom the position of the observer." + This position is chosen to be in the midplane. 2.21077 em (7.13 kpe) from the galaxv's center. as illustrated in figure 2..," This position is chosen to be in the midplane, $2.2 \times 10^{22}$ cm (7.13 kpc) from the galaxy's center, as illustrated in figure \ref{figobs}." + This choice corresponds to a position in an interarm: “spur” ofLLL. similar to the Orion Spur of our Milkv Way.," This choice corresponds to a position in an interarm “spur"" of, similar to the Orion Spur of our Milky Way." + A total of fifteen cubes of angular dimension 6.087« are produced to cover the entire Second Quadrant. with a small amount of overlap between adjacent fields for. mosaicking purposes.," A total of fifteen cubes of angular dimension $6.08^\circ \times 6.08^\circ$ are produced to cover the entire Second Quadrant, with a small amount of overlap between adjacent fields for mosaicking purposes." +" With an image scale of 0.5"" per pixel. cach channel map produced by measures 7327. pixels."," With an image scale of $0.5'$ per pixel, each channel map produced by measures $732^2$ pixels." + Our spectral range covers racial velocities fron: |30 km στο 120 km + sampled at 0.5 km resulting in 300 channels for each cube produced byronus.," Our spectral range covers radial velocities from $+30$ km $^{-1}$ to $-120$ km $^{-1}$ sampled at $0.5$ km $^{-1}$ , resulting in 300 channels for each cube produced by." + For ease of visualisation. the fifteen cubes are combined into five mosaics. summarised in table 1..," For ease of visualisation, the fifteen cubes are combined into five mosaics, summarised in table \ref{tblreg}." + Each mosaic region therefore covers just over LS” of Galactic longitude. centered on the value o£ (oem given in the table.," Each mosaic region therefore covers just over $18^\circ$ of Galactic longitude, centered on the value of $\ell_{central}$ given in the table." + For illustrative purposes we show a channel map from the central mosaic. region GALL. in Figure 3...," For illustrative purposes we show a channel map from the central mosaic, region GHI, in Figure \ref{figgalxy}. ." +" Phis channel mapshows gas near,= 45kms +. as our aim is to study LILSA produced in spiral arm gas with radial velocities correspondingto"," This channel mapshows gas near $v_r = -45$ km $^{-1}$ , as our aim is to study HISA produced in spiral arm gas with radial velocities correspondingto" +A powerful tool to investigate how stellar mass is accreted onto EPCs from their formation until now. is to resolve the spatial clistributions of their stellar populations and observe how they changed with time.,"A powerful tool to investigate how stellar mass is accreted onto ETGs from their formation until now, is to resolve the spatial distributions of their stellar populations and observe how they changed with time." + Indeed. colour gradients are the most direct. measure that can provide us with information on the stellar cistribution within a galaxy. but until ncy instrumental limits have restricted their study only to the local and. intermediate: Universe.," Indeed, colour gradients are the most direct measure that can provide us with information on the stellar distribution within a galaxy, but until now, instrumental limits have restricted their study only to the local and intermediate Universe." + In the last) vears. the advent of the LIST ancl its capability into resolve distant galaxies are opening new possibilities into estimating colour eracicnts even for high-z galaxies.," In the last years, the advent of the HST and its capability into resolve distant galaxies are opening new possibilities into estimating colour gradients even for $z$ galaxies." + Actually. the lack of multiband imaging has preventec an cllective analysis of colour gradients of high-z {ς 1) ERGs in all but. two Cases.," Actually, the lack of multiband imaging has prevented an effective analysis of colour gradients of $z$ $z>1$ ) ETGs in all but two cases." + ? derived the colour-maps for 2 ΓΣ at 1.5 in the PSI4AW-FIGOW LIST. bands. finding Hat graclients out to 2Ry.," \citet{mcgrath08} derived the colour-maps for 2 ETGs at $z\sim$ 1.5 in the F814W-F160W HST bands, finding flat gradients out to $_e$." + Some vears before. 2? stucliecl the rest-frame UV218-U300 colour gradient for two samples of 33 ealaxies ad 0.5«z «1.2 and 50 galaxies at 2.0z «3.5 in the Hubble Deep Field. North.," Some years before, \citet{moth02} studied the rest-frame UV218-U300 colour gradient for two samples of 33 galaxies at $ 1$, and to answer the first question we will show that there is a largest possible $x=x_{max}$ allowed by the QI's if we assume zero energy density outside of the negative pulse, as illustrated in Figure \ref{fig_flux1}: Using \ref{y_def}) ) we can rewrite the inequality as This clearly shows that if we have some negative energy $y \neq 0$ ) then there is an upper bound on $x$, for, recalling that $g(t)$ is positive with a single peak at $t=0$ so that $g(0) \ge g(t/x) \ge g(t)$ , one can see that the ratio of the two integrals in \ref{x_max_ie}) ) is $\le 1$ (but is at least as large as $ \frac{\int_{-t_0/2}^{t_0/2} \rho(t) g(t) dt +}{g(0) \int_{-t_0/2}^{t_0/2} \rho(t)dt}$ )." +ilh steep edges. Butas discussedinthe introduction Quantum interest for massless scalar fields The kev to obt, Thus we can write This upper bound depends on the sampling function and in general will over-estimate the maximum allowed separation since a real distribution of energy must satisfy \ref{x_max}) ) for all choices of $g(t)$. +aining useful information from(he quanti inequalities in light of the sampling function.," Without a specific sampling function or energy distribution we cannot reduce \ref{x_max}) ) any further, but we can see that the range of possible $x$ is most strongly influenced by $y$." + ancl hence lower bound. is (ο choose anappropriate classof sampling function.To prove quantum ⊾qi!), If $y=1$ (we have a state that actually achieves the minimum allowed by $g(t)$ ) then the only way \ref{x_max_ie}) ) or \ref{x_max}) ) can be satisfied is if $x=1$ ; i.e. positive energy must follow andor precede the negative energy. +"xlu cos"" a 2..~ σικς2fo\ (n > nj2) (5)QO . ~. (Pay pe ney (9) qi) o1) 9*5 y 493 9 Q elsewhere. The", If $y$ is close to zero then $x$ can be large and we can approximate the integral in the denominator of \ref{x_max}) ) by evaluating $g(t/x)$ at $t=0$ : +In the Swift era (Gehrelsetal.2004).. (he X-ray telescope (ART) observation 2005) provides the complete light curves of ganunaray bursts (GRBs) in the 0.2-10 keV band.,"In the Swift era \citep{gehrels04}, the X-ray telescope (XRT) observation \citep{burrows05} provides the complete light curves of gamma-ray bursts (GRBs) in the 0.2-10 keV band." +" One of the most interesting discoveries is the so-called shallow decay segment: the flux plateau of Fxt""? within 10*—104 second after thetrigger Pasqualeetal. 2006)."," One of the most interesting discoveries is the so-called shallow decay segment: the flux plateau of $F\propto t^{-0.5}$ within $10^3-10^4$ second after thetrigger \citep{campana05,depasquale06}." +. Recent statistic analyses (Nousekοἱal.2006:O'BrienZhang&2007) have revealed (hat the phase of shallow decay in (he X-ray allerelow might be a common feature of the long GRBs.," Recent statistic analyses \citep{nousek06,obrien06,liang07} have revealed that the phase of shallow decay in the X-ray afterglow might be a common feature of the long GRBs." + The shallow decay in the early X-ray light curve is still a mvstery. although theoretical explanations have been put forward [rom several aspects (see Zhang 2007 Lor a comprehensive review).," The shallow decay in the early X-ray light curve is still a mystery, although theoretical explanations have been put forward from several aspects (see Zhang 2007 for a comprehensive review)." + Most of (he models are: hydrocvuamics of the shock by energy injection(e.g..Granot&Ixumar2006:Zhangetal.2006).. geometry ol the jet (e.g..Eichler&Granot2006:Tomaetal. 2006).. varving microphysical parameters (Fan&Piran2006:Ciranot.INóniglPanaitesenIokaοἱal. 2006).. late," Most of the models are: hydrodynamics of the shock by energy injection\citep{granot06a,zhang06}, geometry of the jet \citep{eichler06,toma06}, , varying microphysical parameters \citep{fan06,granot06b,panaitescu06,ioka06}, , late" +We now discuss the effect of overdensity on luminosity function.,We now discuss the effect of overdensity on luminosity function. + Clearly. overdense regions have enhanced number of sources. lence it is natural that the amplitude of the luminosity function for such regions should be higher than the globally averaged. values.," Clearly, overdense regions have enhanced number of sources, hence it is natural that the amplitude of the luminosity function for such regions should be higher than the globally averaged values." + However. the overdense regions have enhanced radiative feedback oo. and hence we expect a decrease in the number of sources. j»uarticularly towards the fainter end.," However, the overdense regions have enhanced radiative feedback too, and hence we expect a decrease in the number of sources, particularly towards the fainter end." + Figure 3. shows the effect of overdensity on the luminosity 'uncetion at 2=S for our fiducial model., Figure \ref{lf78} shows the effect of overdensity on the luminosity function at $z=8$ for our fiducial model. + The ionised volume filling ‘actor within the overdense region is Qz1.0 for the overdense region under consideration at this redshift., The ionised volume filling factor within the overdense region is $Q \approx 1.0$ for the overdense region under consideration at this redshift. + The average region uminosity function (dashed line) is clearly very different from he luminosity function in the overdense region (solid line) at that redshift., The average region luminosity function (dashed line) is clearly very different from the luminosity function in the overdense region (solid line) at that redshift. + Firstly. we can clearly see an enhancement in the source counts for brighter galaxies. which is as expected.," Firstly, we can clearly see an enhancement in the source counts for brighter galaxies, which is as expected." + In addition. there is a clear sign of a flattening for magnitudes AZyp17. which is a signature of radiative feedback.," In addition, there is a clear sign of a flattening for magnitudes $M_{\rm AB} \gtrsim -17$, which is a signature of radiative feedback." + In comparison. the effect of eedback. for average regions occurs at much fainter magnitudes Alyn~19.," In comparison, the effect of feedback for average regions occurs at much fainter magnitudes $M_{\rm AB} \sim +-12$." + Note that there is no complete suppression of star ‘ormation for halo masses lower than the feedback threshold. rather he luminosity function for magnitudes below the knee continues to grow in the flattened region.," Note that there is no complete suppression of star formation for halo masses lower than the feedback threshold, rather the luminosity function for magnitudes below the knee continues to grow in the flattened region." + This is simply due to the continued star ormation in haloes with mass less than the cutoff mass at 2=8.0. but which collapsed at higher redshifts when the feedback threshold mass was lower.," This is simply due to the continued star formation in haloes with mass less than the cutoff mass at $z=8.0$, but which collapsed at higher redshifts when the feedback threshold mass was lower." + Thus. for instance. if star formation is allowed o happen in a halo for only for a fraction of the dynamical time see equation (3))]. the luminosity function will rise less steeply at the fainter end.," Thus, for instance, if star formation is allowed to happen in a halo for only for a fraction of the dynamical time [see equation \ref{halo-sfr}) )], the luminosity function will rise less steeply at the fainter end." + For small enough star formation time scale. he luminosity function will show an abrupt cutoff.," For small enough star formation time scale, the luminosity function will show an abrupt cutoff." + Of course. an abrupt cutoff is always seen at low enough luminosities. which are not shown in the figure here.," Of course, an abrupt cutoff is always seen at low enough luminosities, which are not shown in the figure here." + It is important to understand here that the data points in Figure 2. do not represent luminosity function of the overdense region., It is important to understand here that the data points in Figure \ref{lf} do not represent luminosity function of the overdense region. + Instead. those data points represent the globally averaged luminosity function derived using a maximum likelihood procedure from the observed luminosity distribution of sources.," Instead, those data points represent the globally averaged luminosity function derived using a maximum likelihood procedure from the observed luminosity distribution of sources." + In this procedure. a likelihood function is defined. which describes the step-wise shape of the luminosity function that is most likely given the observed luminosity distribution in the search fields.," In this procedure, a likelihood function is defined, which describes the step-wise shape of the luminosity function that is most likely given the observed luminosity distribution in the search fields." + Details of this procedure are described. for example. in Section 5.1 of ? and references therein.," Details of this procedure are described, for example, in Section 5.1 of \citet{2010arXiv1006.4360B} and references therein." + Given the fact that the effect of radiative feedback shows up at brighter magnitudes for overdense regions. it is possible to use this feature for studying feedback using near-future observations.," Given the fact that the effect of radiative feedback shows up at brighter magnitudes for overdense regions, it is possible to use this feature for studying feedback using near-future observations." + For this purpose. we consider two additional models (other than the fiducial one) of reionization.," For this purpose, we consider two additional models (other than the fiducial one) of reionization." + These models have parameter values (fy. fi) = (00.06. 0.3) and (0.2. 0.07) and we obtain τι=0.088 and 0.058 respectively for these models.," These models have parameter values $f_*$ , $f_{\rm esc}$ ) = $0.06$, $0.3$ ) and $0.2, 0.07$ ) and we obtain $\tau_e = 0.088$ and $0.058$ respectively for these models." + We tix f. and only change the value of fi... to ensure that any effect on the luminosity function is purely due to feedback., We fix $f_*$ and only change the value of $f_{\rm esc}$ to ensure that any effect on the luminosity function is purely due to feedback. + These two models predict photoionisation rates greater and lesser respectively than what are presented by ?.., These two models predict photoionisation rates greater and lesser respectively than what are presented by \citet{2007MNRAS.382..325B}. + The right panel of Figure + shows the luminosity function at =8 within the overdense region for three different reionization histories. which can be compared with the corresponding luminosity function in average region (shown in the left panel).," The right panel of Figure \ref{lf_reion} shows the luminosity function at $z=8$ within the overdense region for three different reionization histories, which can be compared with the corresponding luminosity function in average region (shown in the left panel)." +" In both cases a distinct ""knee"" is seen in the luminosity function as a signature of feedback.", In both cases a distinct “knee” is seen in the luminosity function as a signature of feedback. + The luminosity function flattens at this luminosity. and is suppressed to very low values at much lower luminosities.," The luminosity function flattens at this luminosity, and is suppressed to very low values at much lower luminosities." + As described in the previous section. this signature of feedback appears at brighter magnitudes for the overdense region.," As described in the previous section, this signature of feedback appears at brighter magnitudes for the overdense region." + This is expected. because the cutoff mass depends directly on the temperature. which is enhanced in the overdense region.," This is expected, because the cutoff mass depends directly on the temperature, which is enhanced in the overdense region." + We also note that in the case of the first model the flattening occurs for Alyy=19 whereas for the second model at a fainter luminosity of Mays16.," We also note that in the case of the first model the flattening occurs for $M_{\rm AB} \gtrsim +-19$ whereas for the second model at a fainter luminosity of $M_{\rm + AB} \simeq -16$." + This is due to the fact that the photoionisation feedback is enhanced in the first model due to enhanced flux., This is due to the fact that the photoionisation feedback is enhanced in the first model due to enhanced flux. + The evolution of the filling factor affects this result through he average temperature which sets the cutoff mass., The evolution of the filling factor affects this result through the average temperature which sets the cutoff mass. + Thus. early and late reionization models are distinguished by the difference in he nature of flattening in both cases.," Thus, early and late reionization models are distinguished by the difference in the nature of flattening in both cases." + This also affects the evolution of the luminosity function., This also affects the evolution of the luminosity function. + We find that the reionization history has a strong effect on he luminosity function at the faint end., We find that the reionization history has a strong effect on the luminosity function at the faint end. + It is known that the bright end of the luminosity function is affected. primarily by the star ormation mode of a halo. and the overall bias. whereas its faint end is affected by the reionization history.," It is known that the bright end of the luminosity function is affected primarily by the star formation mode of a halo, and the overall bias, whereas its faint end is affected by the reionization history." + However. we also find. from Figure 4.. that the effect of reionization history is much stronger in the ease of overdense regions.," However, we also find, from Figure \ref{lf_reion}, that the effect of reionization history is much stronger in the case of overdense regions." + This is because of the enhanced photoionisation feedback. which is more sensitive to changes in reionization history.," This is because of the enhanced photoionisation feedback, which is more sensitive to changes in reionization history." + This order of magnitude change in the overdense region luminosity function should be visible to the James Webb Space Telescope. which can observe up to miyp231.5 CUApz—16.0 at redshifts of interest: 2)).," This order of magnitude change in the overdense region luminosity function should be visible to the James Webb Space Telescope, which can observe up to $m_{\rm AB}\approx 31.5$ $M_{\rm AB} \approx -16.0$ at redshifts of interest; \citealt{2006AAS...20921007W}) )." + We have used a semi-analytic model. based on ?? το study reionization and thermal history of an overdense region.," We have used a semi-analytic model, based on \citet{2005MNRAS.361..577C, 2006MNRAS.371L..55C} to study reionization and thermal history of an overdense region." + Studying such regions is important because observations of galaxy luminosity function at high redshifts typically focus fields of view of limited sizes preferentially containing bright sources: these regions possibly are overdense and hence biased with respect to the globally averaged regions., Studying such regions is important because observations of galaxy luminosity function at high redshifts typically focus fields of view of limited sizes preferentially containing bright sources; these regions possibly are overdense and hence biased with respect to the globally averaged regions. + In particular. we study the effect of radiative feedback arising from reionization on the shape of galaxy luminosity function.," In particular, we study the effect of radiative feedback arising from reionization on the shape of galaxy luminosity function." + In summary. we find that Finally. we criticallyexamine some of the simplifyi assumptions made in this work and how they are likely to affect," In summary, we find that Finally, we criticallyexamine some of the simplifying assumptions made in this work and how they are likely to affect" +required (o explain the origin of a number of p-process isotopes between A = 92 and 126 whose origin in nature has always been unclear.,required to explain the origin of a number of $p$ -process isotopes between A = 92 and 126 whose origin in nature has always been unclear. + The site is the proton-vich bubble that powers the explosion and the early neutrino-powered wind that. develops right behiud it., The site is the proton-rich bubble that powers the explosion and the early neutrino-powered wind that develops right behind it. + The synthesis is primary. so a neutron star derived [rom a metal poor progenitor star would produce the same vields (so long as the neutron star itself had the same properties).," The synthesis is primary, so a neutron star derived from a metal poor progenitor star would produce the same yields (so long as the neutron star itself had the same properties)." + Very metal deficient stars formed [rom these ejecta would be eharacterized by a excess of both p-process nuclei and r-process nuclei compared to the s-process. but since (here is no element (hat is dominantly p-process. observational diagnostics may be cdillicult.," Very metal deficient stars formed from these ejecta would be characterized by a excess of both $p$ -process nuclei and $r$ -process nuclei compared to the $s$ -process, but since there is no element that is dominantly $p$ -process, observational diagnostics may be difficult." +" In particular. large quantities of Ru and ""Pd are produced in our calculations (Fig. 1))."," In particular, large quantities of $^{96,98}{\rm Ru}$ and $^{106}$ Pd are produced in our calculations (Fig. \ref{allFig}) )." +" Synthesis of p-process isotopes as heavy as ""Te can also be achieved by only modifications to the entropy of the baseline simulation.", Synthesis of $p$ -process isotopes as heavy as $^{120}{\rm Te}$ can also be achieved by only factor-of-two modifications to the entropy of the baseline simulation. + It is interesting in (his reearcl io note Chat an even larger increase in entropy is needed later in the neutron-rich wind for the efficient synthesis of the r-process isotopes (e.g..Qian&Woosley1996).," It is interesting in this regard to note that an even larger increase in entropy is needed later in the -rich wind for the efficient synthesis of the $r$ -process isotopes \cite[e.g.,][]{qia96}." +. This is «quite possibly informing us of some additional heating mechanism that operates in (he mass outfIow during the first lew seconds ofa neutron star's life., This is quite possibly informing us of some additional heating mechanism that operates in the mass outflow during the first few seconds ofa neutron star's life. + Possible mechanisms are magnetic field entrainment of the outflowing matter (Thompson2003).. magnetic energy dissipation (Qian&Woosley 1996).. acoustic energv input (Qian&Wooslev1996:Burrows 2005).. or Alfvénn wave dampening (Suzuki&Nagataki2005)..," Possible mechanisms are magnetic field entrainment of the outflowing matter \citep{Tho03}, magnetic energy dissipation \citep{qia96}, acoustic energy input \citep{qia96,Bur05}, or Alfvénn wave dampening \citep{Suz05}." + None of these were included in (he present supernova model. bul we varied the entropy to determine qualitatively (heir effect.," None of these were included in the present supernova model, but we varied the entropy to determine qualitatively their effect." + In the more extreme. but still physically reasonable case that the entropy is multiplied by three. the svnthesis extends all the way to I Yb. with the accompanying production of many isotopes normally attributed to the s-process and even the r-process.," In the more extreme, but still physically reasonable case that the entropy is multiplied by three, the synthesis extends all the way to $^{168}$ Yb, with the accompanying production of many isotopes normally attributed to the $s$ -process and even the $r$ -process." + somewhat disappointinglv. none of our calculations produce a laree overabundance of 7 Mo compared to surrounding isotopes (though some do make of the necessary value).," Somewhat disappointingly, none of our calculations produce a large overabundance of $^{92}$ Mo compared to surrounding isotopes (though some do make of the necessary value)." + This may reflect either the fact that °? Mo has another origin. e.g.. the same neutrino-powered wind a few seconds later when Y; = 0.485. or uncertainties in the nuclear physics.," This may reflect either the fact that $^{92}$ Mo has another origin, e.g., the same neutrino-powered wind a few seconds later when $Y_e$ = 0.485, or uncertainties in the nuclear physics." + In. the current study. the Mo that is made is produced as the odd-odd progenitor ? Rh.," In the current study, the $^{92}$ Mo that is made is produced as the odd-odd progenitor $^{92}$ Rh." +" This does not take advantage of the extra stability that. would be afforded by an even-even nucleus like ""Pd. let alone the magic neutron shell of Mo itself."," This does not take advantage of the extra stability that would be afforded by an even-even nucleus like $^{92}$ Pd, let alone the magic neutron shell of $^{92}$ Mo itself." + Indeed the binding energies and lifetimes of nuclei in the vicinity of Pd are equite uncertain., Indeed the binding energies and lifetimes of nuclei in the vicinity of $^{92}$ Pd are quite uncertain. + Animportant aspect of (he svnthesis caleulated here is that none of the p-nuclei are made as (hemselves: all have proton-rich progenitors., An important aspect of the synthesis calculated here is that none of the $p$ -nuclei are made as themselves; all have proton-rich progenitors. + \lanv of these progenitors are so unstable that even their masses and lifetimes are not measured. let. alone their cross sections [or interacting with neutrons and protons.," Many of these progenitors are so unstable that even their masses and lifetimes are not measured, let alone their cross sections for interacting with neutrons and protons." + À similar situation is encountered in the rp-process in Type I xoay bursts (e.g.Schatzοἱal. 2001)... a critical dillerence being that (he isotopes," A similar situation is encountered in the $rp$ -process in Type I x-ray bursts \citep[e.g.][]{Sch01}, , a critical difference being that the isotopes" +paralcter by from these studies.,parameter $b_X$ from these studies. + Measurements are carried out with a variety of methods. correspoud to different objects. are scusitive to differeut redshifts and also to different scales.," Measurements are carried out with a variety of methods, correspond to different objects, are sensitive to different redshifts and also to different scales." +" Besides that. all dwuamiical estimates actually measure the combination by),o6"," Besides that, all dynamical estimates actually measure the combination $b_X\Omega_0^{-0.6}$." + Measurements of the correlation function are also affected by the cosinological paralucters in the computation of the distauces at siguificant redshifts. bevoud the obvious linear depeudence ou £j.," Measurements of the correlation function are also affected by the cosmological parameters in the computation of the distances at significant redshifts, beyond the obvious linear dependence on $H_0$." + If we live iu an accelerating Universe. the Carrera et al (1998) correlation leugth would have to be scaled wp by.. resulting in a subsequent increase of alinost a factor of 2 in the bias parameter.," If we live in an accelerating Universe, the Carrera et al (1998) correlation length would have to be scaled up by, resulting in a subsequent increase of almost a factor of 2 in the bias parameter." + Caven the uncertainties iu the values of gy and A (even for a flat Universe). the Carrera et al (1998) and Akylas et al (1999) results cannot be considered imcousisteut.," Given the uncertainties in the values of $q_0$ and $\Lambda$ (even for a flat Universe), the Carrera et al (1998) and Akylas et al (1999) results cannot be considered inconsistent." + As expected. clusters are a largely biased population (by~ 1) compared to ACN (by~1 2).," As expected, clusters are a largely biased population $b_X\sim 4$ ) compared to AGN $b_X\sim 1-2$ )." +" The umultipoles of the NRB are expected to be dominated by ACN, as these objects are the main sources of the NRB."," The multipoles of the XRB are expected to be dominated by AGN, as these objects are the main sources of the XRB." + The bias parameter derived frou the XRD umultipoles is cousisteutlv in agreement with the bias parameter derived from ACN clustering (by~1. 2)., The bias parameter derived from the XRB multipoles is consistently in agreement with the bias parameter derived from AGN clustering $b_X\sim 1-2$ ). + The exception to this is the NRB dipole which implies a larger value of by., The exception to this is the XRB dipole which implies a larger value of $b_X$. + This could be partly due to a larger cluster contribution. as the lowest order multipoles are most scusitive to nearest (aud brightest) sources. where the cluster contribution to the source counts (~LOY on average in the deep extragalactie surveys) is ~50% for the Piccinotti et al (1982) sample.," This could be partly due to a larger cluster contribution, as the lowest order multipoles are most sensitive to nearest (and brightest) sources, where the cluster contribution to the source counts $\sim 10\%$ on average in the deep extragalactic surveys) is $\sim 50\%$ for the Piccinotti et al (1982) sample." + N-ray astrouoly is now in a position to address cosmological studies;, X-ray astronomy is now in a position to address cosmological studies. + X-ray selected ACN which produce most of the N-ravs in the Universe. appear to trace lass with a moderate bias paraueter by~12. but that has to be better defined as a function of scale aud redshift.," X-ray selected AGN which produce most of the X-rays in the Universe, appear to trace mass with a moderate bias parameter $b_X\sim 1-2$, but that has to be better defined as a function of scale and redshift." + Chandra and NMM will carry out several deep “pencil bean survevs which. after subsequent identification of the sereudipitous sources discovered. will define the redshift evolution of the ACN N-rav. Πορτ function at photon energies 22keV aud therefore the X-ray. volume. cuussivity as a function of redshift.," $Chandra$ and XMM will carry out several deep `pencil beam' surveys which, after subsequent identification of the serendipitous sources discovered, will define the redshift evolution of the AGN X-ray luminosity function at photon energies $>2 {\rm keV}$ and therefore the X-ray volume emissivity as a function of redshift." + Towever. these surveys will not map sutticicutly large areas," However, these surveys will not map sufficiently large areas" +"The online table even allows users to compute their own relationships based on their needs (specific objects, colours, reddening,...).","The online table even allows users to compute their own relationships based on their needs (specific objects, colours, reddening,...)." +" We remind users that the computed polynomials are only valid in the range of BaSeL3.1 astrophysical-parameters space, and no extrapolation is recommended."," We remind users that the computed polynomials are only valid in the range of BaSeL3.1 astrophysical-parameters space, and no extrapolation is recommended." +" Bolometric corrections have been computed in Gaia's passbands and are also provided in an online table, which allows the correspondence between absolute magnitudes and luminosity."," Bolometric corrections have been computed in 's passbands and are also provided in an online table, which allows the correspondence between absolute magnitudes and luminosity." +" In addition, the passbands are included in the Padova and BASTI isochrones web sites, allowing the computation of any track and isochrone in the colour-magnitude diagram, an essential tool for the derivation of ages or the analysis of clusters."," In addition, the passbands are included in the Padova and BASTI isochrones web sites, allowing the computation of any track and isochrone in the colour-magnitude diagram, an essential tool for the derivation of ages or the analysis of clusters." +" The paper presents some examples of the Padova isochrones in G,Gpp,, and ffor solar metallicity and for different ages."," The paper presents some examples of the Padova isochrones in $G$, and for solar metallicity and for different ages." +" Absorption and colour excess in passbands have been computed as well as the ratios with respect to Ay, Ag, and several colour excesses have been provided for the whole spectral energy distributions in BaSeL3.1 and for three absorption values."," Absorption and colour excess in passbands have been computed as well as the ratios with respect to $A_V$, $A_{H_p}$ and several colour excesses have been provided for the whole spectral energy distributions in BaSeL3.1 and for three absorption values." + A polynomial fitting of Ag/Ay , A polynomial fitting of $A_G/A_V$ +because they provide a useful contrast to the CSO sample.,because they provide a useful contrast to the CSO sample. + The lenses will be discussed in a series of future papers., The lenses will be discussed in a series of future papers. + All of the sources cliseussecl in this paper can be found in the list of VLA calibrators maintained byNRAO?., All of the sources discussed in this paper can be found in the list of VLA calibrators maintained by. +. The data were ealibrated in the AIPS software package developed by NRAO., The data were calibrated in the AIPS software package developed by NRAO. + The standard flux density calibrator 2286 was not observed for all epochs. so the overall flux density calibration was instead tied to the source 3343 (1634+628).," The standard flux density calibrator 286 was not observed for all epochs, so the overall flux density calibration was instead tied to the source 343 (1634+628)." +" This source has a steep two-point radio spectral index between 1.4 and 3.5 GlIz (a~—1.0:S,oxp) and its [ας density has been shown to be stable in past monitoring campaigns1999)."," This source has a steep two-point radio spectral index between 1.4 and 8.5 GHz $\alpha \sim +-1.0; S_\nu \propto \nu^\alpha$ ) and its flux density has been shown to be stable in past monitoring campaigns." +. Although the emission from 3343 is dominated bv the compact central component. there is some low surface-brightness extended emission [rom the source.," Although the emission from 343 is dominated by the compact central component, there is some low surface-brightness extended emission from the source." + Because of the extended emission. 3243 is not an ideal flux calibrator.," Because of the extended emission, 343 is not an ideal flux calibrator." + First. the total [αν density measured [or je source will change with the VLA configuration. since (he more compact configurations are more sensitive to the low surface-brightness emission.," First, the total flux density measured for the source will change with the VLA configuration, since the more compact configurations are more sensitive to the low surface-brightness emission." + To correct for this effect. we sealed ve 3343. flux densities by factors of 0.997 and 0.983 for the BuA and D configurations. --'espectivelv.," To correct for this effect, we scaled the 343 flux densities by factors of 0.997 and 0.983 for the BnA and B configurations, respectively." + Secondly. (he changing (ue) coverage for each monitoring epoch may cause V.nall variations in the measured (lux density since different. (u.0) coverages are sensitive (o lifferent source structures.," Secondly, the changing $(u,v)$ coverage for each monitoring epoch may cause small variations in the measured flux density since different $(u,v)$ coverages are sensitive to different source structures." +" However. these small variations. as well as those caused by the hanging observing conditions and any intrinsic variability in 3343. can easily be corrected for. as shown in relsec, rim."," However, these small variations, as well as those caused by the changing observing conditions and any intrinsic variability in 343, can easily be corrected for, as shown in \\ref{sec_prim}." + Because the CSOs in our sample are compact and bright (5552200 mJy: Table 3)). thev can be used to determine antenna gain solutions without the need [or an external calibrator.," Because the CSOs in our sample are compact and bright $S_{8.5}>200$ mJy; Table \ref{tab_rms}) ), they can be used to determine antenna gain solutions without the need for an external calibrator." + For (wo of the sources. J10354-5628 and J1400-6210. the emission lrom the source is slightly resolved.," For two of the sources, J1035+5628 and J1400+6210, the emission from the source is slightly resolved." + Thus. for these (vo CSOs. (he gun solutions were calculated only for baseline lengths that were less than 400 kA.," Thus, for these two CSOs, the gain solutions were calculated only for baseline lengths that were less than 400 $\lambda$." + For all of the other CSOs. all baselines were used.," For all of the other CSOs, all baselines were used." + For each CSO. (wo iterations of the AIPS task CALIB were run.," For each CSO, two iterations of the AIPS task CALIB were run." + In the first. only (he eain phases were solved for. wilh a solution interval of 10 sec.," In the first, only the gain phases were solved for, with a solution interval of 10 sec." + The phase solutions were applied to the data and then the second iteration of CALID was performed., The phase solutions were applied to the data and then the second iteration of CALIB was performed. + In this iteration. both amplitude ancl phase solutions were obtained. with a solution interval of 30 sec.," In this iteration, both amplitude and phase solutions were obtained, with a solution interval of 30 sec." + The phase calibrators were processed in (he same manner., The phase calibrators were processed in the same manner. + After the data were calibrated. we measured the CSO [flux densities using two separate," After the data were calibrated, we measured the CSO flux densities using two separate" +"The mass distributions for sdB and sdO stars are shown in Figs.4 and 5, respectively.","The mass distributions for sdB and sdO stars are shown in Figs.4 and 5, respectively." +" The error on the mass, AM,, depends on the parameter log), and this dependence is shown in the upper panel of Fig.6, where f (sπατε ) is derived from the M,-log(“at relation."," The error on the mass, $\Delta M_{\rm p}$, depends on the parameter $\log(\frac{T_{\rm eff}^4}{g})$, and this dependence is shown in the upper panel of Fig.6, where $f$ $ \equiv \frac{\Delta M_{\rm p}}{\Delta \log(T_{\rm eff}^4/g) + }$ ) is derived from the $M_{\rm p}$ $\log + (\frac{T_{\rm eff}^4}{g})$ relation." + The log( distributions of sdB and sdO stars from the SPY and the HQS=) are shown in the bottom panel of this figure.," The $\log + (\frac{T_{\rm eff}^4}{g})$ distributions of sdB and sdO stars from the SPY and the HQS are shown in the bottom panel of this figure." + From this figure we see that f is lower than 0.5 for most hot subdwarfs., From this figure we see that $f$ is lower than 0.5 for most hot subdwarfs. +" To discuss the error on the mass obtained from our method, we should consider the error from both theory and observation."," To discuss the error on the mass obtained from our method, we should consider the error from both theory and observation." +" The M,-log(""Thus,Tác) relation here is derived from Pop I models (Z=0..02)."," The $M_{\rm p}$ $\log + (\frac{T_{\rm eff}^4}{g})$ relation here is derived from Pop I models $Z$ =0.02)." + the different metalicities resulti ina different log(Ταν) for the same mass.," Thus, the different metalicities result in a different $\log(\frac{T_{\rm + eff}^4}{g})$ for the same mass." +" For example, Alog(=Ταν is about 0.04 2dex for the models between Z = 0.0001 and Z = 0.06."," For example, $\Delta \log(\frac{T_{\rm + eff}^4}{g})$ is about 0.04 dex for the models between $Z$ = 0.0001 and $Z$ = 0.06." +" For stars from the ESO supernova Ia progenitor survey, the observational errors for sdB stars are ΛΤεῃ=360K and Alog(g)=0.05 dex, and the observational errors for sdO stars are Alog(T.g)=0.011 dex and Alog(g)=0.097 dex, respectively."," For stars from the ESO supernova Ia progenitor survey, the observational errors for sdB stars are $\Delta T_{\rm eff}= 360K$ and $\Delta + \log(\rm g)= 0.05 $ dex, and the observational errors for sdO stars are $\Delta \log(T_{\rm eff})= 0.011$ dex and $\Delta + \log(\rm g)= 0.097 $ dex, respectively." +" These correspond to Alog(T4,/g) of 0.07 dex and 0.14 dex."," These correspond to $\Delta \log(T_{\rm + eff}^4/g)$ of 0.07 dex and 0.14 dex." +" Thus, the total errors, Alog(T-a/8) (theory plus observation), are 0.11 dex and 0.18 dex, respectively."," Thus, the total errors, $\Delta \log(T_{\rm eff}^4/g)$ (theory plus observation), are 0.11 dex and 0.18 dex, respectively." +" According to the f~log:eff) relation shown in Fig.6, the errors on the masses are less than 0.055 Μο and 0.09 Μο for most sdB and sdO stars, respectively."," According to the $f \sim \rm log(\frac{T_{\rm eff}^4}{g})$ relation shown in Fig.6, the errors on the masses are less than 0.055 $M_\odot$ and 0.09 $M_\odot$ for most sdB and sdO stars, respectively." +" For sdB stars from the Hamburg Quasar Survey, we derived the mass errors for each star in a similar way."," For sdB stars from the Hamburg Quasar Survey, we derived the mass errors for each star in a similar way." +" The results show that the majority of errors are in the 0.097 Μο to 0.117 Μο range(95 percent confidence interval), while the mean error is 0.107 Mo."," The results show that the majority of errors are in the 0.097 $M_\odot$ to 0.117 $M_\odot$ range(95 percent confidence interval), while the mean error is 0.107 $M_\odot$." +" As shown in Fig.4, the sdB stars from SPY and HQS have the same mass distributions—the KS test shows that the two samples come from the same distribution at a high level of confidence(> 93.5%)."," As shown in Fig.4, the sdB stars from SPY and HQS have the same mass distributions—the KS test shows that the two samples come from the same distribution at a high level of $> 93.5\%$ )." +" Most of the sdB stars have masses ranging from 0.42 to 0.54 Mo, and the mean mass is about 0.50 Mo, equal to that assumed in previous studies."," Most of the sdB stars have masses ranging from 0.42 to 0.54 $M_\odot$, and the mean mass is about 0.50 $M_\odot$, equal to that assumed in previous studies." +" As a comparison, we also show the mass distributions from the theoretical study of Han et al. ("," As a comparison, we also show the mass distributions from the theoretical study of Han et al. (" +2003) and from asteroseismology (Fontaine et al.,2003) and from asteroseismology (Fontaine et al. +" 2006) in Fig.4, from which we see that the distribution obtained in this paper matches the other two closely."," 2006) in Fig.4, from which we see that the distribution obtained in this paper matches the other two closely." +" Figure 5 shows that most sdO stars are in 0.40 ~ 0.55 Mo, although some sdO stars have much higher masses than these values."," Figure 5 shows that most sdO stars are in 0.40 $\sim$ 0.55 $M_\odot$, although some sdO stars have much higher masses than these values." +" Since low-mass hot subdwarfs (e.g. less than ~0.5 Mo) can not reach 40,000K (the minimum temperature for sdO stars) during the main sequence (see Fig.2 in Han et al."," Since low-mass hot subdwarfs (e.g. less than $\sim$ 0.5 $M_\odot$ ) can not reach 40,000K (the minimum temperature for sdO stars) during the main sequence (see Fig.2 in Han et al." +" 2002), sdO stars with mass less than ~0.5 Μο most likely evolve from sdB stars, i.e., these objects initially appear as sdB stars when they are on the main sequence, and as sdO stars when they evolved off the main sequence (post-EHB)."," 2002), sdO stars with mass less than $\sim$ 0.5 $M_\odot$ most likely evolve from sdB stars, i.e., these objects initially appear as sdB stars when they are on the main sequence, and as sdO stars when they evolved off the main sequence (post-EHB)." +" The typical evolutionary time scales for hot subdwarfs on the MS and post-EHB are ~ 160 and ~ 20Myr, respectively."," The typical evolutionary time scales for hot subdwarfs on the MS and post-EHB are $\sim$ 160 and $\sim$ 20Myr, respectively." +" Thus, observationally the number of sdO stars (evolving from sdB"," Thus, observationally the number of sdO stars (evolving from sdB" +an expanding envelope with a 77 density distribution.,an expanding envelope with a $r^{-2}$ density distribution. + We allow for the possibility that matter in the form of clumps or filaments fills a € part of the envelope volume. Le. & forming an angle « with the axis between the stars., We consider ionization alonga given direction from star $S_2$ forming an angle $\alpha$ with the axis between the stars. + A distance xs from star $5. to which the wind matter is tonized. can be found fromwhere is à AInumber of recombinations in à cone of solid angle dw along the considered direction. ay Is à recombination coefficient. while Nj=No(A/rr is an ion number density (electron density is assumed to be equal to ton density).," A distance $x_2$ from star $S_2$, to which the wind matter is ionized, can be found fromwhere is a number of recombinations in a cone of solid angle $\omega$ along the considered direction, $\alpha_{\rm rec}$ is a recombination coefficient, while $N_{\rm i} = N_0\,(A/r)^2$ is an ion number density (electron density is assumed to be equal to ion density)." + In the following. we assume that A is a unit length. so all the r and x are expressed in terms of A. and x is then related to r and « via In Eq. (2)).," In the following, we assume that $A$ is a unit length, so all the $r$ and $x$ are expressed in terms of $A$, and $x$ is then related to $r$ and $\alpha$ via In Eq. \ref{rec_eq}) )," + νι 1s a distance from star $5 to the wind outer boundary along the considered direction. given by Equation (1)) can be rewritten as which. using Eq. (3)).," $x_1$ is a distance from star $S_2$ to the wind outer boundary along the considered direction, given by Equation \ref{ion_eq}) ) can be rewritten as which, using Eq. \ref{x_eq}) )," + can be evaluated to give where Equation (6)) can be solved numerically to obtain νο., can be evaluated to give where Equation \ref{ion_eq3}) ) can be solved numerically to obtain $x_2$. +" Along the separation axis. Le.. when a=0. v,=1—ro. while Eq. (7) "," Along the separation axis, i.e., when $\alpha = 0$, $x_1 = 1 - r_0$, while Eq. \ref{i_eq}) )" +reduces to Solving Eq. (6)), reduces to Solving Eq. \ref{ion_eq3}) ) + for a grid of « values in the range 0 ro. allows us to obtain the shape and position of the ionization front in the wind.," for a grid of $\alpha$ values in the range $0 \le +\alpha \le \arcsin r_0$ , allows us to obtain the shape and position of the ionization front in the wind." + Matter is ionized between the wind outer boundary and the ionization front., Matter is ionized between the wind outer boundary and the ionization front. + We note that the star separation axis Is a symmetry axis of the ionized region., We note that the star separation axis is a symmetry axis of the ionized region. + There are two free parameters in the above problem. Le.. ro and Co.," There are two free parameters in the above problem, i.e., $r_0$ and $C_0$." + We assume that the tonized region is isothermal. so that the emission line coefficient varies as N7. and that the intrinsic line profile is Gaussian. characterized by à thermal and/or turbulent velocity. Vi.," We assume that the ionized region is isothermal, so that the emission line coefficient varies as $N_i^2$, and that the intrinsic line profile is Gaussian characterized by a thermal and/or turbulent velocity, $V_{\rm t}$." + Integrating the intrinsic. line profile over the ionized region and taking into account the kinematic properties of the ionized wind. a final emission-line profile can be obtained.," Integrating the intrinsic line profile over the ionized region and taking into account the kinematic properties of the ionized wind, a final emission-line profile can be obtained." +" Apart from the above-mentioned parameters determining the ionization front. the resultant line. profile depends on kinematic parameters of the wind and the stellar system. which are: the wind expansion velocity. Vj: the velocity of star $, (source of the wind) relative to the observer. V.: and the angle between the stars separation axis and the line of sight. o."," Apart from the above-mentioned parameters determining the ionization front, the resultant line profile depends on kinematic parameters of the wind and the stellar system, which are: the wind expansion velocity, $V_{\rm wind}$; the velocity of star $S_1$ (source of the wind) relative to the observer, $V_{\rm s}$; and the angle between the stars separation axis and the line of sight, $\alpha_{\rm s}$." + Some of the parameters in the above problem can be estimated from observations., Some of the parameters in the above problem can be estimated from observations. + As discussed in Sect. 2..," As discussed in Sect. \ref{decline_sect}," + we assume that close to the time of the November/December 2006 eclipse. matter ejected during the 2002 eruption of V838 Mon reached the vicinity of the B3V companion.," we assume that close to the time of the November/December 2006 eclipse, matter ejected during the 2002 eruption of V838 Mon reached the vicinity of the B3V companion." + Our observations were completed in October 2005. so we can estimate that ro=0.75.," Our observations were completed in October 2005, so we can estimate that $r_0 \simeq 0.75$." + During the 2002 outburst of V838 Mon. expansion velocities observed reached ~600 kmss7!. although most ofmass loss occurred at 150—400 kmss7! (Munarietal..2002a:Crauseal.2003:Kipperetal..2004:Tylenda. 2005).," During the 2002 outburst of V838 Mon, expansion velocities observed reached $\sim 600$ $^{-1}$, although most ofmass loss occurred at 150–400 $^{-1}$ \citep{muna02,crause03,kipp04,tyl05}." +. As discussed in Tylenda (2005). the nost intense mass loss occurred in March 2002. which was observed as an expanding photosphere of velocity ~270kms7!..," As discussed in \cite{tyl05}, , the most intense mass loss occurred in March 2002, which was observed as an expanding photosphere of velocity $\sim 270$." + We therefore assume Vig250kms7! in the present calculations.," We therefore assume $V_{\rm wind} \simeq 250~{\rm km\,s}^{-1}$ in the present calculations." +" We also assume that the heliocentric radial velocity of V838 Mon is V,=71kms""! (see Sect. 22))."," We also assume that the heliocentric radial velocity of V838 Mon is $V_{\rm s} = 71~{\rm km\,s}^{-1}$ (see Sect. \ref{v_rad}) )." + Thus. there remain 3 free parameters. 1e... Co. ας. and V. which can be obtained by fitting the model profile to the observed profile of the II] emission lines.," Thus, there remain 3 free parameters, i.e., $C_0$ , $\alpha_{\rm s}$ , and $V_{\rm t}$ , which can be obtained by fitting the model profile to the observed profile of the ] emission lines." + A fit of this kind is presented in Fig. 2.., A fit of this kind is presented in Fig. \ref{prof_fig}. . + Points show theobserved profile of the lline., Points show theobserved profile of the line. + This is one of the strongest emission lines of [Fell] in, This is one of the strongest emission lines of ] in +As an example of the procedure we use data of a typical TDC.,As an example of the procedure we use data of a typical TDG. + We first use the broad-band colors to derive a good estimate of the burst streuetl aud a first guess of the burst age (as in Fig. 2.1))., We first use the broad-band colors to derive a good estimate of the burst strength and a first guess of the burst age (as in Fig. \ref{fig:broad}) ). + The observed metal abuucdauce will tell us which metallicity to use for in the moclels., The observed metal abundance will tell us which metallicity to use for in the models. + We then compare the observed equivalent width of H; with the equivalent wicth from these models (two models are shown in Fig. 5a)., We then compare the observed equivalent width of $_\beta$ with the equivalent width from these models (two models are shown in Fig. \ref{fig:specmodobs}{ ). + Que of the possible ages for each model generally turus out to be consistent with the age estimated [rou the broad-band photometry., One of the possible ages for each model generally turns out to be consistent with the age estimated from the broad-band photometry. + The derecddeued observed spectrum of tlie same TDC plotted together with the model spectra ol weak aud stroug bursts preselected for the correct burst age from their H; equivalent widths are eiven in Fie. 5b., The dereddened observed spectrum of the same TDG plotted together with the model spectra of weak and strong bursts preselected for the correct burst age from their $_\beta$ equivalent widths are given in Fig. \ref{fig:specmodobs}{. + We cau finally select the correct. model using the slope of the continuum of the different. models., We can finally select the correct model using the slope of the continuum of the different models. + The results from the broad-band colors are confirmed in this case by using the spectral information. a strong burst with ~20% 2. ?? ," The results from the broad-band colors are confirmed in this case by using the spectral information, a strong burst with $\sim$ \citet{WDF+00} \ref{sec:FR} " +"quite well even for run D1Mal.0.1128 and D1Mal.0, as shown in the right panel of Fig. 3..","quite well even for run 128 and D1Ma1.0, as shown in the right panel of Fig. \ref{fig:3}." +" The power law at these high densities is caused by an effective equation of state (EOS) in this range, which shows a polytropic index γεῃ«1."," The power law at these high densities is caused by an effective equation of state (EOS) in this range, which shows a polytropic index $\gamma_{\mathrm{eff}} < 1$." +" Although the statistics we investigated indicate that the simulations DI1Mal.0.1128 and D1Mal.0 are not fully converged with respect to the density and temperature distributions, we conclude that the approximate behaviour of thermally bistable turbulence can be inferred from simulations with 256? grid cells."," Although the statistics we investigated indicate that the simulations 128 and D1Ma1.0 are not fully converged with respect to the density and temperature distributions, we conclude that the approximate behaviour of thermally bistable turbulence can be inferred from simulations with $256^3$ grid cells." + This is the aim of the parameter study that is presented in the following., This is the aim of the parameter study that is presented in the following. +" To illustrate the properties of thermally bistable gas, Fig."," To illustrate the properties of thermally bistable gas, Fig." +" 4 shows contour plots of the particle density, the temperature, the vorticity norm and the Mach number in 2D slices for simulation ΡΙΜαΙ.05512 in the statistically stationary regime."," \ref{fig:4} shows contour plots of the particle density, the temperature, the vorticity norm and the Mach number in 2D slices for simulation 512 in the statistically stationary regime." +" When comparing the slices in the top panel of Fig. 4,,"," When comparing the slices in the top panel of Fig. \ref{fig:4}," + one can see that regions of high gas density correspond to low temperatures and vice versa., one can see that regions of high gas density correspond to low temperatures and vice versa. +" The most prominent feature that can be seen in the 2D slices is the big clump of cold, dense gas."," The most prominent feature that can be seen in the 2D slices is the big clump of cold, dense gas." +" While the boundaries of this clump are rather sharp, there are also regions in which the cold and warm gas phases entrain each other and form intricate structures."," While the boundaries of this clump are rather sharp, there are also regions in which the cold and warm gas phases entrain each other and form intricate structures." +" The rich small-scale structure becomes apparent in projections of the mass density and the temperature, which are shown in Fig. 5.."," The rich small-scale structure becomes apparent in projections of the mass density and the temperature, which are shown in Fig. \ref{fig:5}." +" Even in these projections, relatively large clumps of cold gas appear prominently."," Even in these projections, relatively large clumps of cold gas appear prominently." +" Remarkably, the vorticity is largely reduced in these clumps in comparison to the surrounding medium, which is filled by more or less homogeneous turbulence (see left bottom panel of Fig. 4))."," Remarkably, the vorticity is largely reduced in these clumps in comparison to the surrounding medium, which is filled by more or less homogeneous turbulence (see left bottom panel of Fig. \ref{fig:4}) )." +" Nevertheless, the two-dimensional PDF of the vorticity magnitude versus the density, which is shown in Fig. 6,,"," Nevertheless, the two-dimensional PDF of the vorticity magnitude versus the density, which is shown in Fig. \ref{fig:6}," + demonstrates that high vorticity is found for the whole range of gas densities., demonstrates that high vorticity is found for the whole range of gas densities. + Also the density-dependend mean value shows no clear trend but is more or less constant over the whole range of densities., Also the density-dependend mean value shows no clear trend but is more or less constant over the whole range of densities. + This seems to contradict the observation made in the vorticity slice in Fig. 4.., This seems to contradict the observation made in the vorticity slice in Fig. \ref{fig:4}. + A possible explanation could be that the vorticity remains low only in, A possible explanation could be that the vorticity remains low only in +Vhe modified Newtonian clynamics (AIOND) is an empiricallv-based modification. of Newtonian gravity or inertia in the limit of low aceclerations (<(s8: cll.) suggested by Milgrom (1983) as an alternative to cosmic dark matter.,The modified Newtonian dynamics (MOND) is an empirically-based modification of Newtonian gravity or inertia in the limit of low accelerations $< a_o \approx cH_o$ ) suggested by Milgrom (1983) as an alternative to cosmic dark matter. + In addition. to explaining galaxy scaling relations (CIullv-Fisher. Faber-Jackson. Fundamental lane) this simple algorithm allows one to accurately wediet the shapes of spiral galaxy rotation curves from the observed distribution of gaseous and stellar matter.," In addition to explaining galaxy scaling relations (Tully-Fisher, Faber-Jackson, Fundamental Plane), this simple algorithm allows one to accurately predict the shapes of spiral galaxy rotation curves from the observed distribution of gaseous and stellar matter." + MOND also accounts for the kinematics of small groups of galaxies (Milgrom 1998) ancl of superclusters. as exemplified by the Perseus-DPisces filament. (Alilerom 1997) without the need or unseen mass.," MOND also accounts for the kinematics of small groups of galaxies (Milgrom 1998) and of superclusters, as exemplified by the Perseus-Pisces filament (Milgrom 1997) without the need for unseen mass." + These well-documentecl phenomenological successes (Sanders MeGaugh 2002 and references therein) challenge. the cold. dark matter (CDM). paradigm. and oovide some support for the suggestion that the current heory of gravity and inertia (General Relativity) may need revision in the limit of low accelerations or field eracdients., These well-documented phenomenological successes (Sanders McGaugh 2002 and references therein) challenge the cold dark matter (CDM) paradigm and provide some support for the suggestion that the current theory of gravity and inertia (General Relativity) may need revision in the limit of low accelerations or field gradients. + Iowever. problems do arise when one attempts to apply AIOND to the Large clusters of galaxies.," However, problems do arise when one attempts to apply MOND to the large clusters of galaxies." + The and White (LOSS) first noted. that. to successfully account for. the discrepancy between the observed mass and the traditional virial mass in the Coma Cluster. the MOND acceleration xwanmeter. supposedly a universal constant. should be about a factor of four larger than the value implied. by galaxy rotation. curves.," The and White (1988) first noted that, to successfully account for the discrepancy between the observed mass and the traditional virial mass in the Coma Cluster, the MOND acceleration parameter, supposedly a universal constant, should be about a factor of four larger than the value implied by galaxy rotation curves." + With MOND. the dvnamical mass of a wessure supported svstem at temporature T is Mx17fa; herefore. the The and White result could also be interpreted as an indication that the NOND dynamical mass is still arecr than the detectable mass in stars ancl gas.," With MOND, the dynamical mass of a pressure supported system at temperature T is $M\propto {T^2}/a_o$; therefore, the The and White result could also be interpreted as an indication that the MOND dynamical mass is still larger than the detectable mass in stars and gas." + 1n astronomical tests involving an individual extragalactic object. such as the Coma cluster. a contradiction is not necessarily a falsification.," In astronomical tests involving an individual extragalactic object, such as the Coma cluster, a contradiction is not necessarily a falsification." + One can abwavs argue that the peculiar aspects of an object. such as deviations from spherical svmmetry or incomplete dynamical relaxation. exempt that particular case.," One can always argue that the peculiar aspects of an object, such as deviations from spherical symmetry or incomplete dynamical relaxation, exempt that particular case." + Llowever. Gerbal ct al. (," However, Gerbal et al. (" +1992). looking at à sample of eight. X-ray emitting clusters. noted that the problem is more general: although MOND reduced the Newtonian discrepancy by a [actor of 10. there is still a need for dark matter. particularly,"1992), looking at a sample of eight X-ray emitting clusters, noted that the problem is more general: although MOND reduced the Newtonian discrepancy by a factor of 10, there is still a need for dark matter, particularly" +Massive star lorming regions are marked by small (<0.1 pc) LIT regions (Gameetal.2005) that are characteristicallv different [rom many of the few thousand,"Massive star forming regions are marked by small $\leq 0.1$ pc) HII regions \citep{Gaume1995b, Depree1997, Tieftrunk1997, Depree1998, +Wilson2003, Depree2000, Depree2004, Depree2005} that are characteristically different from many of the few thousand" +"Therefore, we may diagnose ambiguous pixels (i.e heavy E/B mixing) by comparing(B2(&)) with (B2 (8), where (B2(fü) is the local power contributed by B mode and given by replacing 'E' with ‘B’ inEq. 22,","Therefore, we may diagnose ambiguous pixels (i.e heavy E/B mixing) by comparing$\langle \tilde B^2_E(\mathbf {\hat n})\rangle$ with $\langle \tilde B^2_B(\mathbf {\hat n})\rangle$ , where $\langle \tilde B^2_B(\mathbf {\hat n})\rangle$ is the local power contributed by B mode and given by replacing `E' with `B' inEq. \ref{leakage_power}," + 23 and 24.., \ref{QU_E1} and \ref{QU_E2}. . +" However, estimating Eq. 22,,"," However, estimating Eq. \ref{leakage_power}," + 23 and 24 is prohibitively complicated., \ref{QU_E1} and \ref{QU_E2} is prohibitively complicated. +" Therefore, we are going to resort to Monte-Carlo simulations in order to estimate (B2.(8)/(B2.(f))."," Therefore, we are going to resort to Monte-Carlo simulations in order to estimate $\langle \tilde B^2_E(\mathbf {\hat n})\rangle/\langle \tilde B^2_B(\mathbf {\hat n})\rangle$." +" Depending (52.($))/(B2(&)), we may classify the pixel at fi as ‘pure’ and *ambiguous'."," Depending $\langle \tilde B^2_E(\mathbf {\hat n})\rangle/\langle \tilde B^2_B(\mathbf {\hat n})\rangle$, we may classify the pixel at $\mathbf{\hat n}$ as `pure' and `ambiguous'." +" To be specific, we may retain pixels satisfying: where r is the assumed tensor-to-scalar ratio of Monte-Carlo simulation, from which (52.(8))/(7,8) is estimated."," To be specific, we may retain pixels satisfying: where $r$ is the assumed tensor-to-scalar ratio of Monte-Carlo simulation, from which $\langle \tilde B^2_E(\mathbf {\hat n})\rangle/\langle \tilde B^2_B(\mathbf {\hat n})\rangle$ is estimated." +" Therefore, the level of leakage in retainedpixels is comparable to the primordial B mode power spectrum of tensor-to-scalar ratio τς."," Therefore, the level of leakage in retainedpixels is comparable to the primordial B mode power spectrum of tensor-to-scalar ratio $r_c$." +" In Fig. 4,,"," In Fig. \ref{f_sky}," +" we show the sky fraction for various r;, given a foreground mask shown in Fig. 7.."," we show the sky fraction for various $r_c$, given a foreground mask shown in Fig. \ref{mask}." +" Since sky fraction decreases with lower r., we may not simply set τς to a lowest value."," Since sky fraction decreases with lower $r_c$, we may not simply set $r_c$ to a lowest value." +" Therefore, we need to derive an optimal r,, which minimizes the estimation error."," Therefore, we need to derive an optimal $r_c$, which minimizes the estimation error." + The estimation error of B mode power spectrum is given by: where N; is noise power spectrum., The estimation error of B mode power spectrum is given by: where $N_l$ is noise power spectrum. +" Note that the leakage does not bias the B mode power spectrum estimation, but increases the variance, when the power spectrum estimation is made by a pseudo-C; method and leakage is taken care of (??).."," Note that the leakage does not bias the B mode power spectrum estimation, but increases the variance, when the power spectrum estimation is made by a $C_l$ method and leakage is taken care of \citep{Master_power,Grain_mixing}." +" By requiring ὃAC?/dr,= 0, we get In Fig. 5,,"," By requiring $\partial\,\Delta C^{BB}_l/\partial r_c=0$ , we get In Fig. \ref{dlnf}," + we plot the left and right hand side of Eq., we plot the left and right hand side of Eq. +" 27 for the noise level of Planck HFI instrument, and the multipole |=86, which is the peak multipole of primordial B mode power spectrum."," \ref{derivative} for the noise level of Planck HFI instrument, and the multipole $l=86$, which is the peak multipole of primordial B mode power spectrum." +" From Fig. 5,,"," From Fig. \ref{dlnf}, ," + we find curves intersect at re~4x10? with weak dependence on r., we find curves intersect at $r_c\approx 4\times 10^{-2}$ with weak dependence on $r$. +" It should be noted that the weak dependence is due to the low signal-to-noise ratio of the considered experiment (i.e. N;/C??(r=1)> 0), and the dependence on r is not weak in general."," It should be noted that the weak dependence is due to the low signal-to-noise ratio of the considered experiment (i.e. $N_l/C^{BB}_l(r=1)\gg0$ ), and the dependence on $r$ is not weak in general." +" We are going to use r,&4x107 for the simulation in the next section.", We are going to use $r_c\approx 4\times 10^{-2}$ for the simulation in the next section. +" Using the WMAP concordance ACDM model, we have simulated Stokes parameter Q and U over a whole-sky with a HEALPix pixel resolution (Nside=1024) and 10’ FWHM beam."," Using the WMAP concordance $\Lambda$ CDM model, we have simulated Stokes parameter Q and U over a whole-sky with a HEALPix pixel resolution (Nside=1024) and $10'$ FWHM beam." + We have made the inputmap to contain no B mode polarization., We have made the inputmap to contain no B mode polarization. +" Therefore, any non-zero values in output B map are attributed to leakage."," Therefore, any non-zero values in output B map are attributed to leakage." +" We show our simulated polarization map in Fig. 6,,"," We show our simulated polarization map in Fig. \ref{input}," + where the orientation and length of headless arrows indicates polarization angle and amplitude respectively., where the orientation and length of headless arrows indicates polarization angle and amplitude respectively. +" Note that the polarization map shows only gradient-like patterns, because they contain only E mode polarization."," Note that the polarization map shows only gradient-like patterns, because they contain only E mode polarization." + It is well-known that E/B mixing increases with the length of cut sky boundary (?).., It is well-known that E/B mixing increases with the length of cut sky boundary \citep{Bunn:EB-Separation}. +" We have combined the WMAP team's polarization mask with the point source mask, and prograded it to Nside=1024."," We have combined the WMAP team's polarization mask with the point source mask, and prograded it to Nside=1024." +" In order to reduce sharp boundaries, we have smoothed the mask with 1.5? FWHM Gaussian kernel."," In order to reduce sharp boundaries, we have smoothed the mask with $1.5^\circ$ FWHM Gaussian kernel." + We have referred to the WMAP team's boundary smoothing process of Internal Linear Combination map (?).., We have referred to the WMAP team's boundary smoothing process of Internal Linear Combination map \citep{WMAP3:temperature}. . +" Nevertheless, itshould be noted that smoothed boundary is not essential to our method, and furtherimprovement may bepossible by using more sophisticated smoothing kernel (?).."," Nevertheless, itshould be noted that smoothed boundary is not essential to our method, and furtherimprovement may bepossible by using more sophisticated smoothing kernel \citep{edge_taper}. ." +" In Fig. 7,,"," In Fig. \ref{mask},," +" we show our smoothed mask, whose sky fraction amounts to 0.71."," we show our smoothed mask, whose sky fraction amounts to $0.71$ ." += + 250 K aud logg = + 0.5. aud these caleculatious confirmed the result obtained above.,"= $\pm$ 250 $K$ and $\log{g}$ = $\pm$ 0.5, and these calculations confirmed the result obtained above." +" ""Thus. the spectral analvsis shows that the atmosphere of RZ Psc has a huge excess of Lithium (about LOO times he solar abundance) aud. according to this criterion. RZ Psc is not vet a main sequence star."," Thus, the spectral analysis shows that the atmosphere of RZ Psc has a huge excess of lithium (about 100 times the solar abundance) and, according to this criterion, RZ Psc is not yet a main sequence star." + The considerably uel (for this spectral type) value of esins agrees with lis conclusion (see the discussion bv Bouvier (2008))).," The considerably high (for this spectral type) value of $v\,\sin{i}$ agrees with this conclusion (see the discussion by Bouvier \cite{Bo}) )." + Ou the other hand. in the atmospheres of voung solar-ype stars CE Tauri stars) the excess of αι is usually uuch ereater than iu our case (see Fig.," On the other hand, in the atmospheres of young solar-type stars (T Tauri stars) the excess of lithium is usually much greater than in our case (see Fig." + 2aa )., \ref{Ple}a a ). + For example. τίς Per (about the same spectral type as RZ Psc) has a lithium excess equals to about 3.2-3.5 dex (Caimin ct al. (2008))).," For example, V718 Per (about the same spectral type as RZ Psc) has a lithium excess equals to about 3.2-3.5 dex (Grinin et al. \cite{Grin08}) )," + which is indicative of a primordial Li abuudauce (Pavleuko Magazzu (1996)))., which is indicative of a primordial Li abundance (Pavlenko Magazzu \cite{Pav}) ). + From this point of view. RZ Psc is nof anv more a voung star.," From this point of view, RZ Psc is not any more a young star." + To estimate its age. we used the rough calibration of Li excess as a function of age for clusters of different ages (Nine 1993: Soderblom et i. (1990: 1993):," To estimate its age, we used the rough calibration of Li excess as a function of age for clusters of different ages (King 1993; Soderblom et al. \cite{Sod90,Sod93}; ;" + Sestito Rancdich 2005)., Sestito Randich 2005). + Our analysis of these data shows (see Fig. 2)), Our analysis of these data shows (see Fig. \ref{Ple}) ) + that the excess of Li iu the atiiosphere of RZ Psc corresponds approximately to a stellar age between the age of the Pleiades (about 70 Myr) id the Orion (about 10 Myr) clusters., that the excess of Li in the atmosphere of RZ Psc corresponds approximately to a stellar age between the age of the Pleiades (about 70 Myr) and the Orion (about 10 Myr) clusters. + It is admittedly rough estimate. talking iuto account the high dispersion of Li abundance versus age in both clusters.," It is admittedly a rough estimate, taking into account the high dispersion of Li abundance versus age in both clusters." + Nevertheless. this estimate qualitatively aerees with the abseuce of IR excess in RZ Psc aud its isolated position far from the star-formine regions.," Nevertheless, this estimate qualitatively agrees with the absence of IR excess in RZ Psc and its isolated position far from the star-forming regions." + Another possibility to estimate the age of RZ Psc is the proper motion of the star., Another possibility to estimate the age of RZ Psc is the proper motion of the star. + According to the Tycho-2 catalog by Moe et al. (2000)..," According to the Tycho-2 catalog by Hog et al. \cite{Hog}," + the proper motion of RZ Pse is quite large: piuRA = 25.4 £ 2 mas ο. pmDE = -11.9 + 2.1 mas |.," the proper motion of RZ Psc is quite large: pmRA = 25.4 $\pm$ 2 mas $^{-1}$, pmDE = -11.9 $\pm$ 2.1 mas $^{-1}$." + The conespoudius values of the proper motion in the ealactic coordinate svsteni are: pui=7.89£0.60 dee., The corresponding values of the proper motion in the galactic coordinate system are: $l = 7.89\pm 0.60$ deg. + per Myr. pind = -2.7640.19 dee.," per Myr, $b$ = $\pm 0.49$ deg." + per Myr., per Myr. + Asstuning that RZ Psc has not moved away very far frou its birthplace ucar to the Galaxy. plane (GP). onecan calculate the vertical component of its motion [V ," Assuming that RZ Psc has not moved away very far from its birthplace near to the Galaxy plane (GP), onecan calculate the vertical component of its motion $W$ " +located at the Sedgwick Reserve. a part of the University of California Natural Reserve System.,"located at the Sedgwick Reserve, a part of the University of California Natural Reserve System." + This paper uses observations obtained with the FTN observatory of the Las Cumbres Observatory Global Telescope., This paper uses observations obtained with the FTN observatory of the Las Cumbres Observatory Global Telescope. + ALK was supported by NASA through Hubble Fellowship grant 51257.01 awarded by STScL which is operated by AURA. Inc.. for ANSA. under contract NAS 5-26555.," ALK was supported by NASA through Hubble Fellowship grant 51257.01 awarded by STScI, which is operated by AURA, Inc., for ANSA, under contract NAS 5-26555." + The Robo-AO system is supported by collaborating partner institutions. the California Institute of Technology and the Inter-University Centre for Astronomy and Astrophysics. and by the National Science Foundation. under Grant Nos.," The Robo-AO system is supported by collaborating partner institutions, the California Institute of Technology and the Inter-University Centre for Astronomy and Astrophysics, and by the National Science Foundation under Grant Nos." + AST-0906060 and AST-0960343., AST-0906060 and AST-0960343. + AVF and his group at UC Berkeley acknowledge generous financial assistance from Gary Cynthia Bengier. the Richard Rhoda Goldman Fund. the TABASGO Foundation. and NSF grant AST-0908886.," AVF and his group at UC Berkeley acknowledge generous financial assistance from Gary Cynthia Bengier, the Richard Rhoda Goldman Fund, the TABASGO Foundation, and NSF grant AST-0908886." + This research has also made use of the SIMBAD database. operated at CDS. Strasbourg. France.," This research has also made use of the SIMBAD database, operated at CDS, Strasbourg, France." + We recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawanan community., We recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. +" We are most fortunate to have the opportunity to conduct observations from this mountain,", We are most fortunate to have the opportunity to conduct observations from this mountain. +the Potsdam group for Wolf-Itavet. stars (defined as having surface hydrogen mass [fraction Y0.4 ancl log(Z;4rfly) 1),"the Potsdam group for Wolf-Rayet stars (defined as having surface hydrogen mass fraction $X \le 0.4$ and $\log(T_{\rm eff}/{\rm K}) \ge +4$ )." + These are advanced: atmosphere models that can be related. directly o stellar evolution models., These are advanced atmosphere models that can be related directly to stellar evolution models. + We use not only the publicly available models for WN stars but also a set of WC moclels rom the same group that are preliminary results (λα. Llamann A. Darniske. private communication).," We use not only the publicly available models for WN stars but also a set of WC models from the same group that are preliminary results (W.-R. Hamann A. Barniske, private communication)." + We have compared the atmosphere models to low resolution spectra oocduced. by and. find ο similar results to those from these more detailed models., We have compared the atmosphere models to low resolution spectra produced by and find broadly similar results to those from these more detailed models. + These represent an important step forwards to ooducing a synthetic population spectrum rather than one based on οΠου to interpret empirical observations., These represent an important step forwards to producing a synthetic population spectrum rather than one based on difficult to interpret empirical observations. + These models are on a grid of transformed radius and ellective temperature which we interpolate linearly between the values of our stellar models., These models are on a grid of transformed radius and effective temperature which we interpolate linearly between the values of our stellar models. + We use the Potsdam. WIR atmosphere models in. the parameter space they cover when XN.x0.2 and log(Zuifly) 4.45)., We use the Potsdam WR atmosphere models in the parameter space they cover when $X \le 0.2$ and $\log(T_{\rm eff}/{\rm K}) \ge 4.45$ ). + We use the WNL models when 0.2zX=0.1., We use the WNL models when $0.2 \ge X \ge 0.1$. + When 0.1=XNm0001 we interpolate between the WNL models and the WNI models., When $0.1 \ge X \ge 0.01$ we interpolate between the WNL models and the WNE models. + We use the WNE models alone when Xox0.01., We use the WNE models alone when $X \le 0.01$. + To determine when to switch to WC models we use the variable a=Gro|co)/gy where ure. re and y are the abundance by number of carbon. oxvecn and. helium respectively.," To determine when to switch to WC models we use the variable $\alpha=(x_{\rm C}+x_{\rm O})/y$ where $x_{\rm C}$, $x_{\rm O}$ and $y$ are the abundance by number of carbon, oxygen and helium respectively." + When a>0.01 we begin to interpolate between the WNE and WC atmosphere models until a>0.26., When $\alpha > 0.01$ we begin to interpolate between the WNE and WC atmosphere models until $\alpha>0.26$. + Phis value is chosen as it is the value of the composition. of the atmosphere model., This value is chosen as it is the value of the composition of the atmosphere model. + Above this value we use the WC atmosphere model alone., Above this value we use the WC atmosphere model alone. + This scheme omits a subset of stars that. should. be included as WI stars. those with 4xlog(Tr/lIx)=4.45 ancl 0.3«X0.4.," This scheme omits a subset of stars that should be included as WR stars, those with $4 \le \log(T_{\rm eff}/{\rm K}) \le 4.45$ and $0.2 +\le X \le 0.4$." + For these stars no niocel WR star spectra exist. so we use the corresponding BaSeL or OB spectra but mocified to include the line luminosities of the Holl line at aand the WR blue bump contributed by these stars.," For these stars no model WR star spectra exist, so we use the corresponding BaSeL or OB spectra but modified to include the line luminosities of the HeII line at and the WR blue bump contributed by these stars." + We use the empirical line Iuminosities given in for WNL stars rather than the older values in(1998)., We use the empirical line luminosities given in for WNL stars rather than the older values in. +. We only apply this correction if the star has a luminosity above log(L/L.)z4.9 to prevent a larec contribution to these features due to lower mass stars at [ate times., We only apply this correction if the star has a luminosity above $\log(L/L_{\odot})\ge 4.9$ to prevent a large contribution to these features due to lower mass stars at late times. + By using fixed line Iuminosities given in Table 1. at our assumed Luminosity limit. LO percent of the total stellar emission is in these lines.," By using fixed line luminosities given in Table \ref{brinchman_lums} at our assumed luminosity limit, 10 percent of the total stellar emission is in these lines." + Phis proportion would be larger if we included these line Iuminosities for less luminous stars., This proportion would be larger if we included these line luminosities for less luminous stars. + 1n it was found that this uminosity limit was necessary to reproduce the observed ratio of the number of WC to WN stars., In it was found that this luminosity limit was necessary to reproduce the observed ratio of the number of WC to WN stars. + In Table 2 we show he mean line luminosities predicted for all WIR stars in our svnthetic population., In Table \ref{lineluminosities} we show the mean line luminosities predicted for all WR stars in our synthetic population. + We find that in general we predict slightly lower mean line luminosities than those derived rom observations. but they are similar in magnitude.," We find that in general we predict slightly lower mean line luminosities than those derived from observations, but they are similar in magnitude." + For he WINE stars this is because the Potsdam. atmosphere models provide smaller line luminosities than suggested by ‘Table 1.., For the WNL stars this is because the Potsdam atmosphere models provide smaller line luminosities than suggested by Table \ref{brinchman_lums}. + The WINE line Iuminosities caleulated from the Potsdam atmosphere models do agree in general with the ine luminosities in Table 1.., The WNE line luminosities calculated from the Potsdam atmosphere models do agree in general with the line luminosities in Table \ref{brinchman_lums}. + Phe largest mismatch is for the Xue WR bump line Luminosity., The largest mismatch is for the blue WR bump line luminosity. + ‘Table 2. lists the mean line luminosities at cdilferent metallicities., Table \ref{lineluminosities} lists the mean line luminosities at different metallicities. + The Potsdam Woll-Ravet atmosphere mocels only exist for solar metallicity., The Potsdam Wolf-Rayet atmosphere models only exist for solar metallicity. + However it is possible to use them at other metallicitics because the helium. carbon. nitrogen and oxygen composition of Woll-Ravet stars. is almost independent. of initial metallicity anc is determined by the core nuclear burning reactions.," However it is possible to use them at other metallicities because the helium, carbon, nitrogen and oxygen composition of Wolf-Rayet stars is almost independent of initial metallicity and is determined by the core nuclear burning reactions." + The slight. changes that co occur are accounted for by the lower iron opacity in the evolution models. making the surface temperature ancl radius of the mocelled stars greater and smaller respectively.," The slight changes that do occur are accounted for by the lower iron opacity in the evolution models, making the surface temperature and radius of the modelled stars greater and smaller respectively." + This biases the population towards. earlier. Wolf-Iavet spectra at lower metallicities., This biases the population towards earlier Wolf-Rayet spectra at lower metallicities. + However as Table 2. shows at the lowest metallicities we vastly overpredict the mean line luminosities by using these atmosphere models. unaltered., However as Table \ref{lineluminosities} shows at the lowest metallicities we vastly overpredict the mean line luminosities by using these atmosphere models unaltered. + Therefore we adapt the scheme of in that below one-Lilth solar metallicity we use the reduced. line luminosities for WNL stars ancl also reduce the line strengths of the Hell anc WR blue bump in the Potsdam atmosphere models by a factor of a fifth as indicated [rom the observations of(2006)., Therefore we adapt the scheme of in that below one-fifth solar metallicity we use the reduced line luminosities for WNL stars and also reduce the line strengths of the HeII and WR blue bump in the Potsdam atmosphere models by a factor of a fifth as indicated from the observations of. +. This leads toa closer match to the observed mean ine luminosities., This leads toa closer match to the observed mean line luminosities. + We were uncertain whether to use the reduced line strengths at a metallicity of Z=0.004 or not., We were uncertain whether to use the reduced line strengths at a metallicity of $Z=0.004$ or not. + We calculated. a third set. of model spectra with the line uminosities at this metallicity reduce bv an intermediate value of three fifths., We calculated a third set of model spectra with the line luminosities at this metallicity reduced by an intermediate value of three fifths. + In Table 20 we see that the resulting mean line luminosities are only slightIv ess than those at the ugher metallicity of Z=0.008., In Table \ref{lineluminosities} we see that the resulting mean line luminosities are only slightly less than those at the higher metallicity of $Z=0.008$. + Ht is more physical to expect a gradual reduction in line luminosities with metallicity rather than a sharp drop., It is more physical to expect a gradual reduction in line luminosities with metallicity rather than a sharp drop. + Vherefore in the rest of this paper we alter the line strengths at Z=0.004 by three fifths in the Potsdam models and use the mean of the values listed in Table 1. for the WNL stars not covered by the Potsdam models.," Therefore in the rest of this paper we alter the line strengths at $Z=0.004$ by three fifths in the Potsdam models and use the mean of the values listed in Table \ref{brinchman_lums} + for the WNL stars not covered by the Potsdam models." + The second empirical input into the stellar spectra is to take account of Of stars., The second empirical input into the stellar spectra is to take account of Of stars. + For those we again use the method of(2008).. enhancing the equivalent width of certain emission lines in the O star spectrum when the gravity of the O star is less than that of Of stars as described by(1999).," For those we again use the method of, enhancing the equivalent width of certain emission lines in the O star spectrum when the gravity of the O star is less than that of Of stars as described by." +.. As discussed. by(2008)... Of stars must be accounted for to create an accurate spectrum at low metallicity.," As discussed by, Of stars must be accounted for to create an accurate spectrum at low metallicity." + These are the most luminous type of O star ancl have broad emission lines. but diller from. Wolf-Ravet stars.," These are the most luminous type of O star and have broad emission lines, but differ from Wolf-Rayet stars." + Pherefore when the surface temperature of a model is greater than 33kIx. and the gravity is less than 3.676loe(LiyefIN) 13.253. we supplement the LeLE emission lines at. aanc tto produce line luminosities of 20 and. 1.6LO”cress respectively.," Therefore when the surface temperature of a model is greater than 33kK and the gravity is less than $3.676 \log(T_{\rm eff}/{\rm + K}) -13.253$ , we supplement the HeII emission lines at and to produce line luminosities of $20$ and $1.6 \times +10^{35}{\rm ergs \, s^{-1}}$ respectively." +In this section we applied our model to a (vpical and particular planet. sample: TID 209458b with the radius of 1.4 Ry. the mass of 0.7 M; and the semi-major axis of 0.05 (Murrav-Clay. et al.,"In this section we applied our model to a typical and particular planet sample: HD 209458b with the radius of 1.4 $R_{J}$, the mass of 0.7 $M_{J}$ and the semi-major axis of 0.05 (Murray-Clay et al." + 2009)., 2009). + The upper Ilmit on the observed orbital eccentricity is Q.023(Ibgui Burrows 2009). so we assumed a circular orbit in the ealeulations.," The upper limit on the observed orbital eccentricity is 0.028(Ibgui Burrows 2009), so we assumed a circular orbit in the calculations." + The mass of host star is 1M..., The mass of host star is $M_{\odot}$. + The results for ID 209458b are shown and the single-[h1id results of Alurray-Clay et al. (, The results for HD 209458b are shown and the single-fluid results of Murray-Clay et al. ( +2009) are also plotted in Fie.l.,2009) are also plotted in Fig.1. + Seen [rom Fig.l clearly. except for a detailed difference. (he multi-fIuid model predicts much Che same trends of temperature. velocity ancl particle number densitv as Che single-fliid model does.," Seen from Fig.1 clearly, except for a detailed difference, the multi-fluid model predicts much the same trends of temperature, velocity and particle number density as the single-fluid model does." + The number density of atomic hydrogen decreases (upper left of Fie., The number density of atomic hydrogen decreases (upper left of Fig. + 1) and the ionization fraction increases with radius (lower right of Fig., 1) and the ionization fraction increases with radius (lower right of Fig. + 1)., 1). +" The fact that as much as of hvdrogen at 2=54, is ionized is a consequence of being irradiated bv host star.", The fact that as much as of hydrogen at $R=5R _{p}$ is ionized is a consequence of being irradiated by host star. + With the increase of radius the optical depth becomes smaller. even near to zero. thus the radiation from star can lreely penetrate the wind and ionize particles.," With the increase of radius the optical depth becomes smaller, even near to zero, thus the radiation from star can freely penetrate the wind and ionize particles." +" Current. studies show the wind temperature can attain 5000-1000 at about 272, (Yelle 2004: Tian et al.", Current studies show the wind temperature can attain 8000-10000K at about $R_{p}$ (Yelle 2004; Tian et al. + 2005: Garcia Munoz 2007: Penz οἱ al., 2005; Garcia Munoz 2007; Penz et al. + 2008: Murray-Clay el al., 2008; Murray-Clay et al. + 2009) and our results also verily the fact., 2009) and our results also verify the fact. + The cooling by radiation and. PAV work make (he temperature reduced from 3000I. ancl decrease to about. 0001 in the upper atmosphere., The cooling by radiation and PdV work make the temperature reduced from 8000K and decrease to about 5000K in the upper atmosphere. + The inversion of temperature in the upper alinosphere is a (vpical feature of planetary alinosphere., The inversion of temperature in the upper atmosphere is a typical feature of planetary atmosphere. + To compare our results with the results of other hvdrodynanmic models (Yelle 2004: Tian et al., To compare our results with the results of other hydrodynamic models (Yelle 2004; Tian et al. + 2005: Gareia Munoz 2007: Penz et al., 2005; Garcia Munoz 2007; Penz et al. + 2008 ancl \lurray-Clay et al., 2008 and Murray-Clay et al. + 2009). we found that all models obtain similar temperature profiles besides (he model of Tian et al. (," 2009), we found that all models obtain similar temperature profiles besides the model of Tian et al. (" +2005) which predicts a monotonously increasing temperature profile ancl a higher velocity structure.,2005) which predicts a monotonously increasing temperature profile and a higher velocity structure. + A possible reason is that Tian et al.(2005) applied a higher radiative heating., A possible reason is that Tian et al.(2005) applied a higher radiative heating. +"parameter values lies withing the given range, given the physical assumptions of the model.","parameter values lies withing the given range, given the physical assumptions of the model." +" In reffig:15014, ridweshow68, 90, and95percentcon , /parameterspace."," In \\ref{fig:15014_grid} we show 68, 90, and 95 percent confidence limits in two-dimensional , parameter space." +"W ecalculateagridof model s(typically36by36), opt évitamygth ddth figfireeharwmalees (gfuBt4henormalization, inthiscase)ateaci (Pressetal.2007) to define the extent of the confidence limits."," We calculate a grid of models (typically 36 by 36), optimizing the other free parameters (just the normalization, in this case) at each point in the grid, and use values of $\Delta{\rm C} = 2.30, 4.61, +6.17$ \citep{Press2007} to define the extent of the confidence limits." +" Plots such as this one are a good means of examining correlations between model parameters, in terms of their abilities to produce similar features in the line profiles."," Plots such as this one are a good means of examining correlations between model parameters, in terms of their abilities to produce similar features in the line profiles." + We can see what the trade offs are between parameters in a quantitative way., We can see what the trade offs are between parameters in a quantitative way. +" For example, there is à fidencelimitsintwaedest anti-correl"," For example, there is a modest anti-correlation between and evident in the figure." +ation between and (shock onset close to the photosphere) reduce emission on the line wing relative to the core (because there is more emitting material at low velocity)., Low values of (shock onset close to the photosphere) reduce emission on the line wing relative to the core (because there is more emitting material at low velocity). +" So although low values of (hot plasma as close as 1.15 Π.)) are allowed at the 95 percent confidence limit, they require a large wind optical"," So although low values of (hot plasma as close as 1.15 ) are allowed at the 95 percent confidence limit, they require a large wind optical" +shows the angular beam. separation 9 as a function of lens redshift for certain values of the [lens mass and source redshift.,shows the angular beam separation $\delta$ as a function of lens redshift for certain values of the lens mass and source redshift. + From a qualitative point of view. the curves resemble the curve for the shallow power law case in3.," From a qualitative point of view, the curves resemble the curve for the shallow power law case in." +. This is not surprising. since the NEW profile is shallower than isothermal inside the scale radius ry. and the Einstein radius is (much) less than the scale racius for all cases of interest.," This is not surprising, since the NFW profile is shallower than isothermal inside the scale radius $r_s$, and the Einstein radius is (much) less than the scale radius for all cases of interest." +" The 8(z,)) curves peak at a redshift which is about half that of the source.", The $\delta(z_{\rm l})$ curves peak at a redshift which is about half that of the source. + This is curious but coincidental: it arises from the cdillerent redshift dependences of the image positions and. deflection angles., This is curious but coincidental; it arises from the different redshift dependences of the image positions and deflection angles. +" shows 9 along with its four consituents: the image positions €,» and dellection angles Aye. C"," shows $\delta$ along with its four consituents: the image positions $\theta_{1,2}$ and deflection angles ${\hat\alpha}_{1,2}$. (" +lhese are. plotted: in units of 65. but. that scale factor has a weak dependence on σι),"These are plotted in units of $\theta_0$, but that scale factor has a weak dependence on $z_l$ .)" + Neither the iniage position curves nor the dellection angle curves peak at 2./2: the image position curves peak at lower redshift. in keeping with the rule of thumb that a lens is most effecive when it is about half the to the source.," Neither the image position curves nor the deflection angle curves peak at $\sim z_{\rm s}/2$; the image position curves peak at lower redshift, in keeping with the rule of thumb that a lens is most effective when it is about half the to the source." + As far as we can tell. it is purely coincidental that the different redshift dependences cause the peak of the ὁ curve to be located at ," As far as we can tell, it is purely coincidental that the different redshift dependences cause the peak of the $\delta$ curve to be located at $\sim z_{\rm s}/2$." +Another interesting point from is that the angular beam separation is quite insensitive to the source position even though its constituents do depend on ο., Another interesting point from is that the angular beam separation is quite insensitive to the source position even though its constituents do depend on $\beta$ . +" This is because the imageposition and deflection angle depend on ina similar wav: as 3 increases. 8, and A, both increase while 6 and à» both decrease (in amplitude)."," This is because the imageposition and deflection angle depend on $\beta$ in a similar way: as $\beta$ increases, $\theta_1$ and ${\hat\alpha}_1$ both increase while $\theta_2$ and ${\hat\alpha}_2$ both decrease (in amplitude)." + The way these terms combine to form the angular beam separation means the changes largely cancel and. leave ὃ relatively insensitive to j., The way these terms combine to form the angular beam separation means the changes largely cancel and leave $\delta$ relatively insensitive to $\beta$. + To illustrate one way of interpreting the 9. values. Let us consider lensing of a beamed source.," To illustrate one way of interpreting the $\delta$ values, let us consider lensing of a beamed source." + Depending on the angular beam separation 6 ancl the jet opening 6;4. here may be configurations in which we see only a single image even though conventional lens theory (which assumes an isotropic source) would predict two.," Depending on the angular beam separation $\delta$ and the jet opening $\theta_{\rm jet}$, there may be configurations in which we see only a single image even though conventional lens theory (which assumes an isotropic source) would predict two." +" For example. in the imit that the angular beam separation is larger than the jet opening angle (9> 6,4). there is no way to arrange the jet such that we could see both images: we could. see one image or the other. or nothing at all (if the jet does not »»ut along either light rav). but never both images."," For example, in the limit that the angular beam separation is larger than the jet opening angle $\delta > \theta_{\rm jet}$ ), there is no way to arrange the jet such that we could see both images: we could see one image or the other, or nothing at all (if the jet does not point along either light ray), but never both images." + In this case the probability that we would “miss” one of the images xedieted by conventional lens theory is unity., In this case the probability that we would “miss” one of the images predicted by conventional lens theory is unity. + For ὃ«Gy there dis. some finite probability of missing one of the images., For $\delta < \theta_{\rm jet}$ there is some finite probability of missing one of the images. + Civen 9 and Gar. we use simple numerical simulations to consider all. possible jet orientations and. compute the conditional probability that one image is missed. given that at least one image is seen. (," Given $\delta$ and $\theta_{\rm jet}$, we use simple numerical simulations to consider all possible jet orientations and compute the conditional probability that one image is missed, given that at least one image is seen. (" +The conditional part of the probability just means we clo not consider cases where the jet is pointing “away” from us so that we cannot see anvthine.),The conditional part of the probability just means we do not consider cases where the jet is pointing “away” from us so that we cannot see anything.) + The results are shown in6., The results are shown in. +" In the limit ài,«1 we can derive à useful analytic approximation £zz(40)/(x6,4). which is also shown in the figure."," In the limit $\delta \ll \theta_{\rm jet} \ll 1$ we can derive a useful analytic approximation $P \approx (4\delta)/(\pi\theta_{\rm jet})$, which is also shown in the figure." +" Combining the probability results with the 9 values from4.. we deduce that there is some finite probability that a beamed source could. be ""Iensed? by a massive NEW cluster in such a way that we miss one of the images. and that this probability could be as high as P0.02 0.07(Hy,0.5"")1 depending on the redshift’ of the source."," Combining the probability results with the $\delta$ values from, we deduce that there is some finite probability that a beamed source could be “lensed” by a massive NFW cluster in such a way that we miss one of the images, and that this probability could be as high as $P \sim 0.02$ $0.07\,(\theta_{\rm jet}/{0.5}^\circ)^{-1}$ depending on the redshift of the source." + This probability is largest whenzi 2/2. (, This probability is largest when$z_{\rm l} \sim z_{\rm s}/2$ . ( +By contrast. the corresponding probability for a steep power law mass profile would become ever larger as zi ns),"By contrast, the corresponding probability for a steep power law mass profile would become ever larger as $z_{\rm l} \to z_{\rm s}$ .)" +in this paper tlal appropriate modifications to the standard formulae for the acoustic scale. the P paranieter. al Bie Bane nucleosyutliesis (BBNS) to allow for the possible importance «ark energy ab zz10? or 5=107 will lead to this exclusion automatically.,"in this paper that appropriate modifications to the standard formulae for the acoustic scale, the $\Gamma$ parameter, and Big Bang nucleosynthesis (BBNS) to allow for the possible importance dark energy at $z \approx 10^9$ or $z \approx 10^3$ will lead to this exclusion automatically." + The BBNS. acoustic scale and D limits are οἶνθι in general forms involving poets). which can be used for auy form of tle equation oL state.," The BBNS, acoustic scale and $\Gamma$ limits are given in general forms involving $\rho_{DE}(z)$, which can be used for any form of the equation of state." + But tl et—τςΕυ]--α) form adopted by the Dark Energy Task Force repor (Albrecht 22006) is used or all the specific plots in this paper., But the $w = w_\circ + w_a(1-a)$ form adopted by the Dark Energy Task Force report (Albrecht 2006) is used for all the specific plots in this paper. + This Dorm cau be used for all redshits without introducing a redshift eutoff which would be a new and otherwise uunuecessary parameter., This form can be used for all redshifts without introducing a redshift cutoff which would be a new and otherwise unnecessary parameter. + The distance modulus rredshift data from Riess, The distance modulus redshift data from Riess +The first bounds we consider are those associated with the observed branching ratio for the [Iavor-violating decay.,The first bounds we consider are those associated with the observed branching ratio for the flavor-violating decay. + JA hecombinedresult fromtheC LEOundBelleerperiments [20] 5BIR(b This is cousistent with the expected Standard Model result πα(p—55)23.32x10.1., The combined result from the CLEO and Belle experiments \cite{Yao:2006px} is This is consistent with the expected Standard Model result ${\rm BR}^{SM}(b\rightarrow s\gamma)=3.32\times10^{-4}$. + In moclels with a πομαμια] Higes sector. additional coutributious to the amplituce for )urisealllielooplevel [roidiagramsiuvoleiugvirbualehargedHiggsbosons.asdiscussedabove," In models with a non-minimal Higgs sector, additional contributions to the amplitude for arise at the loop level from diagrams involving virtual charged Higgs bosons, as discussed above." + DEhesediag ran, These diagrams are compiled in Fig. +tsarec in place of HA=..)," \ref{fig:btosgammaDiagrams} (SM contributions to this amplitude come from diagrams of the same sort, but with in place of .)" + The rate for the process can be calculated in the usual manner., The rate for the process can be calculated in the usual manner. + After incorporating the effect of QCD corrections (which can be quite large [23])). one finds that [13.2I] where ez(mi) is the coellicient of the elective operator in the conventions of Ref. [25]..," After incorporating the effect of QCD corrections (which can be quite large \cite{Deshpande:1987nr}) ), one finds that \cite{Barger:1989fj,Hou:1987kf} + where $c_7(m_b)$ is the coefficient of the effective operator in the conventions of Ref. \cite{Grinstein:1987pu}," + evaluated at the scale ay., evaluated at the scale $m_b$. + This coellicient takes the form where the weak-scale amplitude function ezCAAq) in the L2HDM is given by, This coefficient takes the form where the weak-scale amplitude function $c_7(M_W)$ in the L2HDM is given by +accurately reproduced.,accurately reproduced. + 21emFAST's under-prediction of the power spectrum enhancement at small scales is likely also attributable in part to the fact that the Nyquist frequency corresponds to larger scales in the 21e6mFAST boxes. since these are directly computed on a 256° grid. whereas the RT simulation is smoothed down from a 5127 erid.," 21cmFAST's under-prediction of the power spectrum enhancement at small scales is likely also attributable in part to the fact that the Nyquist frequency corresponds to larger scales in the 21cmFAST boxes, since these are directly computed on a $256^3$ grid, whereas the RT simulation is smoothed down from a $512^3$ grid." + This means that our shot noise on small scales in higher than the numerical simulations. and so fractional enhancements in power should be less (see below).," This means that our shot noise on small scales in higher than the numerical simulation's, and so fractional enhancements in power should be less (see below)." + Finally. we note that the curves in the bottom two panels in Fig.," Finally, we note that the curves in the bottom two panels in Fig." + 6 dip below unity at low &., \ref{fig:just_ratios} dip below unity at low $k$. + This means that during the final stages of reionizution. peculiar velocity effects actually power on moderate to large scales.," This means that during the final stages of reionization, peculiar velocity effects actually power on moderate to large scales." + Although not previously noted in the 21-em literature. this again can be readily understood: since reionization is “inside-out” on large scales. remaining neutral regions will preferentially be underdensities in the late stages.," Although not previously noted in the 21-cm literature, this again can be readily understood: since reionization is “inside-out” on large scales, remaining neutral regions will preferentially be underdensities in the late stages." +"Therefore as the average ὁ of the remaining neutral regions becomes negative on large scales. eo,/dr becomes preferentially positive. decreasing power through the (ονfdrsii|1) term in eq. I..","Therefore as the average $\delta$ of the remaining neutral regions becomes negative on large scales, $dv_r/dr$ becomes preferentially positive, decreasing power through the $1/(dv_r/dr/H + 1)$ term in eq. \ref{eq:delT}." + We contirm that both the mean signal and the large-scale power show this decrease due to peculiar velocities in the advanced stages of reionization. and it appears in both the simulations and 2|emFAST.," We confirm that both the mean signal and the large-scale power show this decrease due to peculiar velocities in the advanced stages of reionization, and it appears in both the simulations and 21cmFAST." + We now combine the terms from eq. (1) , We now combine the terms from eq. \ref{eq:delT}) ) +to provide a full comparison of 21e6mFAST and numerical simulations..," to provide a full comparison of 21cmFAST and numerical simulations,." +. For the purposes of these comparisons. the two codes only share the same initial density field: the evolved density. velocity and ionization fields for 2lemFAST are all generated self-consistently as explained above.," For the purposes of these comparisons, the two codes only share the same initial density field; the evolved density, velocity and ionization fields for 21cmFAST are all generated self-consistently as explained above." + In Fig. 7..," In Fig. \ref{fig:compare_slices}," +" we plot slices through the 67%), signal. generated from hydrodynamic simulation. the algorithm outlined inMF07"".. and 21emFAST. left to right columns."," we plot slices through the $\delT$ signal, generated from hydrodynamic simulation, the algorithm outlined in, and 21cmFAST, left to right columns." + Rows correspond to (z.rH) = (9.00. 0.86). (7.73. 0.65). (7.04. 0.38). and (6.71. 0.20). top to bottom.," Rows correspond to $(z, \avenf)$ = (9.00, 0.86), (7.73, 0.65), (7.04, 0.38), and (6.71, 0.20), top to bottom." + As already shown in 32.1. the density fields are modeled quite accurately with perturbation theory.," As already shown in \ref{sec:den}, the density fields are modeled quite accurately with perturbation theory." + One can also see that both semi-numerical schemes reproduce the large-scale HI region morphology (shown in black) of the RT simulations., One can also see that both semi-numerical schemes reproduce the large-scale HII region morphology (shown in black) of the RT simulations. + Differences emerge at moderate to small scales. with the FFRT ionization algorithm of 21emFAST generally resulting in HII regions which are too connected.," Differences emerge at moderate to small scales, with the FFRT ionization algorithm of 21cmFAST generally resulting in HII regions which are too connected." + This difference is mostly attributable to the bubble flagging algorithm: in general the “flagging-the-entire-sphere” algorithm of MFO7 better reproduces HII morphological structure than the “flagging-the-central-cell” algorithm of ?. (e.g. MFO7)}., This difference is mostly attributable to the bubble flagging algorithm; in general the ``flagging-the-entire-sphere'' algorithm of MF07 better reproduces HII morphological structure than the “flagging-the-central-cell” algorithm of \citet{Zahn07} (e.g. MF07). + In Fig. 8..," In Fig. \ref{fig:delT_pdfs}," +" we show the PDFs of 67), for the hydrodynamic simulation curves). 21emFAST curves). and MFO7curves)."," we show the PDFs of $\delT$ for the hydrodynamic simulation ), 21cmFAST ), and MF07." + Panels correspond to (2.μι) = (9.00. 0.86). (7.73. 0.65). (7.04. 0.38). and (6.71. 0.20). top to bottom.," Panels correspond to $(z, \avenf)$ = (9.00, 0.86), (7.73, 0.65), (7.04, 0.38), and (6.71, 0.20), top to bottom." +" The left panel was generated using the unfiltered 375, field with cell length A. = 143/256 Mpe teffectively 2—0.35 Mpe). while the right panel was generated from the 27; field. filtered on ye=5 Mpe seules."," The left panel was generated using the unfiltered $\delT$ field with cell length $\Delta x$ = 143/256 Mpc (effectively $R\sim 0.35$ Mpc), while the right panel was generated from the $\delT$ field, filtered on $R_{\rm filter} = 5$ Mpc scales." +" From the left panel. we see that we under-predict the number of ""almost"" fully-ionized cells. 97;<10 mK. This can be traced to our algorithm for determining the partial ionized fraction in the remaining neutral cells."," From the left panel, we see that we under-predict the number of “almost” fully-ionized cells, $\delT \lsim 10$ mK. This can be traced to our algorithm for determining the partial ionized fraction in the remaining neutral cells." + Our algorithm assumes that cells are partially ionized by sub-grid sources chewing away at their host cell’s HI., Our algorithm assumes that cells are partially ionized by sub-grid sources chewing away at their host cell's HI. + Instead. partially ionized cells on these small scales generally correspond to unresolved ionization fronts from non-local sources (see Appendix in ?)).," Instead, partially ionized cells on these small scales generally correspond to unresolved ionization fronts from non-local sources (see Appendix in \citealt{Zahn10}) )." + This discrepancy decreases as the cell size increases. since then the fraction of cells which are ionized by sources internal to the cell increases. and the assumption implicit in our FFRT algorithm becomes increasingly accurate.," This discrepancy decreases as the cell size increases, since then the fraction of cells which are ionized by sources internal to the cell increases, and the assumption implicit in our FFRT algorithm becomes increasingly accurate." + Aside from this. the distributions in the left panel agree very well.," Aside from this, the distributions in the left panel agree very well." +" This should not be surprising. since for comparison the ionization efficiency of the semi-numerical schemes was chosen so that the mean ionized fraction at these epochs agrees with the numerical simulation (i.e. the spikes at 07),=0 mKmatch)"". The remainder of the signal at 075,z10 mK merely reflects the density distribution of the neutral cells. and we have already demonstrated in $2.1. that our density fields match the hydrodynamic simulation quitewell*?."," This should not be surprising, since for comparison the ionization efficiency of the semi-numerical schemes was chosen so that the mean ionized fraction at these epochs agrees with the numerical simulation (i.e. the spikes at $\delT=0$ mK. The remainder of the signal at $\delT \gsim 10$ mK merely reflects the density distribution of the neutral cells, and we have already demonstrated in \ref{sec:den} that our density fields match the hydrodynamic simulation quite." +. The right panel of Fig., The right panel of Fig. + 8 shows the O7; distributions. smoothed on fie:=5 Mpe scales.," \ref{fig:delT_pdfs} shows the $\delT$ distributions, smoothed on $R_{\rm filter} = 5$ Mpc scales." + As evidenced by the smaller relative spike at 97;=0 mK. the ionization fields on these scales are not as binary (i.e. either fully ionized or fully neutral) as those in the left panel.," As evidenced by the smaller relative spike at $\delT=0$ mK, the ionization fields on these scales are not as binary (i.e. either fully ionized or fully neutral) as those in the left panel." + Thus the PDFs encode more information on the ionization algorithms., Thus the PDFs encode more information on the ionization algorithms. + The top panel at μι=0.86. shows that the predicted distributions of 575 agree well around the mean signal. but the semi-numerical schemes diverge from the RT in the wings.," The top panel at $\avenf=0.86$, shows that the predicted distributions of $\delT$ agree well around the mean signal, but the semi-numerical schemes diverge from the RT in the wings." + As mentioned before. the “flagging-the-entire-sphere” ionization algorithm from MEFO7 results in less connected HIT regions. and so there are more isolated 5.0 Mpe neutral patehes.," As mentioned before, the “flagging-the-entire-sphere” ionization algorithm from MF07 results in less connected HII regions, and so there are more isolated 5.0 Mpc neutral patches." +" This results in an. increased number of high-d7), regions.", This results in an increased number of $\delT$ regions. + The converse is true for the FFRT ionization scheme which is the fiducial setting of 2IemFAST., The converse is true for the FFRT ionization scheme which is the fiducial setting of 21cmFAST. + The agreement between the schemes improves as reionization progresses., The agreement between the schemes improves as reionization progresses. + In Fig. 9..," In Fig. \ref{fig:compare_ps}," + we compare the power spectra of these O7; boxes., we compare the power spectra of these $\delT$ boxes. + Again. the hydrodynamic simulation is shown with red solid curves. MFO7 is shown with dotted magenta curves. and 2]emFAST is shown with dashed blue curves.," Again, the hydrodynamic simulation is shown with red solid curves, MF07 is shown with dotted magenta curves, and 21cmFAST is shown with dashed blue curves." + At all scales. the power spectra agree with each other at the 10s of percent level’?.. At moderate to large scales. agreement is best. with MFO7 performing slightly better than the FFRT algorithm which is default in 2I1emFAST On smaller-scales. MFO7 predicts too much power. while 21emFAST under-predicts the power.," At all scales, the power spectra agree with each other at the 10s of percent At moderate to large scales, agreement is best, with MF07 performing slightly better than the FFRT algorithm which is default in 21cmFAST On smaller-scales, MF07 predicts too much power, while 21cmFAST under-predicts the power." + It was, It was +"rotating system, and the simulation becomes numerically unstable.","rotating system, and the simulation becomes numerically unstable." +" Here, since we are interested in the low coronal structure, we limit the Cartesian simulation domain to extend only up to 15R, in each direction."," Here, since we are interested in the low coronal structure, we limit the Cartesian simulation domain to extend only up to $15R_\star$ in each direction." + We first compare a potential field extrapolation with the non-potential fields from the corresponding stationary MHD simulation in Figure [7]., We first compare a potential field extrapolation with the non-potential fields from the corresponding stationary MHD simulation in Figure \ref{fig:f2}. +" The potential field extrapolation (left panel) has a source surface (not shown in the zoomed in figure) located at 2.5R,, and a number of field lines, both open and closed, are shown."," The potential field extrapolation (left panel) has a source surface (not shown in the zoomed in figure) located at $2.5R_\star$, and a number of field lines, both open and closed, are shown." +" Field lines that cross the source surface are fully open, as required by the boundary condition mentioned in refsec:Intro.."," Field lines that cross the source surface are fully open, as required by the boundary condition mentioned in \\ref{sec:Intro}." +" Similarly, field lines corresponding to the same footpoint locations are also shown for the non-potential field from the MHD solution for Case A (right panel; the other cases show qualitatively similar behavior, as we show below in Figure [§))."," Similarly, field lines corresponding to the same footpoint locations are also shown for the non-potential field from the MHD solution for Case A (right panel; the other cases show qualitatively similar behavior, as we show below in Figure \ref{fig:f3}) )." +" The field lines are color-coded based on their behavior in the two solutions: those that are closed in both are colored blue, those that are open in both are in yellow, and those that change their topology between the potential and MHD solution are shown in red."," The field lines are color-coded based on their behavior in the two solutions: those that are closed in both are colored blue, those that are open in both are in yellow, and those that change their topology between the potential and MHD solution are shown in red." +" The blue, closed field lines are all quite low-lying in both solutions, though are significantly more stretched out in the MHD solution."," The blue, closed field lines are all quite low-lying in both solutions, though are significantly more stretched out in the MHD solution." + The behavior of the red field lines is instead quite striking: these represent a class of field lines that are stretched and twisted when a wind flow and rotation are imposed on the system., The behavior of the red field lines is instead quite striking: these represent a class of field lines that are stretched and twisted when a wind flow and rotation are imposed on the system. + Another important difference between the potential field and MHD solutions is the effect of the fast stellar rotation on the geometry of the field lines., Another important difference between the potential field and MHD solutions is the effect of the fast stellar rotation on the geometry of the field lines. +" Due to the (infinite) conductivity of the plasma in the MHD solution, the magnetic field lines are frozen in to the plasma, which propagates radially in the inertial frame."," Due to the (infinite) conductivity of the plasma in the MHD solution, the magnetic field lines are frozen in to the plasma, which propagates radially in the inertial frame." + The footpoints of the field lines are attached to the rotating stellar surface., The footpoints of the field lines are attached to the rotating stellar surface. +" As a result, the field is wound up and stretched around to form an enhanced, compact version of the Parker spiral (Parker|{1958)."," As a result, the field is wound up and stretched around to form an enhanced, compact version of the Parker spiral \citep{Parker58}." +". A major difference here is that in the solar case, the toroidal component of the coronal field becomes dominantbeyond the Alfvénn point."," A major difference here is that in the solar case, the toroidal component of the coronal field becomes dominant the Alfvénn point." +" In the case of rapidly rotating stars, as exemplified by our simulations, the toroidal component is stronginside the Alfvénn point, and can feedback on the system."," In the case of rapidly rotating stars, as exemplified by our simulations, the toroidal component is strong the Alfvénn point, and can feedback on the system." + This strong toroidal component cannot be predicted by the potential field approximation., This strong toroidal component cannot be predicted by the potential field approximation. +" The global structure of the magnetic field and the radial velocity fields derived from the MHD simulations are shown in Figure | for Cases A (top), B (middle), and C "," The global structure of the magnetic field and the radial velocity fields derived from the MHD simulations are shown in Figure \ref{fig:f3} for Cases A (top), B (middle), and C (bottom)." +"The panels show slices in the u, field at different (bottom).orientations: one to indicate the 3D structure by showing the solutions in the y=0 and z=0 planes and one to show the structure in the y=0 plane containing(left), the rotation axis (right)."," The panels show slices in the $u_r$ field at different orientations: one to indicate the 3D structure by showing the solutions in the $y=0$ and $z=0$ planes (left), and one to show the structure in the $y=0$ plane containing the rotation axis (right)." +" The stellar surface is shown colored with the input radial magnetic field, as in Figure [7], and the 3D magnetic field lines are shown in white."," The stellar surface is shown colored with the input radial magnetic field, as in Figure \ref{fig:f2}, and the 3D magnetic field lines are shown in white." +" The differences in the structure of the velocity fields in the three cases are more apparent in the right panel figures, where there is a clear correlation between the distribution of the radial stellar wind and the surface magnetic topology."," The differences in the structure of the velocity fields in the three cases are more apparent in the right panel figures, where there is a clear correlation between the distribution of the radial stellar wind and the surface magnetic topology." +" In Case A, we have a single dominant fast stream in each latitudinal hemisphere associated with the main strong spots."," In Case A, we have a single dominant fast stream in each latitudinal hemisphere associated with the main strong spots." +" In case C, we obtain three fast streams together with a weaker fast stream, all associated with the equally strong surface spots."," In case C, we obtain three fast streams together with a weaker fast stream, all associated with the equally strong surface spots." +" In case B, the magnitude of the radial flow decreases, since in this case the surface spots are weaker than cases A and C. The weak outflow component of the flow introduces a more turbulent solution and a strong inflow component in the southern hemisphere."," In case B, the magnitude of the radial flow decreases, since in this case the surface spots are weaker than cases A and C. The weak outflow component of the flow introduces a more turbulent solution and a strong inflow component in the southern hemisphere." +" Another notable feature is the fact that magnetic field lines that originate from regions close to the strong spots have a shape similar to the one predicted by the Parker spiral (due to the strong outflow while field lines that originate from regions component),far from the strong spots (where the outflow component is weaker) are more likely to be affected by local changes of the flow."," Another notable feature is the fact that magnetic field lines that originate from regions close to the strong spots have a shape similar to the one predicted by the Parker spiral (due to the strong outflow component), while field lines that originate from regions far from the strong spots (where the outflow component is weaker) are more likely to be affected by local changes of the flow." + The stellar wind structure is determined by the topology of the open/closed field lines and the expansion of the flux tubes., The stellar wind structure is determined by the topology of the open/closed field lines and the expansion of the flux tubes. +" In the solar case, where the solar rotation is not extreme, the input speed from the WSA model is well reproduced by the MHD solution et_al.|/2008).."," In the solar case, where the solar rotation is not extreme, the input speed from the WSA model is well reproduced by the MHD solution \citep{cohen08b}." +" In the case of FKCom however, we use the empirical model to specify the acceleration of the radial wind, while we use the MHD model to study the effect of fast rotation on the coronal structure."," In the case of FKCom however, we use the empirical model to specify the acceleration of the radial wind, while we use the MHD model to study the effect of fast rotation on the coronal structure." + This part cannot be captured by the empirical model., This part cannot be captured by the empirical model. + The difference in the stream structures for the three cases can be attributed to the different density and magnetic field structures present in the stationary solutions., The difference in the stream structures for the three cases can be attributed to the different density and magnetic field structures present in the stationary solutions. +" These are illustrated in Figure [] that shows the number density close to the star in the y—0 plane, as well as an isosurface of constant density, n=1-10? cm? (green surface)."," These are illustrated in Figure \ref{fig:f4} that shows the number density close to the star in the $y=0$ plane, as well as an isosurface of constant density, $n=1\cdot10^9$ $^{-3}$ (green surface)." + It can be seen that the large streamers in Case B (middle panel) are more stretched than case A (left panel) and case C (right panel)., It can be seen that the large streamers in Case B (middle panel) are more stretched than case A (left panel) and case C (right panel). +" This reduces the number of flux tubesassociated with open field lines (with small expansion) and, as a result, the radial outflow component decreases as seen in Figure [E]."," This reduces the number of flux tubesassociated with open field lines (with small expansion) and, as a result, the radial outflow component decreases as seen in Figure \ref{fig:f3}." +" Based on the simulation results, we emphasize two aspects of the results."," Based on the simulation results, we emphasize two aspects of the results." +" First, the non-potential, MHD steady state solution is significantly different from the potential field extrapolation for the FK Com-like flip-flop dynamo system."," First, the non-potential, MHD steady state solution is significantly different from the potential field extrapolation for the FK Com-like flip-flop dynamo system." +" Second, the coronal structure of such an FK Com-like star is expected to be qualitatively different from the solar corona and coronae of more slowly rotating Sun-like stars."," Second, the coronal structure of such an FK Com-like star is expected to be qualitatively different from the solar corona and coronae of more slowly rotating Sun-like stars." +" The former is evident from the class of field lines that change their topology dramatically from the potential field to the MHD simulation (Figure |5)), and the latter can be seen in the large-scale topology of the coronal magnetic field (Figure "," The former is evident from the class of field lines that change their topology dramatically from the potential field to the MHD simulation (Figure \ref{fig:f1}) ), and the latter can be seen in the large-scale topology of the coronal magnetic field (Figure \ref{fig:f3}- \ref{fig:f4}) )." +"This structure is dominated by the tangling of the }49))).rotationally-wound, large-scale magnetic field, unlike the solar case which is dominated by coronal holes and active regions."," This structure is dominated by the tangling of the rotationally-wound, large-scale magnetic field, unlike the solar case which is dominated by coronal holes and active regions." +" The rapidly rotating plasma environment acts to inhibit the radial component of the flow, and the density decrease with radial distance is less pronounced than would be expected in Sun-like coronae."," The rapidly rotating plasma environment acts to inhibit the radial component of the flow, and the density decrease with radial distance is less pronounced than would be expected in Sun-like coronae." +" The strong rotational component causes a toroidal “dragging” and stretching of the field lines, which nevertheless remain closed since the azimuthal forces do not overcome the magnetic tension as in the radial case."," The strong rotational component causes a toroidal “dragging"" and stretching of the field lines, which nevertheless remain closed since the azimuthal forces do not overcome the magnetic tension as in the radial case." +" This stretching, however, stores magnetic energy in the loops and causes an increase in the magnetic tension, Tg=B- ΝΒ/µο, over the entire length of the loops."," This stretching, however, stores magnetic energy in the loops and causes an increase in the magnetic tension, $T_B=\mathbf{B}\cdot\nabla\mathbf{B}/\mu_0$ , over the entire length of the loops." + The magnetic tension, The magnetic tension +times. /;. we fit the times assuming a constant period. P.,"times, $t_j$, we fit the times assuming a constant period, $P$." + We compute the standard deviation. σι of the dilference between the nominal and actualtimes.," We compute the standard deviation, $\sigma$, of the difference between the nominal and actualtimes." + Mathematicallyv. where 2? and fy ave chosen to minimize e.," Mathematically, where $P$ and $t_0$ are chosen to minimize $\sigma$." + Hf the variations are strictly. periodic. then the amplitude of the timing deviation is simply V2 times larger than o.," If the variations are strictly periodic, then the amplitude of the timing deviation is simply $\sqrt{2}$ times larger than $\sigma$." + During the preparation of this paper à proceedings contribution has appeared by Jean Schneider which considers several ol the elfeets discussed here (2): however. we find that Schneider's results are incorrect as he does not consider the dillerential [orce between the star and the transiting planet.," During the preparation of this paper a proceedings contribution has appeared by Jean Schneider which considers several of the effects discussed here \citep{sch03}; however, we find that Schneider's results are incorrect as he does not consider the differential force between the star and the transiting planet." + In addition. calculations similar to those presented here are being carried out by Matt Holman and Norm Murray.," In addition, calculations similar to those presented here are being carried out by Matt Holman and Norm Murray." + We are studying the 3-body system in which the three bodies have labels 0.1.2 and positions R;.;=0.1.2 (with an arbitrary origin).," We are studying the 3-body system in which the three bodies have labels $0,1,2$ and positions ${\bf R}_i, i=0,1,2$ (with an arbitrary origin)." + The exact Newtonian equations of motion are given hy Alultiplving the equations for each. particle by its mass and adding together. one finds: This is simply a statement that the centre of mass of the system has no external forces.," The exact Newtonian equations of motion are given by Multiplying the equations for each particle by its mass and adding together, one finds: This is simply a statement that the centre of mass of the system has no external forces." +" Since light travel time and parallax effects are negligible reflighttravel)). the transit. problem is unallected by the total velocity or position of the centre of mass. so we set This reduces the dillerential equations of motion to two. which we take to be that of the two planets. e, and s (For the two planetary masses)."," Since light travel time and parallax effects are negligible \\ref{lighttravel}) ), the transit problem is unaffected by the total velocity or position of the centre of mass, so we set This reduces the differential equations of motion to two, which we take to be that of the two planets, $R_1$ and $R_2$ (for the two planetary masses)." + We use this svstem of equations for numerically solving the equations of motion., We use this system of equations for numerically solving the equations of motion. + However. for analytic consideration it is more convenient to write the problem in Jacobian coordinates which we discuss next.," However, for analytic consideration it is more convenient to write the problem in Jacobian coordinates which we discuss next." + The Jacobian coordinate svstem is commonly used in perturbation theory for many bodies (see.c.g.222).," The Jacobian coordinate system is commonly used in perturbation theory for many bodies \citep[see, e.g.][]{mur99, mal93a, mal93b}." +" For the problem. the Jacobian coordinates amount to three new coordinates which describe (a) the centre of mass of the system: (b) the relative position of inner planet and the star (the ""inner binary”): (6) the relative position of the outer planet and the barvcentre of the inner binary (the ""outer binary”)."," For the three-body problem, the Jacobian coordinates amount to three new coordinates which describe (a) the centre of mass of the system; (b) the relative position of inner planet and the star (the “inner binary""); (c) the relative position of the outer planet and the barycentre of the inner binary (the “outer binary”)." + To distinguish from the body coordinates. we denote the Jacobian coordinates with a lower case r;.," To distinguish from the body coordinates, we denote the Jacobian coordinates with a lower case ${\bf r}_i$." +" Lhe Jacobian coordinates are Using pp—nu/M~miefry. where AM=ear2m;. the equations of motion may be rewritten in Jacobian coordinates. where roy=jr,|y;ReRo."," The Jacobian coordinates are Using $\mu_i = m_i/M \sim m_i/m_0$, where $M=\sum_{i=0}^2 m_i$, the equations of motion may be rewritten in Jacobian coordinates, where ${\bf r}_{21}=\mu_1{\bf r}_1+{\bf r}_2={\bf R}_2-{\bf R}_0$." +" ""Throughout5 the rest of the paper we make the approximations that (a) the orbits of both planets are aligned5 in the same plane: (b) the system is exactly edge-on. that is. the inclination angle is 907."," Throughout the rest of the paper we make the approximations that (a) the orbits of both planets are aligned in the same plane; (b) the system is exactly edge-on, that is, the inclination angle is $^\circ$ ." + We also approximate the planet ane star as spherical so that the transit is svnunetric with a well-defined: midpoint., We also approximate the planet and star as spherical so that the transit is symmetric with a well-defined midpoint. +We detect (wo absorption svstems (one at the svstemic velocity) towards Cie extended eemission in À426.,We detect two absorption systems (one at the systemic velocity) towards the extended emission in A426. + We do not detect aabsorption towards the extended diffuse eemission in ALT95 and A2597. with upper limits N(II1)<10713 [for optically thin absorbers with unity covering factor.," We do not detect absorption towards the extended diffuse emission in A1795 and A2597, with upper limits $N(HI) \lae + 10^{13}$ for optically thin absorbers with unity covering factor." + Alternately. our data constrain the covering [actor of any high column density gas (VfL)>10 2)) to be less than25%.," Alternately, our data constrain the covering factor of any high column density gas $N(HI) \gae 10^{15}$ ) to be less than." +".. Our results suggest that it is unlikely (hat (he ""missing gas al temperatures below 1 keV in the cooling cores is due to absorption by large columns of absorbing gas with of order unity covering factor."," Our results suggest that it is unlikely that the “missing"" gas at temperatures below 1 keV in the cooling cores is due to absorption by large columns of absorbing gas with of order unity covering factor." + In addition. the low columns of gas on the 100 kpe scales in the ICM suggests that (1) the rate at which cold gas accumulates in the ICM on these scales is very low. ancl (2) the dense nebulae in the central ~LO kpe must have cooled or been depositeds," In addition, the low columns of gas on the $\sim 100$ kpc scales in the ICM suggests that (1) the rate at which cold gas accumulates in the ICM on these scales is very low, and (2) the dense nebulae in the central $\sim 10$ kpc must have cooled or been deposited." +"ilat, We are erateful to Andy Fabian. Jerry Kriss. and Rajib Ganguly for helpful discussions."," We are grateful to Andy Fabian, Jerry Kriss, and Rajib Ganguly for helpful discussions." + We thank the anonvmous referee for helpful comments., We thank the anonymous referee for helpful comments. + Support for program SLOT was provided by NASA through a grant. trom the Space Telescope Science Institute. which is operate bv the Association of Universities for Research in Astronomy. Inc.. under NASA contract NAS 5-26555.," Support for program 8107 was provided by NASA through a grant from the Space Telescope Science Institute, which is operate by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555." + This research made se of (1) the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration: and (2) NASA's Astrophvsies Data Svstem Abstract Service.," This research made use of (1) the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration; and (2) NASA's Astrophysics Data System Abstract Service." +Energy. the National Aeronautics and Space Administration. the Japanese Monbukagakusho. the Max Planck Society. and the Higher Education Funding Council for England.,"Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is http://www.sdss.org/., The SDSS Web Site is http://www.sdss.org/. +Table 2. show the best fitting parameters for these two models.,Table \ref{tab:fitresults} show the best fitting parameters for these two models. + To reduce the number of free parameters. we only used a single set of metallicities for the temperature components (tieing O. Ne. Mg. Si. Ca. Fe and ΝΟ.," To reduce the number of free parameters, we only used a single set of metallicities for the temperature components (tieing O, Ne, Mg, Si, Ca, Fe and Ni)." + We however split the components by temperature to allow for two N values. otherwise there are obvious residuals around the N line.," We however split the components by temperature to allow for two N values, otherwise there are obvious residuals around the N line." + Rather than allow the spatial scale of euch of the components to vary. or fixing them to be all the same. we apply three different spatial smoothing scales to groups of the temperature components.," Rather than allow the spatial scale of each of the components to vary, or fixing them to be all the same, we apply three different spatial smoothing scales to groups of the temperature components." + We plot the abundance of each variable relative to solar in Fig., We plot the abundance of each variable relative to solar in Fig. + 8. for the 5x model., \ref{fig:metals} for the $5\times$ model. + In Fig., In Fig. + 9 is shown the best fitting HEW sizes from the line widths against the temperature of the component., \ref{fig:sizesT} is shown the best fitting HEW sizes from the line widths against the temperature of the component. + We note that velocity broadening of the lines could mimic spatial broadening. however. velocities above 700kms| are required to make a substantial difference to these measurements.," We note that velocity broadening of the lines could mimic spatial broadening, however, velocities above $700\kmps$ are required to make a substantial difference to these measurements." + The emission measure of each component per unit temperature (assuming a temperature bin size which is half the logarithmic change to the next adjacent temperature value) is plotted as a function of temperature in Fig. 10.., The emission measure of each component per unit temperature (assuming a temperature bin size which is half the logarithmic change to the next adjacent temperature value) is plotted as a function of temperature in Fig. \ref{fig:norms}. + In this plot we also show values from a spatially-resolved analysis of the inner 2 arcmin., In this plot we also show values from a spatially-resolved analysis of the inner 2 arcmin. + These were created from spectra extracted from contour-binned (?) regions containing around 107 .," These were created from spectra extracted from contour-binned \citep{SandersBin06} regions containing around $\sim +10^4$ ." +. The spectra were fit with a multi-temperature 5x model with the same five fixed temperatures as the RGS fit. but assuming Solar abundance ratios.," The spectra were fit with a multi-temperature $5 \times$ model with the same five fixed temperatures as the RGS fit, but assuming Solar abundance ratios." + The model assumes each temperature component in individual regions has the same metallicity., The model assumes each temperature component in individual regions has the same metallicity. + The RGS and results are roughly similar. considering we are comparing the results in the inner 2 aremin radius with the larger field of view of the RGS instruments and the decline of the RGS effective area off-axis.," The RGS and results are roughly similar, considering we are comparing the results in the inner 2 arcmin radius with the larger field of view of the RGS instruments and the decline of the RGS effective area off-axis." + The one major discrepancy is the apparent lack of any gas above 3 keV in the RGS results (see Section 5.4 for a discussion)., The one major discrepancy is the apparent lack of any gas above 3 keV in the RGS results (see Section \ref{sect:metals} for a discussion). + We alsoplot the HEW size from the, We alsoplot the HEW size from the + White dwarts are well stucied objects aud the plysica processes that coutrol their evolution are relatively wel understood.,] White dwarfs are well studied objects and the physical processes that control their evolution are relatively well understood. + Iu fact. most pliases of white dwarf evolution ean be succesfully characterized as a cooling process.," In fact, most phases of white dwarf evolution can be succesfully characterized as a cooling process." + That is. white dwarfs slowly radiate at the expense of the residual thermal cuereyv of their ious.," That is, white dwarfs slowly radiate at the expense of the residual thermal energy of their ions." +" The release of thermal energy lasts for loug time scales of the order of the age of the galactic disk (~10 ον),", The release of thermal energy lasts for long time scales — of the order of the age of the galactic disk $\sim10$ Gyr). +" While their detailed energy budect is still today somehow controversia the reason being basically the release. of eravitatioua energv associated to pliase separation upon crystallization (Mochisovitch 1983: (αναBerro et al L988a.do: Iseru ot al 1997) their mechanical structures, which are largely supported by the pressure of the eas of degenerate electrous. are verv well modeled except for the outer lavers."," While their detailed energy budget is still today somehow controversial — the reason being basically the release of gravitational energy associated to phase separation upon crystallization (Mochkovitch 1983; a–Berro et al 1988a,b; Isern et al 1997) — their mechanical structures, which are largely supported by the pressure of the gas of degenerate electrons, are very well modeled except for the outer layers." + These lavers control tlhe cucrey output aud their correct modeling is necessary to properly understand tle evolution of white dwarfs., These layers control the energy output and their correct modeling is necessary to properly understand the evolution of white dwarfs. + This is especially true at very low luminosities when most of the white dwarf interior has already crystallized and the cooling process is controlled alinost exclusively by the behavior of the very outer layers., This is especially true at very low luminosities when most of the white dwarf interior has already crystallized and the cooling process is controlled almost exclusively by the behavior of the very outer layers. + The situation was quite unsatisfactory until very recently. when new developements in the physies of white dwarf atimospheres allowed the calculation of reliable hydrogeudominated white dwarf atmospheres down to effective temperatures as low as 1500 Is (Sammon Jacobson 1999: Iauseu 1999).," The situation was quite unsatisfactory until very recently, when new developements in the physics of white dwarf atmospheres allowed the calculation of reliable hydrogen--dominated white dwarf atmospheres down to effective temperatures as low as 1500 K (Saumon Jacobson 1999; Hansen 1999)." + The study. of very cool white dwiurfs bears important consequences. since the recent results of the microlensing experiments carried out by the MACTIO team (Alcock et al 1997) vield that perhaps a substautial fraction of the halo dark matter could be iu the form of very cool white dwarfs.," The study of very cool white dwarfs bears important consequences, since the recent results of the microlensing experiments carried out by the MACHO team (Alcock et al 1997) yield that perhaps a substantial fraction of the halo dark matter could be in the form of very cool white dwarfs." + The search for this clusive white ciwarts has not been successful vet. although there are evidences that perhaps the observational counterparts of these white chvarts could be the stellar objects recently reported ii tle IIubble Deep Field (bata ct al 1999: Méunudez Miuniti 1999).," The search for this elusive white dwarfs has not been successful yet, although there are evidences that perhaps the observational counterparts of these white dwarfs could be the stellar objects recently reported in the Hubble Deep Field (Ibata et al 1999; Ménndez Minniti 1999)." + Most probably one of the reasous for this fülure iu detecting very cool white dwarfs was that their colors were expected to be redder than they really are (Iauseu 1999)., Most probably one of the reasons for this failure in detecting very cool white dwarfs was that their colors were expected to be redder than they really are (Hansen 1999). + Moreover. the huninosity function of disk white dwarfs has been repeatedly used during the last decade to provide independent estimates of the age of galactic disk (Winget et al 1987: GarciaBerro et al 1988b: Heruauz et al 1991).," Moreover, the luminosity function of disk white dwarfs has been repeatedly used during the last decade to provide independent estimates of the age of galactic disk (Winget et al 1987; a–Berro et al 1988b; Hernanz et al 1994)." + Iu view of the recent progresses in the physics of the dense hydrogen plasma we compute new cooling sequences which will be invaluable for the study of the structure aud age of our Galaxy and its halo., In view of the recent progresses in the physics of the dense hydrogen plasma we compute new cooling sequences which will be invaluable for the study of the structure and age of our Galaxy and its halo. + The paper is organized as follows: in 5393 we briefiv describe the evolutionary code and the adopted physical inputs. i ξ we discuss in detail the cooling sequences. we compare them to other cooling sequences available so far. and we show their evolution iu the colormagnitude diagram.," The paper is organized as follows: in 2 we briefly describe the evolutionary code and the adopted physical inputs, in 3 we discuss in detail the cooling sequences, we compare them to other cooling sequences available so far, and we show their evolution in the color–magnitude diagram." + Finally. our couclusious are drasen du 811.," Finally, our conclusions are drawn in 4." + The adopted cooling code is the same evolutionary code, The adopted cooling code is the same evolutionary code +"generalized spectral function C(x,x»,T;) equals 0.","generalized spectral function $C (x_{1}, x_{2}, T_{e})$ equals 0." + It means that this function is insensitive to low-temperature electron components. (, It means that this function is insensitive to low-temperature electron components. ( +Note that a SZ intensity cavity at a frequency of 90 GHz produced by mildly relativistic electrons in an AGN cocoon due to relativistic SZ effect corrections (Pfrommer et al.,Note that a SZ intensity cavity at a frequency of 90 GHz produced by mildly relativistic electrons in an AGN cocoon due to relativistic SZ effect corrections (Pfrommer et al. + 2005) can vanish if the assumption of pressure equilibrium doesn’t hold., 2005) can vanish if the assumption of pressure equilibrium doesn't hold. +" This is because the SZ signal at a frequency of 90 GHz produced by a gas with a low temperature can be reproduced by a mildly relativistic gas with a high temperature and higher pressure, see Fig.[I))."," This is because the SZ signal at a frequency of 90 GHz produced by a gas with a low temperature can be reproduced by a mildly relativistic gas with a high temperature and higher pressure, see Fig. \ref{Fig90}) )." +" Equation (7)) defines a family of spectral functions: each choice of values for frequencies ΧΙ, X2 produces a different spectral function."," Equation \ref{C}) ) defines a family of spectral functions: each choice of values for frequencies $x_1$, $x_2$ produces a different spectral function." + The common property of spectral functions of this family is that they are more sensitive to mildly relativistic electron populations than to non-relativistic electron populations., The common property of spectral functions of this family is that they are more sensitive to mildly relativistic electron populations than to non-relativistic electron populations. +" Therefore, this choice for the combined generalized spectral function is motivated by studying of high energy electron populations."," Therefore, this choice for the combined generalized spectral function is motivated by studying of high energy electron populations." +" Let us consider different choices of frequencies of x, and x».", Let us consider different choices of frequencies of $x_1$ and $x_2$. +" There are three basic spectral features that characterize the thermal, non-relativistic SZ effect signal: a minimum of its intensity located at a dimensionless frequency 2.26 (v=128 GHz), a crossover frequency x9=3.83 (v=217 GHz), and a maximum of its intensity whose frequency location at a dimensionless frequency 6.51 (v=369 GHz)."," There are three basic spectral features that characterize the thermal, non-relativistic SZ effect signal: a minimum of its intensity located at a dimensionless frequency 2.26 $\nu$ =128 GHz), a crossover frequency $x_0=3.83$ $\nu$ =217 GHz), and a maximum of its intensity whose frequency location at a dimensionless frequency 6.51 $\nu=369$ GHz)." +" If the αι=3.83 then the values of generalized (αι) and C(x,x2) are coincident."," If the $x_{1}=3.83$ then the values of generalized $G(x_1)$ and $C(x_1, x_2)$ are coincident." +" If x;=3.83, the combined generalized function is undetermined because the value of g(x=3.83) equals 0."," If $x_2=3.83$, the combined generalized function is undetermined because the value of $g(x=3.83)$ equals 0." +" We noticed that values of the spectral function of G(x,Τε) at high temperatures at frequencies of x,=2.26 and x.= cannot be simultaneously fitted by the spectral function of cXg(x), where c is the arbitrary constant."," We noticed that values of the spectral function of $G(x, T_{\mathrm{e}})$ at high temperatures at frequencies of $x_1 = 2.26$ and $x_2 = 6.51$ cannot be simultaneously fitted by the spectral function of $c \times g(x)$, where $c$ is the arbitrary constant." +" Therefore, the choice of frequencies x, = 2.26 and x» = 6.51 corresponding to minimum and maximum values of the SZ intensity in the Kompaneets approximation is suitable to analyze high energy electron populations."," Therefore, the choice of frequencies $x_1$ = 2.26 and $x_2$ = 6.51 corresponding to minimum and maximum values of the SZ intensity in the Kompaneets approximation is suitable to analyze high energy electron populations." +" The dependence of the combined generalized function with x,=2.26 and x;=6.51 on the plasma temperature is shown in Fig. B].", The dependence of the combined generalized function with $x_1=2.26$ and $x_2=6.51$ on the plasma temperature is shown in Fig. \ref{Fig217}. +" The combined function of C(1.59,6.51,Τε) where the lower frequency corresponds to 90 GHz is shown in Fig."," The combined function of $C(1.59, 6.51, +T_{\mathrm{e}})$ where the lower frequency corresponds to 90 GHz is shown in Fig." + by dotted line., \ref{Fig217} by dotted line. +" Figure shows that the curves which correspond to the generalized spectral function at frequency 217 GHz and the combined generalized function C(2.26,6.51,T) are very similar and have peaks at temperatures higher than 100 keV. Therefore, using the combined generalized function provides us with an alternative and equivalent method for studying a population of electrons with energies higher than 100 keV. Such peaks at temperatures higher than 100 keV as that in the Fig."," Figure \ref{Fig217} shows that the curves which correspond to the generalized spectral function at frequency 217 GHz and the combined generalized function $C(2.26, 6.51, T)$ are very similar and have peaks at temperatures higher than 100 keV. Therefore, using the combined generalized function provides us with an alternative and equivalent method for studying a population of electrons with energies higher than 100 keV. Such peaks at temperatures higher than 100 keV as that in the Fig." + | permit us to maximize the SZ effect from very hot gas which is expected inside AGN cocoons from numerical simulations., \ref{Fig217} permit us to maximize the SZ effect from very hot gas which is expected inside AGN cocoons from numerical simulations. +" To calculate the intensity map of the SZ effect using combined generalized spectral functions, we use Eq. (4))"," To calculate the intensity map of the SZ effect using combined generalized spectral functions, we use Eq. \ref{form}) )" +" where the generalized spectral function G(x,Τε) should be changed to the combined generalized spectral function x»,C(x,Te)."," where the generalized spectral function $G(x, T_{\mathrm{e}})$ should be changed to the combined generalized spectral function $C(x_{1}, +x_{2}, T_{\mathrm{e}})$." + The kinematic Sunyaev-Zel'dovich effect which is a possible source of bias in the observations of the SZ effect by energetic electrons will be considered in Sect., The kinematic Sunyaev-Zel'dovich effect which is a possible source of bias in the observations of the SZ effect by energetic electrons will be considered in Sect. + 4.1., 4.1. +" In the next section, an analysis of the SZ effect by means of the generalized spectral functions is considered for a specific astrophysical important case - the Sedov self-similar solution."," In the next section, an analysis of the SZ effect by means of the generalized spectral functions is considered for a specific astrophysical important case - the Sedov self-similar solution." +" Self-similar solutions for a strong point explosion in an ambient medium are used for modelling adiabatic supernova remnants, solar flares and processes in active galactic nuclei (Ostriker McKee 1988)."," Self-similar solutions for a strong point explosion in an ambient medium are used for modelling adiabatic supernova remnants, solar flares and processes in active galactic nuclei (Ostriker McKee 1988)." + Sedov (1959) gives the analytical self-similar solution for description of the motion of a shock front and the distribution of fluid parameters inside the shocked region for a strong point explosion in a uniform ambient medium., Sedov (1959) gives the analytical self-similar solution for description of the motion of a shock front and the distribution of fluid parameters inside the shocked region for a strong point explosion in a uniform ambient medium. +" The gas flow pattern is determined by only two parameters: the ambient gas density p,, and the amount of energy E released in the explosion."," The gas flow pattern is determined by only two parameters: the ambient gas density $\rho_{1}$, and the amount of energy $E$ released in the explosion." + The distance of the shock from the origin is given by where(= β is a numerical constant., The distance of the shock from the origin is given by where $\beta$ is a numerical constant. + The density p as a function of the dimensionless radial coordinate r/R decreases rapidly into the sphere and almost all the gas is in a relatively thin layer behind the shock wave (Sedov 1959)., The density $\rho$ as a function of the dimensionless radial coordinate $r/R$ decreases rapidly into the sphere and almost all the gas is in a relatively thin layer behind the shock wave (Sedov 1959). +" As r/R—0, the pressure p tends to a constant limit and the temperature accordingly becomes very high."," As $r/R\rightarrow0$, the pressure $p$ tends to a constant limit and the temperature accordingly becomes very high." +" Since the SZ effect depends on the thermal energy density of the electron population along a line of sight, a significant SZ effect is expected from the central region although the density is very small there."," Since the SZ effect depends on the thermal energy density of the electron population along a line of sight, a significant SZ effect is expected from the central region although the density is very small there." + Yamada et al. (, Yamada et al. ( +1999) investigated the SZ effect produced by cocoons of radio galaxies and constructed a model for the evolution of a cocoon after the jet is turned off.,1999) investigated the SZ effect produced by cocoons of radio galaxies and constructed a model for the evolution of a cocoon after the jet is turned off. + They examined the evolution of a cocoon after the jet turns off by analogy with the evolution of a supernova remnant and showed that the cocoon remains hot enough to be the source of the SZ effect only during the free expansion and Sedov (adiabatic) phases., They examined the evolution of a cocoon after the jet turns off by analogy with the evolution of a supernova remnant and showed that the cocoon remains hot enough to be the source of the SZ effect only during the free expansion and Sedov (adiabatic) phases. + The Sedov stage of the evolution of the cocoon surrounding an AGN was also considered by Platania et al. (, The Sedov stage of the evolution of the cocoon surrounding an AGN was also considered by Platania et al. ( +2002) and Chatterjee Kosowsky (2007).,2002) and Chatterjee Kosowsky (2007). +" In these papers, for simplicity the density of the gas inside the cocoon was assumed to be uniform and only the time evolution of the Comptonization parameter was taken into account."," In these papers, for simplicity the density of the gas inside the cocoon was assumed to be uniform and only the time evolution of the Comptonization parameter was taken into account." + We will consider a more realistic case where the gas density depends on the position inside a cocoon., We will consider a more realistic case where the gas density depends on the position inside a cocoon. +" The values of pressure and temperature at any radius inside a cocoon are determined by the ambient gas density pi, the amount of energy E released in the explosion, and time 1."," The values of pressure and temperature at any radius inside a cocoon are determined by the ambient gas density $\rho_{1}$, the amount of energy $E$ released in the explosion, and time $t$." +" However, the parameters directly observed by X-ray telescopes are the ambient number density πι=p;/my, the shock radius R and the Mach number M of the shock."," However, the parameters directly observed by X-ray telescopes are the ambient number density $n_{1}=\rho_{1}/m_{\mathrm{p}}$, the shock radius $R$ and the Mach number $M$ of the shock." +" The Mach number of a shock is usually derived from the Rankine-Hugoniot jump conditions (for a review, see Markevitch Vikhlinin 2007)."," The Mach number of a shock is usually derived from the Rankine-Hugoniot jump conditions (for a review, see Markevitch Vikhlinin 2007)." + Another way to derive the Mach number of a shock is based on measurements of the flux ratio of the FeXXV and FeXXVI iron lines (Prokhorov 2010)., Another way to derive the Mach number of a shock is based on measurements of the flux ratio of the FeXXV and FeXXVI iron lines (Prokhorov 2010). + Since the amount of energy released and time can be expressed in terms of the shock radius and the, Since the amount of energy released and time can be expressed in terms of the shock radius and the +Several voung. self-Iuminous gas giant planets have been detected. by direct. imaging (Chauvinctal.2004:Alarois2010) around nearby stars.,"Several young, self-luminous gas giant planets have been detected by direct imaging \citep{Cha04, Mar08, Mar10, Lag10, Laf10} around nearby stars." + These objects are now being characterized by photometry and even spectroscopy (Bowleretal.2011) in an attempt to characterize their atmospheres and constrain the planetary masses.," These objects are now being characterized by photometry and even spectroscopy \citep{Bow10, Pat10, Cur11,Bar11} in an attempt to characterize their atmospheres and constrain the planetary masses." + In the next few vears many more such planets are almost certainly to be detected by ground-based adaptive optics coronagraphs. such as the P1640 coronagraph on Palomar. the Gemini Planet Imager. and SPHERE on the VET (Beichmanetal.2010).," In the next few years many more such planets are almost certainly to be detected by ground-based adaptive optics coronagraphs, such as the P1640 coronagraph on Palomar, the Gemini Planet Imager, and SPHERE on the VLT \citep{Bei10}." +. The characterization of the mass of a given directly imaged planet can be problematical. since such planets typically lic at large star-planct separations (tens of AU and ereater) and are thus not amenable to detection. by raclial-velocity methods.," The characterization of the mass of a given directly imaged planet can be problematical, since such planets typically lie at large star-planet separations (tens of AU and greater) and are thus not amenable to detection by radial-velocity methods." + Losteacl masses must be estimated either by comparison. of photometry ancl spectroscopy o planctary evolutionary ancl atmospheric models or by heir gravitational influence on other planets or disk (e.g.lxalasctal.2005:Fabrveky&Alurray-Clay 2010).," Instead masses must be estimated either by comparison of photometry and spectroscopy to planetary evolutionary and atmospheric models or by their gravitational influence on other planets or disk \citep[e.g.][]{Kal05,Fab10}." +.. Alodel comparisons as a method for constraining mass can » ambiguous. however.," Model comparisons as a method for constraining mass can be ambiguous, however." + Evolution models which predict uminositv às a function of age have vet to be fully tested in this mass range for voung planets and at very. voung ages (<100 Myr) the model luminosity can depend: on he unknown initial conditions (Marleyctal.2007:Fortneyetal. 2008).," Evolution models which predict luminosity as a function of age have yet to be fully tested in this mass range for young planets and at very young ages $< 100$ Myr) the model luminosity can depend on the unknown initial conditions \citep{Mar07, For08}." +. The masses of the planets around. HIU 8799 estimated: by cooling. models are apparently inconsistent with standard model spectra (Bowleretal.2010:Barmanetal.2011:Currie2011) and can leacl to rapid orbital instabilities if circular. face-on orbits are assumed (Fabrvcky&Alurrayv-Clay 2010).," The masses of the planets around HR 8799 estimated by cooling models are apparently inconsistent with standard model spectra \citep{Bow10, Bar11, Cur11} and can lead to rapid orbital instabilities if circular, face-on orbits are assumed \citep{Fab10}." +. Finally the mass of the planetary mass companion to the brown cdwarl 2M1I207 b (Chauvin inferred from fitting of spectral models. to," Finally the mass of the planetary mass companion to the brown dwarf 2M1207 b \citep{Cha04} + inferred from fitting of spectral models to" + , +equation (3)) gives a peak energy densitv in (he inner region (cf.,equation \ref{eq:EXr}) ) gives a peak energy density in the inner region (cf. +line in Fig., in Fig. + 1) and a significant radiation pressure gradient., 1) and a significant radiation pressure gradient. + In addition. when (here is strong Comptonization. the contribution from the inner region can be significantly enhanced.," In addition, when there is strong Comptonization, the contribution from the inner region can be significantly enhanced." + Moreover. (he amount of Compton heating is determined by Che Iuminosity. (nes the photon energy. and is largely dominated by the inner hot region.," Moreover, the amount of Compton heating is determined by the luminosity times the photon energy, and is largely dominated by the inner hot region." + The radiation temperature. delined as AD(r) being the energv-weighted mean photon energyv. al a given radius r is determined by (he equation This quantity is more concentrated (han Ly(1). especially in the presence of strong Comptonization [seecurve in Fig.," The radiation temperature, defined as $kT_X(r)$ being the energy-weighted mean photon energy, at a given radius $r$ is determined by the equation This quantity is more concentrated than $E_X(r)$, especially in the presence of strong Comptonization [see in Fig." + 1 for Tx(7)]., 1 for $T_X(r)$ ]. + In presence of an overheated wind. some region along the pole in CDAF will not be able lo accrete matter. while the remaining equatorial region normally accretes (see 833.3).," In presence of an overheated wind, some region along the pole in CDAF will not be able to accrete matter, while the remaining equatorial region normally accretes (see 3.3)." + In most of the relevant parameter space. the overheated ;funnel. is very narrow. and we assume (with regard to energy generation) that the sell-ximilar CDAF flow is filling the whole space including the polar region. omitting the small correction due to (he solid angle O4: (~0.2 sr) occupied by the outflowing wind/jet.," In most of the relevant parameter space, the overheated `funnel' is very narrow, and we assume (with regard to energy generation) that the self-similar CDAF flow is filling the whole space including the polar region, omitting the small correction due to the solid angle $\Omega_W$ $\sim 0.2$ sr) occupied by the outflowing wind/jet." + The resulting profiles of radiation moments and (he radiation temperature show the aforementioned characteristics of CDAFs., The resulting profiles of radiation moments and the radiation temperature show the aforementioned characteristics of CDAFs. + The Iuminosity. increases al large radiuscurve in Fie.," The luminosity, increases at large radius in Fig." + 1). while the radiation temperature is roughly flat or decreasing slowly outward alter peaking al some intermediate radiuscurve in Fig.," 1), while the radiation temperature is roughly flat or decreasing slowly outward after peaking at some intermediate radius in Fig." + 1)., 1). + The mathematical self-similar CDAF has zero mass accretion rate (NLA). and this. of course. corresponds (o zero luminosity.," The mathematical self-similar CDAF has zero mass accretion rate (NIA), and this, of course, corresponds to zero luminosity." + However. (he accretion flow must lose energy bv radiative cooling. and (his energy loss is very likely provided by (he convective energy transport (NIA. BNQ).," However, the accretion flow must lose energy by radiative cooling, and this energy loss is very likely provided by the convective energy transport (NIA, BNQ)." + We follow BNQ to assume that the total huminositv of ADAF is, We follow BNQ to assume that the total luminosity of ADAF is +The first test to the model is to apply it to the two transiting plauets described in Section 2.2.. where Craussiau noise has been added similar to that of CoRoT aud Ixepler observations.,"The first test to the model is to apply it to the two transiting planets described in Section \ref{secao_transito_planeta}, where Gaussian noise has been added similar to that of CoRoT and Kepler observations." + Lu this fit. all the stellar parameters aud the orbital period (or semi-major axis) of the plauet were Lixecl. aud the only [ree parameters were the planetary radius aud the orbital inclination augle.," In this fit, all the stellar parameters and the orbital period (or semi-major axis) of the planet were fixed, and the only free parameters were the planetary radius and the orbital inclination angle." + The comparison between the originalfae) parameters aud those obtained from the fit of the noisy uiiodeled light curve are seen in Tables 1. aud 2.. aud and in Figures τα) aud 7(b) for HD 20915s and CoRoT-2.," The comparison between the original parameters and those obtained from the fit of the noisy modeled light curve are seen in Tables \ref{tab:ajuste_planetas_corot} and \ref{tab:ajuste_planetas_kepler}, and and in Figures \ref{fig:fit_planetas_sem_lua_a} and \ref{fig:fit_planetas_sem_lua_b} for HD 209458 and CoRoT-2." + Both light curves had noise level similar to the CoRoT satellite., Both light curves had noise level similar to the CoRoT satellite. + The two panels show the simulated data points as dots aud the fit as a solid liue., The two panels show the simulated data points as dots and the fit as a solid line. + The residuals are shown iu the lower part of each pauel., The residuals are shown in the lower part of each panel. + If the planet has a moon in orbit around it. there are two factors that make its detection difficult.," If the planet has a moon in orbit around it, there are two factors that make its detection difficult." + The first one is the noise. as expected.," The first one is the noise, as expected." + In. cases where the moon is very siuall. their siguature in the light curve is [Iooded by the noise level. leaving it undetectable.," In cases where the moon is very small, their signature in the light curve is flooded by the noise level, leaving it undetectable." + Another clilliculty is the preseuce ol starspots ou the stellar surface. meutioned above.," Another difficulty is the presence of starspots on the stellar surface, mentioned above." +obtained during 2002 May. 16-17 covering 2.4 and 2.8 binary orbits on (he respective nights.,obtained during 2002 May 16-17 covering 2.4 and 2.8 binary orbits on the respective nights. + The reduction of the raw frames was conducted using the most recent standard recipe pipeline release of the Common Pipeline Library (CPL)) recipes., The reduction of the raw frames was conducted using the most recent standard recipe pipeline release of the Common Pipeline Library ) recipes. + The resultant optimallv-extracted spectra covered a wavelength range of AL020-5240A aab a dispersion of pixel.! and a spectral resolution of ')) as measured [rom the skvlines., The resultant optimally-extracted spectra covered a wavelength range of $\lambda$ at a dispersion of $^{-1}$ and a spectral resolution of ) as measured from the skylines. + The spectra were wavelength: calibrated with one Thorium Argon arc per night., The spectra were wavelength calibrated with one Thorium Argon arc per night. + This calibration was tested against the two skv linesvisible ai À5191.92A and A5200.23A., This calibration was tested against the two sky linesvisible at $\lambda$ and $\lambda$. +. The corresponding science frames were corrected for any remaining shifts., The corresponding science frames were corrected for any remaining shifts. + The residuals were scattered around zero with a maximum amplitude of 0.01 kms |., The residuals were scattered around zero with a maximum amplitude of $0.01$ km $^{-1}$. + Next. heliocentric velocity. corrections were applied to the individual frames to deliver spectra in a common heliocentric rest frame.," Next, heliocentric velocity corrections were applied to the individual frames to deliver spectra in a common heliocentric rest frame." + No standard was observed in the correct settings on the nights ancl as no master response curve exists for the non-standard setup used. the frames were not flux calibrated.," No standard was observed in the correct settings on the nights and as no master response curve exists for the non-standard setup used, the frames were not flux calibrated." + The exposure time was 500 seconds giving a signal to noise of 6.5 per spectrum., The exposure time was 500 seconds giving a signal to noise of $\sim$ 6.5 per spectrum. + Details of the observations can be found in Table 3. while Figure 1. shows the average spectrum of GW Lib on (he 16th of May., Details of the observations can be found in Table \ref{tab:observations} while Figure \ref{fig:spectrum} shows the average spectrum of GW Lib on the 16th of May. + Prominent features are the Balmer cise emission lines on top of broad absorption troughs Irom the WD. visible due to the low mass accretion rate in the svstem.," Prominent features are the Balmer disc emission lines on top of broad absorption troughs from the WD, visible due to the low mass accretion rate in the system." + Ie Lis also seen in emission as is Ile αἱ75A., He is also seen in emission as is He at. +.. Our pre-outburst. intermediate resolution spectra of GW Lib showed Mg at iin absorption (see ligure 2. vanSpaandonketal. 2010)).," Our pre-outburst, intermediate resolution spectra of GW Lib showed Mg at in absorption (see figure 2, \citealt{vanspaandonketal09-1}) )." + The archival data confirm (he presence of this line and (hanks to the superior spectral resolution combined with the low inclination of the svstem shows it (o be unblended [rom the nearby He emission al 4471A., The archival data confirm the presence of this line and thanks to the superior spectral resolution combined with the low inclination of the system shows it to be unblended from the nearby He emission at . +. We measure an EW of 0.25+0.01AÀ ((similar to 0.24+0.03AÀ , We measure an EW of $0.25\pm0.01$ (similar to $0.24\pm 0.03$ +"The second eror source is due to the assignineut of Fy,,,. computed for the VD. to cach pCοορ.","The second error source is due to the assignment of ${\bf F}_{far}$, computed for the VB, to each $p \in C_{group}$." + We fond that the Sphere criteriou allows us to reduce this error to values much lower than for N>10° if the dimeusion of the Cyronpy collis fixed with the critical level as mecutioucd above. aud the is three times the radius of the sphere enclosiug the Ον cell (Fig.," We found that the Sphere criterion allows us to reduce this error to values much lower than for $ N \ge 10^6$ if the dimension of the $C_{group}$ cell is fixed with the critical level as mentioned above, and the is three times the radius of the sphere enclosing the $C_{group}$ cell (Fig." + Another iiportaut constraint to be fixed is the value of Αρη., Another important constraint to be fixed is the value of $N_{crit}$. +" All the eloeiieuts p€C,,,,, ave listed in the LEjeg, list aud there is a direct body-body interaction among the Vy, CV,€INug] elements forming the group.", All the elements $p \in C_{group}$ are listed in the $IL_{near}$ list and there is a direct body-body interaction among the $N_{gp}$ $N_{gp} \le N_{crit}$ ) elements forming the group. +" This introduces a term QCGV,,N,) in the algoritlin complexity.", This introduces a term $O(N_{gp} N_p)$ in the algorithm complexity. +" Th order to avoid a decrease of the code efficiency. and to maintain a good code accuracy. as with the original DII aleorithim. it seenis reasonable. ruuniug LSS simulation with more than 1 milliou particles, to maintain ορ<32."," In order to avoid a decrease of the code efficiency and to maintain a good code accuracy, as with the original BH algorithm, it seems reasonable, running LSS simulation with more than 1 million particles, to maintain $N_{crit} \le 32$." + We adopted. m our runs. a safe value Nig=16 even if we obtained good results with Αρης32. Tn the next section we show the errors obtained using the above-mentioned constraints when applying WD99 to LSS simulation with both ταον and clustered distributions.," We adopted, in our runs, a safe value $N_{crit} = 16$ even if we obtained good results with $N_{crit} = 32$ In the next section we show the errors obtained using the above-mentioned constraints when applying WD99 to LSS simulation with both uniform and clustered distributions." + We carried out many tests to estimate the error introduced im the WD99 aud obtained mereased performances using several values of ρε, We carried out many tests to estimate the error introduced in the WD99 and obtained increased performances using several values of $N_{crit}$. + Therefore. this section is subdivided as follows: first we test whether our algorithin increases the average leneth of the interaction list. then we measure the resulting percentage error. and we conchidle with an overall performance analysis.," Therefore, this section is subdivided as follows: first we test whether our algorithm increases the average length of the interaction list, then we measure the resulting percentage error, and we conclude with an overall performance analysis." + As a test case we ran a simulation using 2 million particles for LSS in a cubic region of 50 Alpe. starting from a homogencous initial condition (redshift Z= 50) aud reaching a clustered configuration (redshift Z— 0).," As a test case we ran a simulation using 2 million particles for LSS in a cubic region of 50 Mpc, starting from a homogeneous initial condition (redshift $Z = 50$ ) and reaching a clustered configuration (redshift $Z = 0$ )." + We used an opening anele parauucter Ó ranging from 0.8 to 1.2., We used an opening angle parameter $\theta$ ranging from $0.8$ to $1.2$. + Our tests were executed ou a Cray T3E system aud the results will be shown in the following sections., Our tests were executed on a Cray T3E system and the results will be shown in the following sections. + The aim of this first test is to verify that the WD99 aleorithim docs not introduce a siguificaut coluputational cost when the force for a ecueric particle is computed., The aim of this first test is to verify that the WD99 algorithm does not introduce a significant computational cost when the force for a generic particle is computed. + This iieasuremoeut is substantially performed on the average leneth of the ££ we form acopting our code., This measurement is substantially performed on the average length of the $IL$ we form adopting our code. + Fig., Fig. + 6 reports the result we obtain when the simulation evolves at redshift Z=50., 6 reports the result we obtain when the simulation evolves at redshift $Z = 50$. + Tests were executed for several values of redshift. but the differences between BIT aud our algorithia was computed only at the cud of the run.," Tests were executed for several values of redshift, but the differences between BH and our algorithm was computed only at the end of the run." + The curves were obtained by fixiug Αρης32 and varviug the critical level from 5 to 8., The curves were obtained by fixing $N_{crit} = 32$ and varying the critical level from 5 to 8. + In all cases the differeuces we obtained are uceligible. which means that the computed JL for the VB (with the adopted Sphere criterion) is about equal to the ZL we obtain for a generic particle with the original DIT aleorithin.," In all cases the differences we obtained are negligible, which means that the computed $IL$ for the VB (with the adopted Sphere criterion) is about equal to the $IL$ we obtain for a generic particle with the original BH algorithm." + The first iuaportanut result is that WD99 does not produce auy increment in the IL length aud cousequeutly (77)=(Tyr)., The first important result is that WD99 does not produce any increment in the IL length and consequently $\langle T_l \rangle = \langle T_{gl} \rangle$. + We carry out this measurement in two phases., We carry out this measurement in two phases. + First we run a single time-step of the simulation at redshlitt Z=50., First we run a single time-step of the 2-million-particle simulation at redshift $Z = 50$. + We compare the values we obtain zuuniug the DIT original aleorithim aud the WD99., We compare the values we obtain running the BH original algorithm and the WD99. + As a reference case. we adopt the critical level equal to 6.," As a reference case, we adopt the critical level equal to 6." + A similar comparison is wade at Z=0 aud the BIT and WD99 histograms of the forces of cach conrponeut are compared., A similar comparison is made at $Z=0$ and the BH and WD99 histograms of the forces of each component are compared. + The comparison shows a ucelieible difference in the force distribution ina sinele time-step. at least an order of magnitude less than the error of the original DI," The comparison shows a negligible difference in the force distribution in a single time-step, at least an order of magnitude less than the error of the original BH" + The comparison shows a ucelieible difference in the force distribution ina sinele time-step. at least an order of magnitude less than the error of the original DIT," The comparison shows a negligible difference in the force distribution in a single time-step, at least an order of magnitude less than the error of the original BH" +Q=100 induces a substantial change in the results.,$Q = 100$ induces a substantial change in the results. + ILowever. recent investigations sugeest (hat impurity scattering in the crusts of accreting neutron stars that exhibit superbursts is rather insignificant (Schatzetal.2003a).," However, recent investigations suggest that impurity scattering in the crusts of accreting neutron stars that exhibit superbursts is rather insignificant \citep{SBC03}." +". If the impurity. concentration Q~1 in the crust ol a neutron star with a core that emits neutrinos via pionic or direct URCA reactions. then the carbon fuel will solidify ancl burn stably via pvenonuclear reactions al lower accretion rales,"," If the impurity concentration $Q \sim 1$ in the crust of a neutron star with a core that emits neutrinos via pionic or direct URCA reactions, then the carbon fuel will solidify and burn stably via pycnonuclear reactions at lower accretion rates." + We have shown in $3.6 (hat. for a completely disordered neutron star crust. the thermal profile (1acluding Chat of the superburst ignition region) is highly insensitive to the core newlring emission mechanism.," We have shown in $\S 3.6$ that, for a completely disordered neutron star crust, the thermal profile (including that of the superburst ignition region) is highly insensitive to the core neutrino emission mechanism." + In (his case. superburst energies and recurrence times should be insensitive to (he core cooling mechanism. as confirmed in Figure 15.," In this case, superburst energies and recurrence times should be insensitive to the core cooling mechanism, as confirmed in Figure 15." + Thus we verily the result of Brown(2004) that superburst energies and recurrence times from neutron stars wilh highly efficient. core neutrino cooling mechanisms may still be consistent with observations if (he crust is disordered., Thus we verify the result of \citet{B04} that superburst energies and recurrence times from neutron stars with highly efficient core neutrino cooling mechanisms may still be consistent with observations if the crust is disordered. + However. in (his case we find that superbursts should occur even al relatively low accretion rates MomOAMag. whereas observations indicate a cutoff at ALο ο th," However, in this case we find that superbursts should occur even at relatively low accretion rates $\dot{M} < 0.1 \dot{M}_{\mathrm{Edd}}$, whereas observations indicate a cutoff at $\dot{M} \approx 0.1 \dot{M}_{\mathrm{Edd}}$." +e carbon would burn stably at these low accretion rates because (he enerev generated would be efficiently transported away [rom the burning region.," Normally, the carbon would burn stably at these low accretion rates because the energy generated would be efficiently transported away from the burning region." + However. the low thermal conductivitv due to the disordered. lattice inhibits the flow of energv away from the carbon-burning region.," However, the low thermal conductivity due to the disordered lattice inhibits the flow of energy away from the carbon-burning region." + Therefore. even a low carbon energy generation rate can initiate a (hermonuclear instability.," Therefore, even a low carbon energy generation rate can initiate a thermonuclear instability." + Note that in deriving these results we assume (hat the entire crust is completely disordered. which is clearly an extreme situation.," Note that in deriving these results we assume that the entire crust is completely disordered, which is clearly an extreme situation." + Further investigations into the nuclear structure of neutron star crusts are necessary {ο determine the significance of (hese results., Further investigations into the nuclear structure of neutron star crusts are necessary to determine the significance of these results. + The radius of a neutron star depends «quite sensitivelv on (he core equation of state. but it is virtually independent of the stellar mass.," The radius of a neutron star depends quite sensitively on the core equation of state, but it is virtually independent of the stellar mass." + Accurate measurements of the radius to within about one kilometer can potentially constrain (he equation of state 2001)., Accurate measurements of the radius to within about one kilometer can potentially constrain the equation of state \citep{LP01}. +. To demonstrate the effects of the stellar radius on superburst characteristics. we choose three different values. 2=16.4. 10.4. and 6.5 kin. whieh likely bracket the true radii of neutron stars.," To demonstrate the effects of the stellar radius on superburst characteristics, we choose three different values, $R = 16.4$, $10.4$, and $6.5$ km, which likely bracket the true radii of neutron stars." + We find (hat stars with larger radii have more energetic superbursts and longer recurrence (times al a given accretion rate., We find that stars with larger radii have more energetic superbursts and longer recurrence times at a given accretion rate. + Thev also have superbursts at lower accretion rates., They also have superbursts at lower accretion rates. + See Figure 16., See Figure 16. + Al a given accretion rate. a neutron star with a lareer radius requires a larger column density of fuel in order [or a superburst to be triggered.," At a given accretion rate, a neutron star with a larger radius requires a larger column density of fuel in order for a superburst to be triggered." + This is a result of the lower eravitational acceleration near the stellar surface., This is a result of the lower gravitational acceleration near the stellar surface. + Thus the effect. of radius on superburst, Thus the effect of radius on superburst +frequency between the Neplerian rotation aud that of the neutron star magnetosphere (e.g.Alpar&Shahaim1985).,frequency between the Keplerian rotation and that of the neutron star magnetosphere \cite[e.g.][]{alpar85}. +. Actually we can try to combine our present RATE nieasurenmieuts with ΟΡΟ studies by Finger.Tarimon(1996) making use of two facts: The dependence of the ΟΡΟ frequency. ou the X- flux during its 1991 outburst. renormalized using the above factors. is shown in Fig.," Actually we can try to combine our present RXTE measurements with QPO studies by \cite{finger96} + making use of two facts: The dependence of the QPO frequency on the X-ray flux during its 1994 outburst, renormalized using the above factors, is shown in Fig." + 3. (solid open circles)., \ref{correlation} (solid open circles). + The renormalized depeudence (solid. open circles) perfectly continues the observed break frequeucv-fiux. depeudence (filled circles) and correspouds to Eq. (1)) (, The renormalized dependence (solid open circles) perfectly continues the observed break frequency-flux dependence (filled circles) and corresponds to Eq. \ref{fb}) ) ( +the dashed linc).,the dashed line). + Promincnt ΟΡΟ features similar to those detected by Finger.Wilson.&Harmon(1996) are not always observed in the power spectra of accreting N-rav pulsars., Prominent QPO features similar to those detected by \cite{finger96} are not always observed in the power spectra of accreting X-ray pulsars. + Ou the other haud a break iu the PDS is more ubiquitous aud therefore the diagnostics of the accretion flow based ou the break frequency cau be applied to larger datasets., On the other hand a break in the PDS is more ubiquitous and therefore the diagnostics of the accretion flow based on the break frequency can be applied to larger datasets. + For example. the break frequeucy in the noise power spectrum can be used as an estimate of the dipole magnetic moment of compact objects using Eq. (1)).," For example, the break frequency in the noise power spectrum can be used as an estimate of the dipole magnetic moment of compact objects using Eq. \ref{fb}) )." + We studied aperiodic variability of the N-rav fiux. frou accreting binaries. in which the truucation of the disk-like accretion flow by the maguetosphere of the compact object is portant.," We studied aperiodic variability of the X-ray flux from accreting binaries, in which the truncation of the disk-like accretion flow by the magnetosphere of the compact object is important." + The results can be stumarized as follows:, The results can be summarized as follows: +in exactly the same path or at the same time as the light from a star.,in exactly the same path or at the same time as the light from a star. + We choose a Th-Ar lamp as the RV caibration source in {ἱ band. where strong Argon lines exist that saturate the CCD.," We choose a Th-Ar lamp as the RV calibration source in $R$ band, where strong Argon lines exist that saturate the CCD." + Since we exclude Argon lines in RV calibration uncertainty calculation. a more practical result when Areou liues are considered is expectec to be worse unless a CCD with |igher clyuaimiὁ range js usecl.," Since we exclude Argon lines in RV calibration uncertainty calculation, a more practical result when Argon lines are considered is expected to be worse unless a CCD with higher dynamic range is used." + Jun Y anc J band. a U-Ne emission laup is proposed by ?7.. we use a lines list of Uraul oxovided by 5eplen Recluanu (?).," In $Y$ and $J$ band, a U-Ne emission lamp is proposed by \citet{Mahadevan2010}, we use a lines list of Uranium provided by Stephen Redman \citep{Redman2011}." +". lu A baud. a series of abso‘plion cells is pro;»osed by. ?.. in wl a mixture of eas cells including HMCTY, ?CSHs. PCO. at(LBCO creates i| series of absorp ines that spans over 120 um of the Η baud."," In $H$ band, a series of absorption cells is proposed by \citet{Mahadevan2009}, in which a mixture of gas cells including $H^{13}C^{14}N$, $^{12}C_2H_2$, $^{12}CO$, and $^{13}CO$ creates a series of absorption lines that spans over 120 nm of the $H$ band." + ? deioustraed that an Amuιο] absorytlou i» a good candidate for calibration source in fv baud., \citet{Bean2010} demonstrated that an Ammonia absorption cell is a good candidate for calibration source in $K$ band. + Therefore. we assume an ΑΠΛΟΙla celi he calculation of RV calibration uncertainty in the A. band.," Therefore, we assume an Ammonia cell in the calculation of RV calibration uncertainty in the $K$ band." + ? proposed a gas absorptlon ce with the mixture of acetylene. uitrous oxide. amanonia. chlorouethaues. aud hydrocarbous €Overlngine nost of the H and A bands.," \citet{Valdivielso2010} proposed a gas absorption cell with the mixture of acetylene, nitrous oxide, ammonia, chloromethanes, and hydrocarbons covering most of the $H$ and $K$ bands." + We do not cosider this cell in «ur paper since a detailed liues list of he cell is not availlable., We do not consider this cell in our paper since a detailed lines list of the cell is not available. + Stellar 1Olse ls a siguilicant contribuor to RV uncerainty budget. therefore we devote the following part to discuss a method of quattilvine its iulflueice on precision Doppler measurement.," Stellar noise is a significant contributor to RV uncertainty budget, therefore we devote the following part to discuss a method of quantifying its influence on precision Doppler measurement." + Cranulation is cousiderec to be the major obstacle in detecion of Earth planets in the HZ because it produces au RV signal with au ampituc eof 8-10 m.s 1Iowed oni observation on the 5un (?).., Granulation is considered to be the major obstacle in detection of Earth planets in the HZ because it produces an RV signal with an amplitude of $\sim$ 10 $\rm{m\cdot s}^{-1}$ based on observation on the Sun \citep{Meunier2010}. + In addition. here is by ar no good rethlod of removing he RV ixjse from this pheuouieol.," In addition, there is by far no good method of removing the RV noise from this phenomenon." + provided a iode of noise contributin iu RV measuremenults base on precision RV observation on stars of «illerent spectral type a ds different evoltion stages., \citet{Dumusque2011} provided a model of noise contribution in RV measurements based on precision RV observation on stars of different spectral type and at different evolution stages. + We acopt this model aud quautifv the RV ncertaluly contribte of granulatiou based their ineasurenuent of three stars. l.e.. a Cen A (C9V). r Ceti (GV). acL ¢| Cen B (IXIV).," We adopt this model and quantify the RV uncertainty contribution of granulation based their measurement of three stars, i.e., $\alpha$ Cen A (G2V), $\tau$ Ceti (G8V), and $\alpha$ Cen B (K1V)." + The stui of three exponentially «ecaying μοιτοι5 represet sa power spectrum. density function wih 'ontribtious from granulatiorl. eranulation and stper-gr:uiulatiou. usi18oO he values given i1 Tabe 2 [rom ?..," The sum of three exponentially decaying functions represents a power spectrum density function with contributions from granulation, meso-granulation and super-granulation, using the values given in Table 2 from \citet{Dumusque2011}." + An RV RMS e‘ror due o eranulatiou is heu caculation based on Equation (6) jutheir payer assumiug a 100-d:w consecutive ¢observation for Ix (C) type star with an optim:d strategy [ouxd in the payer. Le.. lree measurenmetts per Ισ ol 10 min exposure each. 2 αραt.," An RV RMS error due to granulation is then calculation based on Equation (6) in their paper assuming a 100-day (300-day) consecutive observation for K (G) type star with an optimal strategy found in the paper, i.e., three measurements per night of 10 min exposure each, 2 h apart." + The total length of cousecutive observation is oughly iu accordance wl1 tlie orbital period. of a planet in the HZ., The total length of consecutive observation is roughly in accordance with the orbital period of a planet in the HZ. + We fiud that he RV RMS error due ο granulatioli is 0.55. 1.05 ancl 1.05 1ves+ for a WIV. GSV aid CV slar res»ectively.," We find that the RV RMS error due to granulation is 0.55, 1.05 and 1.05 $\rm{m\cdot s}^{-1}$ for a K1V, G8V and G2V star respectively." + These luinyer are goi& to be used later iu us study to estimate a total RV micertaintv., These number are going to be used later in this study to estimate a total RV uncertainty. + De πο.μεν of RV uicertainty iduced by stellar nolse ias so [ar been limited in Ix aud G type slars ¢ue to practical concerns stich as stellar photou flix ancl stellar activity., Detailed study of RV uncertainty induced by stellar noise has so far been limited in K and G type stars due to practical concerns such as stellar photon flux and stellar activity. + Despite their intriusic alutnuess aud relative higer level of stellar activity due to [ast rotation aud deep convectiou zone. M dwarfs are amoung primary targets in searcl of planets in the HZ.," Despite their intrinsic faintness and relative higher level of stellar activity due to fast rotation and deep convection zone, M dwarfs are among primary targets in search of planets in the HZ." + TIve RMS, The RMS +The cross-shaped white area (for retrograde orbits) of the parameter space would lead to unstable orbits even in short time scales.,The cross-shaped white area (for retrograde orbits) of the parameter space would lead to unstable orbits even in short time scales. + Several formulas have been published to calculate the duration of transits (e.g.??)..," Several formulas have been published to calculate the duration of transits \citep[e.g.][]{Kip08,Sea03}." +" To determine the transit duration of CoRoT-7b for different apparent inclinations we applied the following formula of ? Gp) ), being valid only for circular orbits."," To determine the transit duration of b for different apparent inclinations we applied the following formula of \citet*{Sea03} + ( ), being valid only for circular orbits." +" Note that in our calculations we always consider the total transit duration, i.e. including ingress and egress of the planetary disk."," Note that in our calculations we always consider the total transit duration, i.e. including ingress and egress of the planetary disk." +" The numerical integrations of the ,ssystem for ten years (see Fig. 12))", The numerical integrations of the system for ten years (see Fig. \ref{fig:10y}) ) + resulted in a change in, resulted in a change in +llshlv relativistic jel motion is one of the most interesting phenomena observed in active galactic nuclei (AGN). mieroquasars anc possibly s-rav bursts (GRB). and many works have been devoted to numerical and analytical investigations of the mechanisms [or producing. collimating aud accelerating matter to relativistic speeds (Sautyellini&Celotti 2002).,"Highly relativistic jet motion is one of the most interesting phenomena observed in active galactic nuclei (AGN), microquasars and possibly $\gamma$ -ray bursts (GRB), and many works have been devoted to numerical and analytical investigations of the mechanisms for producing, collimating and accelerating matter to relativistic speeds \citep{stt01, + gc02}." +. AC present (he most promising approach to the jet phenomena seenis to consider magnetically driven outflows within the framework of relativistic magnetohvedrocdynanmies MIID)., At present the most promising approach to the jet phenomena seems to consider magnetically driven outflows within the framework of relativistic magnetohydrodynamics (MHD). + Based on the MILID scenario. the jet ejection is expected to be realized under the nagnelic energv-dominated state (i.e.. the Povating jet) in the vieinity of a central source.," Based on the MHD scenario, the jet ejection is expected to be realized under the magnetic energy-dominated state (i.e., the Poynting jet) in the vicinity of a central source." + This initial Povnting flux will be originated by electromagnetic extraction of rotational energy rom a spinning black hole or/and an accretion disk. as was first discovered by Blandlord and numerically studied by the time-dependent MIID simulations in Ixerr geometry (see Ixomissarov 2001 for the magnetically dominated regime: IXoide et al.," This initial Poynting flux will be originated by electromagnetic extraction of rotational energy from a spinning black hole or/and an accretion disk, as was first discovered by \citet{bz77} and numerically studied by the time-dependent MHD simulations in Kerr geometry (see Komissarov 2001 for the magnetically dominated regime; Koide et al." + 2002 for the full MIDID regime)., 2002 for the full MHD regime). + Then. a significant fraction of the huge energy in the outflow will be converted [rom the Povnting flux into the fluid kinetic energv of bulk motion.," Then, a significant fraction of the huge energy in the outflow will be converted from the Poynting flux into the fluid kinetic energy of bulk motion." + Such an efficient energv conversion may be able (o occur unsteadilv in the inner magnetosphere close to the black hole as a result of (he MIID interaction with infalling matter., Such an efficient energy conversion may be able to occur unsteadily in the inner magnetosphere close to the black hole as a result of the MHD interaction with infalling matter. + Ixoideetal.(2000) discussed this problem and found a magneticallv driven jet inside a gas pressure-driven jet in the counter-rotating black hole case against the disk rotation.," \citet{ko00} + discussed this problem and found a magnetically driven jet inside a gas pressure-driven jet in the counter-rotating black hole case against the disk rotation." + However. the poloidal velocity ol the jet is only sub-relativistic.," However, the poloidal velocity of the jet is only sub-relativistic." + Otherwise. (he steady magneto-cenirifugal acceleration in the propagation over a large enough clistance should become important.," Otherwise, the steady magneto-centrifugal acceleration in the propagation over a large enough distance should become important." +" It is well-known that (he ideal stationary axisvimnietric ALLID equations reduce to a set of (vo equations describing the local force-balance along the field ancl across the field. and called (he poloidal wind equation and the Grad-Shalranov ((irans-field) equation (for reference. see. θ,ο.. Okamoto 1992: Beskin 1997)."," It is well-known that the ideal stationary axisymmetric MHD equations reduce to a set of two equations describing the local force-balance along the field and across the field, and called the poloidal wind equation and the Grad-Shafranov (trans-field) equation (for reference, see, e.g., Okamoto 1992; Beskin 1997)." + Sell-similar solutions of magnetosphere. where the magnetic field lines are anchored (o a thin accretion disk. were discussed lor jet collimation and acceleration (Blandford&Pavne1936:Li.Chineh&Begelman1992:Contopoulos 1994).," Self-similar solutions of magnetosphere, where the magnetic field lines are anchored to a thin accretion disk, were discussed for jet collimation and acceleration \citep{bp82,lcb92,co94}." +. Unlortunately. the outflows given by the self-similar solutions (Contopoulos1994) reach some maximum radius and recollimate allerwards.," Unfortunately, the outflows given by the self-similar solutions \citep{co94} reach some maximum radius and recollimate afterwards." + The self-similar scaling will not be valid in the asymptotic region., The self-similar scaling will not be valid in the asymptotic region. + Using the stationary axisvmmnmetrie model. the asvanptotic flow structure has been found to vary logarithmically wilh radius. aud (he kinetic energv-dominated solutions describing collimating jet magnelospheres have been presented," Using the stationary axisymmetric model, the asymptotic flow structure has been found to vary logarithmically with radius, and the kinetic energy-dominated solutions describing collimating jet magnetospheres have been presented" +it; levels from RH. we firstly calculate the line source function with the standard equation where Aye and By are the Einstein coefficients.,"$u_i$ levels from RH, we firstly calculate the line source function with the standard equation where $A_{kk'}$ and $B_{kk'}$ are the Einstein coefficients." + The source function given by Eq. (21)), The source function given by Eq. \ref{eq:lineSst}) ) + has to be equal to the intensity part of the source function given by Eq. (10))., has to be equal to the intensity part of the source function given by Eq. \ref{eq:lineS}) ). + There are three main types of inelastic collisions with molecules., There are three main types of inelastic collisions with molecules. + The first one alters onlv the total angular momentum number J of the molecular state. the second also the vibrational state. and the third the electronic state.," The first one alters only the total angular momentum number $J$ of the molecular state, the second also the vibrational state, and the third the electronic state." + There are many theoretical approximations and parametrizations for the rates of these three collision types (cf.Thompson1973:Hinkle&Lambert1975;AyresWiedemann 1989).," There are many theoretical approximations and parametrizations for the rates of these three collision types \citep[cf.][]{thompson1973,hinkle1975,ayreswiedemann1989}." +. The accuracy of these approximations is very low. and the parameters for the CN molecule are unknown.," The accuracy of these approximations is very low, and the parameters for the CN molecule are unknown." + Moreover it is not possible to distinguish the elastic and inelastic collisions from our observations., Moreover it is not possible to distinguish the elastic and inelastic collisions from our observations. + Therefore. we neglect elastic collisions.," Therefore, we neglect elastic collisions." + It does not influence our conclusions but can slightly affect the value of the deduced magnetic field strength., It does not influence our conclusions but can slightly affect the value of the deduced magnetic field strength. + In our calculations we used the Landau-Teller formula for the relaxation time of the excited state (Ayres&Wiedemann1989) where Px is the partial pressure of the collision. partner UXU. few-x ds the relaxation time of the excited CN state. 7 is the temperature. and Ax and By are free parameters.," In our calculations we used the Landau-Teller formula for the relaxation time of the excited state \citep{ayreswiedemann1989} + where $P_{\rm X}$ is the partial pressure of the collision partner “X”, $t_{\rm CN-X}$ is the relaxation time of the excited CN state, $T$ is the temperature, and $A_{\rm X}$ and $B_{\rm X}$ are free parameters." + The associated collisional de-excitation rate per one molecule ts where B(1=AE/KT 1s the|. excitation parameter., The associated collisional de-excitation rate per one molecule is where $\beta = \Delta E / kT $ is the excitation parameter. + As there are several collisional agents (most importantly neutral hydrogen and electrons) the collisional rates depend on many free parameters., As there are several collisional agents (most importantly neutral hydrogen and electrons) the collisional rates depend on many free parameters. + However for computing the branching coefficient and scattering polarization only the total collisional rate (independently on collisional agent and type) is relevant (see Sect. 22))., However for computing the branching coefficient and scattering polarization only the total collisional rate (independently on collisional agent and type) is relevant (see Sect. \ref{sec:branching}) ). + We assume then that the total collisional rate can be also calculated with Eqs. (24))-(25)).," We assume then that the total collisional rate can be also calculated with Eqs. \ref{eq:LT}) \ref{eq:C}) )," + using the partial pressure of neutral hydrogen (as the collisions with neutral hydrogen seems to be the strongest and moreover the depth dependence of the electron particle density is close to the one of neutral hydrogen in the region of the CN lines formation)., using the partial pressure of neutral hydrogen (as the collisions with neutral hydrogen seems to be the strongest and moreover the depth dependence of the electron particle density is close to the one of neutral hydrogen in the region of the CN lines formation). + With such an approximation the collisional rate depends only on two free parameters: A and B. which define the temperature and density dependence. respectively.," With such an approximation the collisional rate depends only on two free parameters: $A$ and $B$, which define the temperature and density dependence, respectively." + At the CN line formation height the density drops much faster than the temperature., At the CN line formation height the density drops much faster than the temperature. + Therefore. the parameter A only slightly affects the dependency of the collisional rates on height in the atmosphere. in particular also when considering the small exponent of the temperature in Eq. (24)).," Therefore, the parameter $A$ only slightly affects the dependency of the collisional rates on height in the atmosphere, in particular also when considering the small exponent of the temperature in Eq. \ref{eq:LT}) )." + We found that the best fit quality can. be reached if we put the value of A parameter equal to zero., We found that the best fit quality can be reached if we put the value of $A$ parameter equal to zero. +" Let us notice. however. that even under this approximation the branching coetficients oj, and Oy, still depend on temperature due to the Einstein coefficients. which connect excitation and de-excitation collisional rates and affect the level populations."," Let us notice, however, that even under this approximation the branching coefficients $\delta_{\rm th}$ and $\delta_{\rm th}$ still depend on temperature due to the Einstein coefficients, which connect excitation and de-excitation collisional rates and affect the level populations." + Finally we end up with only one free parameter B which defines the dependency of the collisional rate on height., Finally we end up with only one free parameter $B$ which defines the dependency of the collisional rate on height. +" For convenience we have replaced it with the oy, coefficient. at the temperature minimum layer (hereafter omm),", For convenience we have replaced it with the $\delta_{\rm th}$ coefficient at the temperature minimum layer (hereafter $\delta_{\rm th}^{\rm min}$ ). + Considering the strong limitations of the current. collision. theory with molecules. the unknown collision parameters for CN. and our need to know only the total collision rate such approximation becomes very practicle and improves the stability of the procedure to fit observations.," Considering the strong limitations of the current collision theory with molecules, the unknown collision parameters for CN, and our need to know only the total collision rate such approximation becomes very practicle and improves the stability of the procedure to fit observations." + We can control the collision rate with a single free parameter and nonetheless account for the height dependence via the Landau-Teller expression., We can control the collision rate with a single free parameter and nonetheless account for the height dependence via the Landau-Teller expression. + In fact. by fitting observations we can even gain empirical constrains for collisional rates with the CN molecule.," In fact, by fitting observations we can even gain empirical constrains for collisional rates with the CN molecule." +We only have one really long flare remaimine.,We only have one really long flare remaining. + A 50 ks flare Las been deected in NTE 302 as à coutiunous period of activity., A 50 ks flare has been detected in XTE $-$ 302 as a continuous period of activity. + It is very structured and made of at least3 differeut peaks., It is very structured and made of at least 3 different peaks. + It could be interpreted as a close sequence of shorer flares., It could be interpreted as a close sequence of shorter flares. + Tae lists the sources together with their quiesceut COIut rate (Fi). typical flare count rate( nuuber of short ©15 durationsdss) aud long (215 ks) flaresuUfares(Nui). range of flare (fy) for short aud. lous and total SOlree observing clapsed tine (1554).," Table \ref{tab2} lists the sources together with their quiescent count rate $(F_{q})$, typical flare count rate $(F_{fl})$ , number of short $<15$ ks) and long $>15$ ks) flares $(N_{fl})$, range of flare durations $(t_{fl})$ for short and long flares and total source observing elapsed time $(T_{obs})$." + The sources are ordered frou ligh to low variability factor (ΕμFy)., The sources are ordered from high to low variability factor $(F_{fl}/F_{q})$. + The source observing time {νι is the stm of the ela5ed time of all poutiugs with the source within 11 of the FOV center., The source observing time $T_{obs}$ is the sum of the elapsed time of all pontings with the source within $14\degr$ of the FOV center. + As the instrument effective area decreases: between the borders of the fully aud. partially coded. fields of view. the probability to detect a flare οπουνο decreases when the source gets outside of the fully coded field of view.," As the instrument effective area decreases between the borders of the fully and partially coded fields of view, the probability to detect a flare effectively decreases when the source gets outside of the fully coded field of view." + The effective observing time for fiue detection can be estimated as 0.61., The effective observing time for flare detection can be estimated as $0.6~T_{obs}$. + The effective time period between two flares is typically PF=7davs onaverage but varies between 1 day iu IGR 1511 aud two weeks in ICR 1503 (this is uncertain as ouly two flares were detected)., The effective time period between two flares is typically $T=7~\rm{days}$ onaverage but varies between 1 day in IGR $-$ 4514 and two weeks in IGR $-$ 4503 (this is uncertain as only two flares were detected). + The flare count rates (CF) are averaged over t ciation of each flare., The flare count rates $(F_{fl})$ are averaged over the duration of each flare. + Peak count rates could be sjenificantvo huger than listed in table especially for Hares slor ertiui the pointing duration (seec.g.?)..," Peak count rates could be significantly larger than listed in table \ref{tab2}, especially for flares shorter than the pointing duration \citep[see e.g.][]{Leyder2007}." + The sources have heen separated in two categories., The sources have been separated in two categories. +" T SEXT incudes svstenis featuring hard N-rvav variability oa factor =100. """, The SFXT includes systems featuring hard X-ray variability by a factor $\gtrsim100$. “ +Iuteiuediate systems are candidate SENT with snaller variabilitv factors that could be compared with those of classical systems.,Intermediate” systems are candidate SFXT with smaller variability factors that could be compared with those of classical systems. + The dividing iue between the two source categorics is uot very well defined., The dividing line between the two source categories is not very well defined. + From the variability poiut of view. sources closer o the bottom of the table are more similar to classical SSIMND.," From the variability point of view, sources closer to the bottom of the table are more similar to classical sgHMXB." + The distance to the SEXT systems has |con evaluated iu a few cases (??2)..," The distance to the SFXT systems has been evaluated in a few cases \citep{Leyder2007, Negueruela2006a, Pellizza2006}." +" ""They range between 2 to 7 kpc with large uncertaimties.", They range between 2 to 7 kpc with large uncertainties. + We will asstue. for the rest of the discussion a distauce of 3 kpe.," We will assume, for the rest of the discussion a distance of 3 kpc." +" The average count rate observed caine flares lies between 3 and 60 ct/s which translates to hard N-vay Iuninosities of (0.2Ls1079ere /s, ", The average count rate observed during flares lies between 3 and 60 ct/s which translates to hard X-ray luminosities of $(0.2-4)\times 10^{36}~\rm{erg/s}$ . +Such huninosities are not exceptional for seIININD but verv significantly larecr than the typical N-rav huninositv.of sinele massive stars of 1079οςή at soft Noravs ( 7?).., Such luminosities are not exceptional for sgHMXB but very significantly larger than the typical X-ray luminosityof single massive stars of $10^{30-33}~\rm{erg/s}$ at soft X-rays \citep{Cassinelli1981}. . + The observed nou thermallard N-ray euissiou is therefore, The observed non thermalhard X-ray emission is therefore +lamp emission lines. the latter even recorded in separate exposures and often hours apart from the science spectra.,"lamp emission lines, the latter even recorded in separate exposures and often hours apart from the science spectra." + We have thus investigated the feasibility of calculating theoretical atmospheric transmission spectra in order to use them for wavelength calibration and to remove their signature from the astronomical spectra. thus. replacing standard stars as a source of telluric calibrators.," We have thus investigated the feasibility of calculating theoretical atmospheric transmission spectra in order to use them for wavelength calibration and to remove their signature from the astronomical spectra, thus, replacing standard stars as a source of telluric calibrators." + This idea is not new and has been used successfully before (Lallementetal..1993;Wide-mannetal..1994;Bailey 2007).," This idea is not new and has been used successfully before \citep{Lallement93,Widemann94,Bailey07}." +. Nevertheless. modeling telluric spectra has not evolved to a standard technique in optical and infrared spectral data reduction because suitable radiative transfer codes were hard to access and synthesising adequate spectra was hindered by the incompleteness of molecular line databases.," Nevertheless, modeling telluric spectra has not evolved to a standard technique in optical and infrared spectral data reduction because suitable radiative transfer codes were hard to access and synthesising adequate spectra was hindered by the incompleteness of molecular line databases." + This situation has improved m the last years., This situation has improved in the last years. + In an effort to characterise the abilities and the efficiei= usage of the CRIRES spectrograph. we have developed à£5 general method to model the transmission and emission spectrum of the Earth's atmosphere above Cerro Paranal.," In an effort to characterise the abilities and the efficient usage of the CRIRES spectrograph, we have developed a general method to model the transmission and emission spectrum of the Earth's atmosphere above Cerro Paranal." + This method can be used to perform a wavelength calibration. of CRIRES and to subsequently remove the telluric absorption lines apparent in these spectra., This method can be used to perform a wavelength calibration of CRIRES and to subsequently remove the telluric absorption lines apparent in these spectra. + Moreover the model can also be used to predict the performance of planned CRIRES observations using a forecast of the atmospheric conditions during a planned observing run., Moreover the model can also be used to predict the performance of planned CRIRES observations using a forecast of the atmospheric conditions during a planned observing run. + The paper is structured as follows: In Sect., The paper is structured as follows: In Sect. + 2 we describe the data reduction of the CRIRES observations., \ref{sec:Observations} we describe the data reduction of the CRIRES observations. + In Sect., In Sect. + 3. we describe the the radiative transfer code and input parameters used to synthesise the telluric spectra. which we compare to the observations in Sect. ??..," \ref{sec:Synthesis} we describe the the radiative transfer code and input parameters used to synthesise the telluric spectra, which we compare to the observations in Sect. \ref{sec:performance}." + We summarise our findings in Sect., We summarise our findings in Sect. + ?? and close with conclusions about the performance of the presented technique., \ref{sec:Summary} and close with conclusions about the performance of the presented technique. + CRIRES is a high resolution (Ro€ 100000) near-infrared (41Ξ960--nnm) adaptive optics (AO) - fed spectrograph at the VLT on Paranal. Chile (Kiufletal..2004.2006a.b;Pau-fiqueetal. 2006).," CRIRES is a high resolution $R\leq100\,000$ ) near-infrared $\lambda\lambda$ nm) adaptive optics (AO) - fed spectrograph at the VLT on Paranal, Chile \citep{kaufl04,kaufl06a,kaufl06b,jerome06}." +. Commissioning and science verification (SV) observations were executed in October 2006 and February 2007., Commissioning and science verification (SV) observations were executed in October 2006 and February 2007. + The spectrograph ts available to the community and has been used for regular observations since April 2007., The spectrograph is available to the community and has been used for regular observations since April 2007. + We selected observations from both SV periods as well as more recent observations from the ESO data archive to test the telluric model spectra described in Sect. 3.., We selected observations from both SV periods as well as more recent observations from the ESO data archive to test the telluric model spectra described in Sect. \ref{sec:Synthesis}. + For this purpose we chose observations of standard stars at different wavelengths. observed at different airmasses with nominal spectral resolving powers ofR=50000 and 0000.," For this purpose we chose observations of standard stars at different wavelengths, observed at different airmasses with nominal spectral resolving powers of $R=50\,000$ and 000." + The log of observations is given in Tab. 1.., The log of observations is given in Tab. \ref{tab:obslog}. + Observations were always obtained in an AB or ABBA nodding pattern., Observations were always obtained in an AB or ABBA nodding pattern. + Data reduction followed the standard. steps for long-slit spectrographs as applicable to the CRIRES data format., Data reduction followed the standard steps for long-slit spectrographs as applicable to the CRIRES data format. + All raw frames were treated with a non-linearity correction before pairwise subtraction removed the atmospheric emission features., All raw frames were treated with a non-linearity correction before pairwise subtraction removed the atmospheric emission features. + The individual A-B and B-A frames were then divided by a normalised flattield., The individual A-B and B-A frames were then divided by a normalised flatfield. + Optimally extracted 1D spectra at both nodding positions were obtained by using a custom made IDL seript based on Horne(1986)., Optimally extracted 1D spectra at both nodding positions were obtained by using a custom made IDL script based on \citet{Horne86}. + Due to the curvature of the slit. it is inadvisable to combine the 2D spectra before the extraction and wavelength calibration step as Is done in the current. version of the CRIRES data reduction pipeline.," Due to the curvature of the slit, it is inadvisable to combine the 2D spectra before the extraction and wavelength calibration step as is done in the current version of the CRIRES data reduction pipeline." +" The amount of curvature can be of the order of 1 pixel between two nodding positions at a nod throw of IO""and is variable in both spatial and spectral directions.", The amount of curvature can be of the order of 1 pixel between two nodding positions at a nod throw of and is variable in both spatial and spectral directions. + We thus combined the individual 1D spectra after correcting for the slit curvature by producing a telluric model spectrum using the method outlined in Sect., We thus combined the individual 1D spectra after correcting for the slit curvature by producing a telluric model spectrum using the method outlined in Sect. + 3. and interpolating the wavelength calibrated spectra to à common wavelength vector., \ref{sec:Synthesis} and interpolating the wavelength calibrated spectra to a common wavelength vector. + All reduction steps were performed individually for the four chips of the CRIRES focal plane array., All reduction steps were performed individually for the four chips of the CRIRES focal plane array. + To compute theoretical transmission and radiance spectra of the Earth’s atmosphere. a radiative transfer code is used that takes as an input a model of the atmosphere in terms of vertical temperature. pressure and molecular abundance profiles. as well as line data (frequency. line strength. pressure broadening coefficients. etc.).," To compute theoretical transmission and radiance spectra of the Earth's atmosphere, a radiative transfer code is used that takes as an input a model of the atmosphere in terms of vertical temperature, pressure and molecular abundance profiles, as well as line data (frequency, line strength, pressure broadening coefficients, etc.)." + In this section we describe the usage of such acode as well as the necessary inputs in further detail., In this section we describe the usage of such a code as well as the necessary inputs in further detail. + There are several radiative transfer codes tailored for the construction of telluric spectra., There are several radiative transfer codes tailored for the construction of telluric spectra. + These codes are based on line-by-line computations of a layered model of the Earth's atmosphere., These codes are based on line-by-line computations of a layered model of the Earth's atmosphere. + STRANSAC (Scott.1974) is one the oldest of such codes., STRANSAC \citep{Scott74} is one the oldest of such codes. +" It utilises the GEISA spectral line catalogue (Jacquinet-Hussonetal..1999, 2003)."," It utilises the GEISA spectral line catalogue \citep{GEISA99,GEISA03}." + The 4A (Automatized Atmospheric Absorption Atlas) code also uses GEISA. and it provides a fast and accurate line-by-line radiative transfer model that is particularly efficient in the infrared region between nnm and nnm.," The 4A (Automatized Atmospheric Absorption Atlas) code also uses GEISA, and it provides a fast and accurate line-by-line radiative transfer model that is particularly efficient in the infrared region between nm and nm." +" The latest version of 4À can be retrieved free of charge for commercial usage fromNOVELTIS"".. France."," The latest version of 4A can be retrieved free of charge for non-commercial usage from, France." + ATRAN (Lord.1992) tis another code to compute synthetic spectra of atmospheric transmission., ATRAN \citep{Lord92} is another code to compute synthetic spectra of atmospheric transmission. + It i$ based on a fixed atmospheric layering (see Sect. ??)), It is based on a fixed atmospheric layering (see Sect. \ref{sec:atmos}) ) + and uses the HITRAN database (see Sect. 22)), and uses the HITRAN database (see Sect. \ref{sec:database}) ) + for line data input., for line data input. + REM (Reference Forward Model) is a line-by-line radiative transfer model originally developed at Oxfordsity.. under an ESA contract to provide reference spectral calculations for the MIPAS instrument launched on the ENVISAT satellite in 2002.," RFM (Reference Forward Model) is a line-by-line radiative transfer model originally developed at Oxford, under an ESA contract to provide reference spectral calculations for the MIPAS instrument launched on the ENVISAT satellite in 2002." + The code uses HITRAN 2000 as its line database., The code uses HITRAN 2000 as its line database. + In this paper we only consider FASCODE (Clough 1992). and used both its commercial version," In this paper we only consider FASCODE \citep{Clough81,Clough92}, , and used both its commercial version" +Cataclysinic variables (CVs) are binary stars in wlich a white dwarf accretes matter from a close coiipanion. \vhich usually. resembles a lower-maiu-sequeuce star.,"Cataclysmic variables (CVs) are binary stars in which a white dwarf accretes matter from a close companion, which usually resembles a lower-main-sequence star." + The dwarf novae are a subclass of “CVs αἱch show distinctive outbursts. thorelit to result. from an instability in an accretion cisk about the white dwarf," The dwarf novae are a subclass of CVs which show distinctive outbursts, thought to result from an instability in an accretion disk about the white dwarf." +" The AM Herculis stars (sometimes called ""polars"") are another type of CV. iu which the accreted material is entrained in a stroug magnetic field anchored in the whie clwarl. forming au accretion Cunuel above he magnetic poles."," The AM Herculis stars (sometimes called “polars”) are another type of CV, in which the accreted material is entrained in a strong magnetic field anchored in the white dwarf, forming an accretion funnel above the magnetic poles." + Warner(1995) has wrltten an excellent nonograph on CVs., \citet{warn} has written an excellent monograph on CVs. + Distaices for va‘ious types of CVs are fundamentally: important to physical mocels (see. e.g.. Beuermauuetal. 2000)). but they have uot been easyto obtain (Berritnan1987).," Distances for various types of CVs are fundamentally important to physical models (see, e.g., \citealt{beuermanneferi}) ), but they have not been easyto obtain \citep{berriman87}." +. Historically. noue were near enough for trigonometric parallax.," Historically, none were near enough for trigonometric parallax." + Ixamper(1979). published parallaxes for some of the brightest dwarf novae. but these haveproven to be incorrect (Harrisonetal. 1999).," \citet{kamper79} published parallaxes for some of the brightest dwarf novae, but these haveproven to be incorrect \citep{harrison99}. ." +. The, The +. The , The +. The A, The +. The Ai, The +. The Aip, The +. The Aipp, The +. The Aippa, The +. The Aippar, The +. The Aipparc, The +. The Aipparco, The +. The Aipparcos, The +must be compensated for by making Np very large in (he range 0.54«q<0.65.,must be compensated for by making $\hat{N}_T$ very large in the range $0.54 < q < 0.65$. + In fact. Np has another local maximum at q=0.62.," In fact, $\hat{N}_T$ has another local maximum at $q = 0.62$." + And so the oscillations continue. with decreasing wavelength. until >=1 is reached.," And so the oscillations continue, with decreasing wavelength, until $\gamma = 1$ is reached." + Tremblay&Merritt(1995). [ound that NG) for bright elliplical galaxies was significantly bimoclal if the galaxies were assumed to be highly triaxial: (his bimodality also had its origin in the shape of the conditional probability function for triaxial galaxies., \citet{tm95} found that $\hat{N} (\gamma)$ for bright elliptical galaxies was significantly bimodal if the galaxies were assumed to be highly triaxial; this bimodality also had its origin in the shape of the conditional probability function for triaxial galaxies. + For both bright and faint ‘de’ galaxies. using gay as the apparent axis ratio. oblate fits are statisticallyunacceptable. producing a negative number of galaxies with 4=>0.9 (see the upper left panel of Figure 5)).," For both bright and faint `de' galaxies, using $q_{\rm am}$ as the apparent axis ratio, oblate fits are statisticallyunacceptable, producing a negative number of galaxies with $\gamma \ga 0.9$ (see the upper left panel of Figure \ref{fig:de_adapt}) )." + For bright ‘cle’ galaxies. statistically acceptable fits are found [or T=0.4. 0.6. and 0.3: that is. their confidence intervals never [all entirely below zero.," For bright `de' galaxies, statistically acceptable fits are found for $T = 0.4$, $0.6$, and $0.8$; that is, their confidence intervals never fall entirely below zero." + The mean intrinsic axis ratio for the acceptable fits ranges from (5)=0.66 for T'=0.4 to (5)=0.69 lor T'=0.8., The mean intrinsic axis ratio for the acceptable fits ranges from $\langle \gamma \rangle = 0.66$ for $T = 0.4$ to $\langle \gamma \rangle = 0.69$ for $T = 0.8$. +" The permissible lits for the bright ‘ce’ galaxies are consistent with the deduced (riaxial shape of (he nearby bright (M,~—22.2) elliptical galaxy NGC 4365. for which a combination of photometric ancl kinematic data vields T£0.45 and 5~0.6 2004)."," The permissible fits for the bright `de' galaxies are consistent with the deduced triaxial shape of the nearby bright $M_r \sim -22.2$ ) elliptical galaxy NGC 4365, for which a combination of photometric and kinematic data yields $T \sim 0.45$ and $\gamma \sim 0.6$ \citep{se04}." +. Although the bright ‘cle’ galaxies are best fit bv highly triaxial shapes. the faint ‘de’ galaxies are best fit by nearly prolate shapes. wilh Z'=0.8 and T=1 both giving statistically acceptable fits. (," Although the bright `de' galaxies are best fit by highly triaxial shapes, the faint `de' galaxies are best fit by nearly prolate shapes, with $T = 0.8$ and $T = 1$ both giving statistically acceptable fits. (" +The highly oscillatory solution for 7=0.8 maybe physically dubious— why should galaxy shapes be quantized? —,The highly oscillatory solution for $T = 0.8$ maybe physically dubious– why should galaxy shapes be quantized? – + but it is statistically acceptable.), but it is statistically acceptable.) + The nean intrinsic shape of faint ‘de’ galaxies is (5)=0.53 if T'—0.8 and (5)=0.58 if T—1.," The mean intrinsic shape of faint `de' galaxies is $\langle \gamma \rangle = 0.53$ if $T = 0.8$ and $\langle +\gamma \rangle = 0.58$ if $T = 1$." + Figure G shows the deduced distribution of intrinsicshapes for ‘de’ galaxies when the isophotal axis ratio qosis used. rather (han (he adaptive moments axis ratio.," Figure \ref{fig:de_iso} shows the deduced distribution of intrinsicshapes for `de' galaxies when the isophotal axis ratio $q_{25}$is used, rather than the adaptive moments axis ratio." + The bright de ealaxies have a statistically acceptable fit when 7=0.4. 7=0.6. £—0.3. and T=1.," The bright `de' galaxies have a statistically acceptable fit when $T = 0.4$, $T = 0.6$, $T = 0.8$, and $T = 1$." + The nean intrinsic shape ranges from (5)=0.51 when T=0.4 to (5)=0.62 when T'=1.," The mean intrinsic shape ranges from $\langle \gamma +\rangle = 0.51$ when $T = 0.4$ to $\langle \gamma \rangle = 0.62$ when $T = 1$." + The ainter ‘cle’ galaxies ave acceptably fit. assuming constant παντααν. only when 2=1. which results in (5)=0.51.," The fainter `de' galaxies are acceptably fit, assuming constant triaxiality, only when $T = 1$, which results in $\langle \gamma \rangle = 0.51$." + The T=0 case. which can be rejected at the confidence level but rol at the level. would produce (5)=0.28: this axis ratio is [latter than that of an ice hockey puck. (," The $T = 0$ case, which can be rejected at the confidence level but not at the level, would produce $\langle \gamma +\rangle = 0.28$; this axis ratio is flatter than that of an ice hockey puck. (" +Although the T=0 and T=0.2 fits awe statistically unacceptable at the confidence level. the data are consistent with a population of nearly oblate shapes if we relax the assumption of uniform 7.,"Although the $T = 0$ and $T = 0.2$ fits are statistically unacceptable at the confidence level, the data are consistent with a population of nearly oblate shapes if we relax the assumption of uniform $T$." + For instance. the faint ‘de’ galaxies can be fit at the confidence level. with a Gaussian distribution of Z' peaking at T=0 and with op= 0.2.)," For instance, the faint `de' galaxies can be fit at the confidence level, with a Gaussian distribution of $T$ peaking at $T = 0$ and with $\sigma_T = 0.2$ .)" + The shapes of de/ex' galaxies can be analvzed in the same wav as the shapes of de ealaxies., The shapes of `de/ex' galaxies can be analyzed in the same way as the shapes of `de' galaxies. + For instance. (he distributions of intrinsic shapes [or «de/ex galaxies. using (fau as (he apparent axis ratio. are shown in Figure 7..," For instance, the distributions of intrinsic shapes for `de/ex' galaxies, using $q_{\rm am}$ as the apparent axis ratio, are shown in Figure \ref{fig:deex_adapt}. ." +" For the brighter galaxies with ""de/ex profiles. acceptable fits are found when 7= 0.8. vielding (5)= 0.51. and when 7= I. vielding (5)= 0.57."," For the brighter galaxies with `de/ex' profiles, acceptable fits are found when $T = 0.8$ , yielding $\langle \gamma \rangle += 0.51$ , and when $T = 1$ , yielding $\langle \gamma \rangle = 0.57$ ." + For the fainter *de/ex’ galaxies. only the 7=1 fit is statistically acceptable. vielding a mean intrinsic axis ratio of (5)=0.48 for the prolate galaxies.," For the fainter `de/ex' galaxies, only the $T = 1$ fit is statistically acceptable, yielding a mean intrinsic axis ratio of $\langle \gamma \rangle = 0.48$ for the prolate galaxies." + Notice, Notice +The nuclei of some Sevlert 2 galaxies are home to powerful GGIIz water masers located in a circumnuclear disk within a parsec of the central massive black hole.,The nuclei of some Seyfert 2 galaxies are home to powerful GHz water masers located in a circumnuclear disk within a parsec of the central massive black hole. + In almost edge-on svstems. VLBI observations of the maser kinematics enable an accurate determination of the black hole mass.," In almost edge-on systems, VLBI observations of the maser kinematics enable an accurate determination of the black hole mass." + The archetypal svstem is NGC 4258. for which the black hole mass has been measured to accuracy (e.g.. IHerrnstein οἱ al.," The archetypal system is NGC 4258, for which the black hole mass has been measured to accuracy (e.g., Herrnstein et al." + 2005: Lnimphrevs οἱ al., 2005; Humphreys et al. + 2008)., 2008). + Recent VLBA observations of Sevlert 2 galaxies have discovered a limited number of additional examples wilh high inclination angles. allowing precise measurements of the mass of their host black holes as well as the physical size of (he maser disks. which range from ppc (IIerrnstein et 22008: IXuo et al.," Recent VLBA observations of Seyfert 2 galaxies have discovered a limited number of additional examples with high inclination angles, allowing precise measurements of the mass of their host black holes as well as the physical size of the maser disks, which range from pc (Herrnstein et 2008; Kuo et al." + 2010)., 2010). + The physical parameters of (he disks can be inferred [rom the conditions necessary (o eenerale (he masers., The physical parameters of the disks can be inferred from the conditions necessary to generate the masers. + Collisional inversion of the GGlIIz IbO transition requires densities o[10* 10!em7. temperatures in the range KIX. and a sullicient column of water {ο ensure maser amplification (e.g. Neufeld Melnick 1991).," Collisional inversion of the GHz $_2$ O transition requires densities of $10^7$ $10^{11}\percc$, temperatures in the range K, and a sufficient column of water to ensure maser amplification (e.g. Neufeld Melnick 1991)." + These conditions are plausibly produced by irradiation of a molecular disk bv the central N-ray source as long as the surface density exceeds ~σαι7 and warping exposes the disk surface to the center (Neuleld οἱ al., These conditions are plausibly produced by irradiation of a molecular disk by the central X-ray source as long as the surface density exceeds $\sim 1\un g \ut cm -2 $ and warping exposes the disk surface to the center (Neufeld et al. + 1994: Maloney 2002)., 1994; Maloney 2002). + Parsec-scale maser disks must therefore have masses >10!M.., Parsec-scale maser disks must therefore have masses $\ga 10^4$. +. Further insight is provided by examining the center of (he Alilky Way Galaxy. where (here is strong evidence of star formation occurring in a sub-parsec scale disk zz6x109 vears ago (Paumard et al.," Further insight is provided by examining the center of the Milky Way Galaxy, where there is strong evidence of star formation occurring in a sub-parsec scale disk $\approx 6\times 10^6$ years ago (Paumard et al." + 2006)., 2006). + Approximately 100 massive stars orbit within a few tenths of a parsec of the ~4x109ML. black hole Ser A* (Dartko et al., Approximately 100 massive stars orbit within a few tenths of a parsec of the $\sim 4\times10^6\msol$ black hole Sgr A* (Bartko et al. + 2010: Lu et al., 2010; Lu et al. + 2010: Do et al., 2010; Do et al. + 2009: see also the recent review by Genzel et al., 2009; see also the recent review by Genzel et al. + 2010 and references cited therein)., 2010 and references cited therein). + About 2/3 ol these are localized in a clockwise rotating stellar disk with a wide range olf eccentricities (Levin Beloborodoy 2003). with the remainder loosely distributed. possibly in a larger counter-rotating disk (Daumard et al.," About 2/3 of these are localized in a clockwise rotating stellar disk with a wide range of eccentricities (Levin Beloborodov 2003), with the remainder loosely distributed, possibly in a larger counter-rotating disk (Paumard et al." + 2006: but see Lu οἱ al., 2006; but see Lu et al. + 2009)., 2009). + Stellar clisks could be created. by the (dal disruption of an inspiralling stellar cluster (Gerhard 2001: McMillan Portegies Zwart 2003: Portegies Zwart et al., Stellar disks could be created by the tidal disruption of an inspiralling stellar cluster (Gerhard 2001; McMillan Portegies Zwart 2003; Portegies Zwart et al. + 2003: Nim et al., 2003; Kim et al. + 2004: Gitrkan Rasio 2005). but the modelling implies that this mechanism produces a lar more disordered stellar svstem than observed. and a non-existent population of massive stars shed [rom the cluster extending bevond 0.3 pe from Ser Αν furthermore the inspiralling time scale is longer than the stellar ages (απατά οἱ al.," 2004; Gürrkan Rasio 2005), but the modelling implies that this mechanism produces a far more disordered stellar system than observed, and a non-existent population of massive stars shed from the cluster extending beyond 0.3 pc from Sgr A*; furthermore the inspiralling time scale is longer than the stellar ages (Paumard et al." + 2006: but see Fuji et al., 2006; but see Fujii et al. + 2008)., 2008). + A more attractive alternative is (hat (hese disks could form vin-sitw” by gravitational collapse in a disk of gas captured bv the black hole (Levin Beloborodoy 2003: Navakshin et 22007). a process previously considered in the context of AGN (IXolvkhalov Sunvaev 1980; Shlosman Begelman 1937: Collin Zahn 1999: Goodman 2003).," A more attractive alternative is that these disks could form “in-situ” by gravitational collapse in a disk of gas captured by the black hole (Levin Beloborodov 2003; Nayakshin et 2007), a process previously considered in the context of AGN (Kolykhalov Sunyaev 1980; Shlosman Begelman 1987; Collin Zahn 1999; Goodman 2003)." + The compactness of the stellar disks relative to molecular cloud cdimensions implies that, The compactness of the stellar disks relative to molecular cloud dimensions implies that +be modelled carefully (seeBernstein2009;Joachimi&Bridle2010 for an overview on the types of signals contributing to correlations between galaxy number density and ellipticity).,"be modelled carefully (see\citealp{bernstein08,joachimi10} for an overview on the types of signals contributing to correlations between galaxy number density and ellipticity)." + The IL signal is less of a concern because. in order to intrinsically align. a pair of galaxies has to have interacted physically. and hence to be both close on the sky and in redshift.," The II signal is less of a concern because, in order to intrinsically align, a pair of galaxies has to have interacted physically, and hence to be both close on the sky and in redshift." + This fact can be used to remove II correlations (King&Schnei- 2004). partly 1n a fully model-independent way with only marginal loss of statistical power if precise redshift information is available.," This fact can be used to remove II correlations \citep{king02,king03,heymans03,takada04b}, partly in a fully model-independent way with only marginal loss of statistical power if precise redshift information is available." + The GI signal ts not restricted to physically close pairs of galaxies. but it can also be eliminated in a purely geometrical way via nulling techniques (Joachimi&Schnei-der2008. 2009).," The GI signal is not restricted to physically close pairs of galaxies, but it can also be eliminated in a purely geometrical way via nulling techniques \citep{joachimi08b,joachimi09}." +. However. a considerable loss of cosmological information ts inherent to nulling. and hence. it is still desirable to have a reliable model of GI correlations at one’s disposal to be used with other methods controlling this systematic (King2005:Bridle&King2007:Bernstein2009;Zhang2010:Joachimi&Bridle 2010).," However, a considerable loss of cosmological information is inherent to nulling, and hence, it is still desirable to have a reliable model of GI correlations at one's disposal to be used with other methods controlling this systematic \citep{king05,bridle07,bernstein08,zhang08,joachimi10}." + In the following we will develop a model-independer= technique to extract the GI signal from a cosmic shear data set. thereby allowing for direct measurements of GI correlations on the most relevant galaxy samples.," In the following we will develop a model-independent technique to extract the GI signal from a cosmic shear data set, thereby allowing for direct measurements of GI correlations on the most relevant galaxy samples." +" This ""GI aapproach can be regarded as complementary to nulling both in its purpose and in its implementation.", This GI approach can be regarded as complementary to nulling both in its purpose and in its implementation. + Analogous to the nulling technique. we will construct linear combinations of secondorder cosmic shear measures. making only use of the well-known characteristic redshift dependence of the GI and GG terms.," Analogous to the nulling technique, we will construct linear combinations of second-order cosmic shear measures, making only use of the well-known characteristic redshift dependence of the GI and GG terms." + This paper is organised as follows., This paper is organised as follows. + In 2 wepresent the principle of GI boosting and derive general conditions. which are used in Seet.3 to explicitly construct weight functions for the boosting transformation of the cosmic shear signal.," In $\,$ \ref{sec:method} wepresent the principle of GI boosting and derive general conditions, which are used in $\,$ \ref{sec:weights} to explicitly construct weight functions for the boosting transformation of the cosmic shear signal." + Section 4. details the modelling which we apply in Sect.5 to assess the performance of the boosting technique.," Section \ref{sec:modelling} details the modelling which we apply in $\,$ \ref{sec:performance} to assess the performance of the boosting technique." + In Sect.6 we construct a method to remove GI correlations based on the GI boosting technique and investigate the relation between the new approach and the standard nulling method of Joachimi&Schneider(2008. 2009).. before we summarise and conclude in 7..," In $\,$ \ref{sec:nulling} we construct a method to remove GI correlations based on the GI boosting technique and investigate the relation between the new approach and the standard nulling method of \citet{joachimi08b,joachimi09}, before we summarise and conclude in $\,$ \ref{sec:conclusions}." + We will base our technique on a tomographic cosmic shear data set. Le. correlations of galaxy ellipticities which are in addition split into subsamples according to the available redshift information.," We will base our technique on a tomographic cosmic shear data set, i.e. correlations of galaxy ellipticities which are in addition split into subsamples according to the available redshift information." + Analogous to the nulling technique the method outlined in the following does not affect angular scales. so that we can without loss of generality use tomographic power spectra as our two-point cosmic shear measures.," Analogous to the nulling technique the method outlined in the following does not affect angular scales, so that we can without loss of generality use tomographic power spectra as our two-point cosmic shear measures." + For an overview on the basics of cosmic shear see e.g. whose notation we mostly follow., For an overview on the basics of cosmic shear see e.g. \citet{schneider06} whose notation we mostly follow. + The convergence power spectrum of cosmic shear. correlating two galaxy samples 7 and j. reads where P; is the three-dimensional matter power spectrum. { the angular frequency. and z the redshift.," The convergence power spectrum of cosmic shear, correlating two galaxy samples $i$ and $j$, reads where $P_{\delta}$ is the three-dimensional matter power spectrum, $\ell$ the angular frequency, and $z$ the redshift." +The integration runs over all comoving distances y up to the comoving distance horizon γιων.,The integration runs over all comoving distances $\chi$ up to the comoving distance horizon $\chi_{\rm hor}$. +" Moreover we have introduced the lensing efficiency where p'""(y) is the probability distribution of comoving distances for galaxy sample i.", Moreover we have introduced the lensing efficiency where $p^{(i)}(\chi)$ is the probability distribution of comoving distances for galaxy sample $i$. + Note that we assume a spatially flat universe throughout., Note that we assume a spatially flat universe throughout. +" Similar to (1)). one can define a tomographic power spectrum of shear-ellipticity correlations (fordetailsseee.g.Hirata&Seljak2004).. where Ps, denotes the three-dimensional Cross-power spectrum between matter density contrast and intrinsic shearfield?."," Similar to \ref{eq:GGdef}) ), one can define a tomographic power spectrum of shear-ellipticity correlations \citep[for details see e.g.][]{hirata04}, where $P_{\delta {\rm I}}$ denotes the three-dimensional cross-power spectrum between matter density contrast and intrinsic shear." +. Only one of the terms in (3) is non-vanishing unless the probability distributions overlap., Only one of the terms in \ref{eq:GIdef}) ) is non-vanishing unless the probability distributions overlap. + As HH correlations ean readily be removed before applying a treatment of the GI signal. we neglect them in this work. so that the total power spectrum. 1.8. the actual observable in our study. is given by A discussion on how II correlations affect the boosting technique is provided in 7..," As II correlations can readily be removed before applying a treatment of the GI signal, we neglect them in this work, so that the total power spectrum, i.e. the actual observable in our study, is given by A discussion on how II correlations affect the boosting technique is provided in $\,$ \ref{sec:conclusions}." + To derive expressions for the transformed signals. we assume that precise redshift. or equivalently distance. information is available. so that the survey can be sliced into thin tomographic bins.," To derive expressions for the transformed signals, we assume that precise redshift, or equivalently distance, information is available, so that the survey can be sliced into thin tomographic bins." + One can then approximate py)x yi. where y; is an appropriately chosen comoving distance in bin /. Here 0p denotes the Dirac delta distribution.," One can then approximate $p^{(i)}(\chi) \approx \delta_{\rm D}(\chi - \chi_i)$ , where $\chi_i$ is an appropriately chosen comoving distance in bin $i$ Here $\delta_{\rm D}$ denotes the Dirac delta distribution." + The lensing efficiency (2)) can then be written in the form g) > gjvo) - uv)W iththeseapproximationsthe⋅∙ powerspectra( |jand," The lensing efficiency \ref{eq:lenseff}) ) can then be written in the form \eq{ } (χ_i) → g(χ_j,χ_i) \equiv With these approximations the power spectra ) and ) turn into" +Define yj. 7€Z. as the inverse Fourier transform ofey. Le. à;=c; where we let It ds worth noticing that 42; satisfies: The above Littlewood-Paley decomposition asserts that amy tempered distributionf€SUR”+) can be decomposed as: Here SUZ”I) is the usual Schwartz class of rapidly decreasing functions aud S'(E?.+) is its corresponding dual. represents the space of tempered distributions.,"Define $\vphi_{j}$ , $j\in \Z$, as the inverse Fourier transform of$\psi_{j}$, i.e. $\hat{\vphi}_{j} = \psi_{j}$ where we let It is worth noticing that $\vphi_{j}$ satisfies: The above Littlewood-Paley decomposition asserts that any tempered distribution$f\in \mathcal{S}'(\R^{n+1})$ can be decomposed as: Here $\mathcal{S}(\R^{n+1})$ is the usual Schwartz class of rapidly decreasing functions and $\mathcal{S}'(\R^{n+1})$ is its corresponding dual, represents the space of tempered distributions." + We uow defiue parabolic Lizorkiu-Triebel spaces., We now define parabolic Lizorkin-Triebel spaces. + As a convention. fors€ IR. aud 1€q< x. we denote aud," As a convention, for$s\in \R$ , and $1\leq q<\infty$ , we denote and" +distance moduli based ou Popowski(2000) 7s aud. (2000) 7s calibration of ML. (see below).,distance moduli based on \citet{pop00}' 's and \citet{uda00}' 's calibration of $M^I_{RC}$ (see below). + As cimphasized earlier. imodels predict that Mh epeuds on inetallicityo and age (Cole1998:Cürardietal.1998:Carardi2000:Cüridi&Salaris 2001).," As emphasized earlier, models predict that $M^{I}_{RC}$ depends on metallicity and age \citep{col98, gir98, gir00, gir01}." + The seusitivitv to metal abundance is explicitly shown in Fie., The sensitivity to metal abundance is explicitly shown in Fig. + 9(c) aud quantified iu the discussion above., 9(c) and quantified in the discussion above. + The epeudeuce on age is likely to be manifested in the ispersion around the dotted line in Fig., The dependence on age is likely to be manifested in the dispersion around the dotted line in Fig. + 9(c)., 9(c). + This dispersion amounts to a root-mean-square deviation of he points from the fit of 0.03 mae. which is larger than he typical error iu Jyee: of ~O.0L mae.," This dispersion amounts to a root-mean-square deviation of the points from the fit of 0.03 mag, which is larger than the typical error in $I_{0,RC}$ of $\sim$ 0.01 mag." + If taken at face value. this represcuts an age dispersion of ~1.5 Car among he RC stars (based on 0.02 mae(ιν from the models xeseuted by Sarajedini (1999))).," If taken at face value, this represents an age dispersion of $\sim$ 1.5 Gyr among the RC stars (based on 0.02 mag/Gyr from the models presented by \citet{sar99}) )." + The aean value of the distance moduli for ten regions ds derived to be (aADype=2L8041.0 Lvandom)+0.05(svstematic) using eq.(6).," The mean value of the distance moduli for ten regions is derived to be $(m-M)_{0,RC} = 24.80\pm0.04$ $\pm0.05$ (systematic) using eq.(6)." + The errorA are derived following the error budget in Table 5., The errors are derived following the error budget in Table 5. + If we use the calibration by Udalski(2000).. we obtain GnM)pee=2176£0.0 Lvandom)j+0.05(svstematic," If we use the calibration by \citet{uda00}, we obtain $(m-M)_{0,RC}=24.76\pm0.04$ $\pm0.05$ (systematic)." + These values are in excellent agreement with those frou). the TRGB., These values are in excellent agreement with those from the TRGB. + To date the distance to M33 has been studied using a munber of standard caudles: Cepheid variables (SaudageLeeetal. 2001). horizontal brauch stars in globular clusters (Sarajedinietal.2000).. red supergiant lone-period variables (SLPVs)(Pierce.Jurcevic.&Crabtree 2000).. the huninosity function of the planctary nebulae (PNLF)(Alaerinietal.2000). aud the TROB (Mould 1998).. as sunimniuized in Table 6 (see also Bereh (1991)..vaudenBerel (1999)..van.deuDergh (200033).," To date the distance to M33 has been studied using a number of standard candles: Cepheid variables \citep{san83a, san83b, chr87, mou87, mad91, +fre91,fre01,lee01}, , horizontal branch stars in globular clusters \citep{sar00}, red supergiant long-period variables \citep{pie00}, the luminosity function of the planetary nebulae \citep{mag00} and the TRGB \citep{mou86,lee93,sal98}, as summarized in Table 6 (see also \citet{van91}, \citet{van99}, \citet{van00}) )." + These distance moduli range frou as low as 21.11 to a high of 21.55., These distance moduli range from as low as 24.41 to a high of 24.85. + Our values of 2180. 2L81 Crom the RC with Popowski (2000) calibration aud the TRGB) aud 276 (from the RC with Udalski (2000) calibration) are at the hieh eud of the published rauge of distances.," Our values of 24.80, 24.81 (from the RC with Popowski (2000) calibration and the TRGB) and 24.76 (from the RC with Udalski (2000) calibration) are at the high end of the published range of distances." + Among the previous distance estimates. Leeetal.(2001) determined the distance to M32 using the single phase {-baud photometry of 21 Cepheids with logP20.8 based ou the same data as used in this paper.," Among the previous distance estimates, \citet{lee01} determined the distance to M33 using the single phase $I$ -band photometry of 21 Cepheids with $\log P >0.8$ based on the same data as used in this paper." + Leeetal.(2001) obtained (aAM)g=2152450.13 for for an adopted total reddening of M33. E(BV)2020x001 (EWfF)=0.27 250.05) eiven by Freeciananetal.(2001).. the reddening to the LMC. E(BVy)=010. aud the distance to the LMC. GaM)y=18.50.," \citet{lee01} obtained $(m-M)_0=24.52\pm0.13$ for for an adopted total reddening of M33, $E(B-V)=0.20\pm0.04$ $E(V-I)=0.27\pm0.05$ ) given by \citet{fre01}, the reddening to the LMC, $E(B-V)=0.10$, and the distance to the LMC, $(m-M)_0=18.50$." + This value is ~0.3 mae sanaller than those derived using the TRGD and RC in this study., This value is $\sim 0.3$ mag smaller than those derived using the TRGB and RC in this study. + This difference is considered partially due to the uncertainty in the estimates of the total reddening for Cepheids in M33., This difference is considered partially due to the uncertainty in the estimates of the total reddening for Cepheids in M33. + Note that Freediian.Wilson.&Madore(1991) derived the total reddening of N33 Cepheids from. BVRI photometry to be E(BVj=0.10x0.09. while Freecananetal.(2001) revised this value to E(BV)—0.20dE0.01 uxing the different period-liuminosity relatious for V and £ with the same data.," Note that \citet{fre91} derived the total reddening of M33 Cepheids from $BVRI$ photometry to be $E(B-V)=0.10\pm0.09$, while \citet{fre01} revised this value to $E(B-V)=0.20\pm0.04$ using the different period-luminosity relations for $V$ and $I$ with the same data." + Better estimates of the reddening of M33 Cepheids are needed to investigate further this problem., Better estimates of the reddening of M33 Cepheids are needed to investigate further this problem. + In the previous section we have exanuued the dependence on ietallicity of the f-band magnitude of he red chuup aud the maguitude of the TRGB., In the previous section we have examined the dependence on metallicity of the $I$ -band magnitude of the red clump and the magnitude of the TRGB. + Here we investigate the dependence ou ietallicity of both ogether usine the difference of the L-band magnitude tween the RC aud the TRGB. AJ(RC. TRGDB) ={μεἵπτμουρ.," Here we investigate the dependence on metallicity of both together using the difference of the $I$ -band magnitude between the RC and the TRGB, $\Delta I$ (RC–TRGB) $ = I_{RC} - I_{TRGB}$ ." + M(OORC ΤΠ) cau be measured directly your the photometry and has the added acvantage of cine extinction-free (Dersier2000)., $\Delta I$ (RC–TRGB) can be measured directly from the photometry and has the added advantage of being extinction-free \citep{ber00}. +.. Figure 10 displays AI(RC TRGB) versus |Fe/TI] for the teu regions in M33., Figure 10 displays $\Delta I $ (RC–TRGB) versus [Fe/H] for the ten regions in M33. + It is seen clearly that there is a positive correlation ietweeu ΑΠΟ TRGB) and |Fo/TI]., It is seen clearly that there is a positive correlation between $\Delta I $ (RC–TRGB) and [Fe/H]. +" The data for the outer δ regions in MDO3 are fit well by AJ( TRGD)—V.L5|40.18] |3.95,40.101).", The data for the outer 8 regions in M33 are fit well by $\Delta I $ $=0.45[\pm0.18]$ $+3.95[\pm0.14]$. + Th we use the data for all regions including the immer two regions. we derive Αίας TROBJ=0.56|3:0.15]|Fe |LOLOL.," If we use the data for all regions including the inner two regions, we derive $\Delta I $ $=0.56[\pm0.15]$ $+4.04[\pm0.11]$." + The error for he slope is rather large. because the rauge of |Fe/TI used for this fif is suall.," The error for the slope is rather large, because the range of [Fe/H] used for this fit is small." + Since the TROB magnitudes and foreground extinctions for all the regions are aluost constant. =LO and A;=0.08 (as given iu Table 2). μα...the slope in this fit represeuts basically the dependence of the RC magnitude on [Fe/TI].," Since the TRGB magnitudes and foreground extinctions for all the regions are almost constant, $M_{I}^{TRGB}=-4.0$ and $A_I=0.08$ (as given in Table 2), the slope in this fit represents basically the dependence of the RC magnitude on [Fe/H]." + The slope derived from the data of N33 is rather steeper than the slope given by Popowski(2000) which is based ou the galactic RC stars (shown by the dashed line in Figure 10)., The slope derived from the data of M33 is rather steeper than the slope given by \citet{pop00} which is based on the galactic RC stars (shown by the dashed line in Figure 10). + For a better determination of the depeudeuce of AZ(RC TRGB} on |Fe/II|. a large range of |Fo/TI] is required.," For a better determination of the dependence of $\Delta I $ (RC--TRGB) on [Fe/H], a large range of [Fe/H] is required." + We have compared Ας TROD) for N33 with those for other nearby galaxies compiled bv Dersier(2000) 1- Figure 11., We have compared $\Delta I $ (RC–TRGB) for M33 with those for other nearby galaxies compiled by \citet{ber00} in Figure 11. + For M33 the mean difference =3.6240.05 aud mean metallicity <[PeΠΠ>=0.75£0.07 of the outer cight regions (excluding R1t aud R12) are used from this study., For M33 the mean difference $<\Delta I>=3.62\pm0.05$ and mean metallicity $<[Fe/H]>=-0.75\pm0.07$ of the outer eight regions (excluding R14 and R12) are used from this study. + Figure 11 shows that the data for ΑΟ is consistent with those for other galaxies. following the relation plotted in Figure 10.," Figure 11 shows that the data for M33 is consistent with those for other galaxies, following the relation plotted in Figure 10." + We present VI photometry of ficld stars in teu regions located at R=2.6 to 17.5 arcuuinfrom the ceuter of A133 based on LESTAVPPC? images., We present $VI$ photometry of field stars in ten regions located at $R=2.6$ to 17.8 arcminfrom the center of M33 based on $HST/WFPC2$ images. + From this photometry we have determined the distance to M33 using the tip of the red giant branch (TROB) and the red clump (RC)., From this photometry we have determined the distance to M33 using the tip of the red giant branch (TRGB) and the red clump (RC). + Main results obtained m this study are sunuuarized as follows., Main results obtained in this study are summarized as follows. +pressureless matter and with gravity governed by general relativity (essοἱal.1905:Perlmutteretal.1999:Ixnop2003:Riess 2004).,"pressureless matter and with gravity governed by general relativity \citep{Riess1, Perlmutter, Knop, Riess2}." +. This implies that the expansion rate ol the Universe is accelerating., This implies that the expansion rate of the Universe is accelerating. + Furthermore. if we restrict ourselves (ο fitting the observed redshifts and magnitudes of (wpe Ia SNe to the predictions of FRW models. we find that the data appear to be best fit bv a flat model with a matter density Q3;20.25 and a cosmological constant density Q4zz0.75.," Furthermore, if we restrict ourselves to fitting the observed redshifts and magnitudes of type Ia SNe to the predictions of FRW models, we find that the data appear to be best fit by a flat model with a matter density $\Omega_M\approx 0.25$ and a cosmological constant density $\Omega_{\Lambda}\approx 0.75$." + In this model. (he Universe is presently undergoing accelerated expansion because of the current phase of dark energy domination.," In this model, the Universe is presently undergoing accelerated expansion because of the current phase of dark energy domination." + There have been recent claims that we mav not be justified in filling SN data with FRW models. and thus doing so max have led {ο an incorrect assessment of the composition and behavior of the Universe: for a review. see Celerier (2007) and references therein.," There have been recent claims that we may not be justified in fitting SN data with FRW models, and thus doing so may have led to an incorrect assessment of the composition and behavior of the Universe; for a review, see Celerier (2007) and references therein." + Of course. even if the Universe is homogeneous on large scales. local large scale structure does undoubtedly perturb the redshifts ancl apparent magnitudes of type Ia SNe.," Of course, even if the Universe is homogeneous on large scales, local large scale structure does undoubtedly perturb the redshifts and apparent magnitudes of type Ia SNe." + So the question ab hand is: Can such perturbations have a non-negligible impact on the inferences that we draw from these data?, So the question at hand is: Can such perturbations have a non-negligible impact on the inferences that we draw from these data? + It has been suggested that the answer could be ves. with the largest effects coming from peculiar velocities and weak lensing (hu&Greene&Caldwell 2006).," It has been suggested that the answer could be “yes"", with the largest effects coming from peculiar velocities and weak lensing \citep{HG,CC}." +. We will focus here on peculiar velocities. whereas Sarkar et al. (," We will focus here on peculiar velocities, whereas Sarkar et al. (" +2007) performs a complementary analvsis with the focus on lensing.,2007) performs a complementary analysis with the focus on lensing. + Although it is really the total combined effect of inhomogeneity that is gauge invariant and observable. we are nonetheless allowed to look at the peculiar velocity effect alone here in the Newtonian regime.," Although it is really the total combined effect of inhomogeneity that is gauge invariant and observable, we are nonetheless allowed to look at the peculiar velocity effect alone here in the Newtonian regime." + The goal of this paper is to theoretically quantify the parameter errors (hat result [rom the peculiar velocities of (wpe la SNe in (he most realistic Irunework possible., The goal of this paper is to theoretically quantify the parameter errors that result from the peculiar velocities of type Ia SNe in the most realistic framework possible. + We will (hus make use of N-body simulation data. making this the first theoretical study of this effect that robustly takes into account not only correlated. bulk flows. but also fully nonlinear (Newlonian) structure formation. both of which are thought to enhance the effect.," We will thus make use of N-body simulation data, making this the first theoretical study of this effect that robustly takes into account not only correlated bulk flows, but also fully nonlinear (Newtonian) structure formation, both of which are thought to enhance the effect." + We will find that our results are in accordance with recent estimates from. actual SN data., We will find that our results are in accordance with recent estimates from actual SN data. + A kev benefit of our theoretical approach. however. is that we can now estimate the size of the effect that we will expect for future SN surveys. such as SNAP [or which we find the peculiar velocitv-induced error in à constant dark enerev equation of state to be at the 1% level.," A key benefit of our theoretical approach, however, is that we can now estimate the size of the effect that we will expect for future SN surveys, such as SNAP for which we find the peculiar velocity-induced error in a constant dark energy equation of state to be at the $1\%$ level." + This is subdominant to the ~5% error. that we would find with the same survey and model fitting. due to a 0.1 mae intrinsic scatter.," This is subdominant to the $\sim 5\%$ error, that we would find with the same survey and model fitting, due to a $0.1$ mag intrinsic scatter." + We will also address (he question of whether it is beneficial to throw away very low redshift (2< 0.02) SN data when fitting to a model. as such data points will be the most allected by these errors: we find (hat such a practice could lead to error reductions of LOW at most. for low redshift surveys.," We will also address the question of whether it is beneficial to throw away very low redshift $z\lesssim 0.02$ ) SN data when fitting to a model, as such data points will be the most affected by these errors; we find that such a practice could lead to error reductions of $10\%$ at most, for low redshift surveys." + These issues are of ereat importance at a time when the dark energy problem is at the forefront of modern, These issues are of great importance at a time when the dark energy problem is at the forefront of modern +for each region (120 K for 122198. 210 K for A5142-MM1. and 140 K for A3142-MM2).,"for each region (120 K for I22198, 210 K for A5142-MM1, and 140 K for A5142-MM2)." + Third. we adopted the derived temperatures. as well as the average linewidths of the involved transitions (given in Fig.," Third, we adopted the derived temperatures, as well as the average linewidths of the involved transitions (given in Fig." + 3). to compute synthetic spectra for both aand(CH>OH)>.. summed them. and subtract the sum to the observed spectrum.," 3), to compute synthetic spectra for both and, summed them, and subtract the sum to the observed spectrum." + Finally. the definitive line identification of molecules different from aand wwas performed in the residual spectrum (Fig.," Finally, the definitive line identification of molecules different from and was performed in the residual spectrum (Fig." + 3-right) for lines with flux above do (0=4.5 mJy for 122198; σ=7.5 mJy for A5142)., 3-right) for lines with flux above $\sigma$ $\sigma=4.5$ mJy for I22198; $\sigma=7.5$ mJy for A5142). + The systemic velocity used for 122198 was derived from the strongest isolated lines and was found to be —12.3 kms., The systemic velocity used for I22198 was derived from the strongest isolated lines and was found to be $-12.3$ kms. + As for A5142. we adopted the systemic velocities derived by Zhang (2007); 21.0 ffor AS142-MMI. and 23.4 Που AS142-MM2.," As for A5142, we adopted the systemic velocities derived by Zhang (2007): $-1.0$ for A5142-MM1, and $-3.4$ for A5142-MM2." +" The synthetic spectra were computed using the estimates of temperature and linewidth given above. and assuming local thermodynamic. equilibrium. optically thin emission. and the molecular data from the Jet Propulsion Laboratory (Pickett 11998) or the Cologne Database forMolecular Spectroscopy catalogs (Mülller 22005), except for CH:OD (Anderson 11988)."," The synthetic spectra were computed using the estimates of temperature and linewidth given above, and assuming local thermodynamic equilibrium, optically thin emission, and the molecular data from the Jet Propulsion Laboratory (Pickett 1998) or the Cologne Database forMolecular Spectroscopy catalogs (Mülller 2005), except for $_3$ OD (Anderson 1988)." + The final identification is presented in Fig 3-right and the column densities used to build the synthetic spectra are listed in Table I., The final identification is presented in Fig 3-right and the column densities used to build the synthetic spectra are listed in Table 1. + In addition to aand(CH>OH)>.. the strongest lines found in the spectra of the three sources are from aandCH3sCOCHs.. and for none of the sources CN-bearing species such asCH:CHCN.. wwere required to fit the spectra.," In addition to and, the strongest lines found in the spectra of the three sources are from and, and for none of the sources CN-bearing species such as, were required to fit the spectra." +Molecules detected only in 122198 areCH3CHO..CH;OCHO.. CH;OD and HCOOD.,"Molecules detected only in I22198 are, $_3$ OD and HCOOD." + On the other hand. for A5142-MMI. no deuterated species were detected. wwas found to dominate the line at 230.317 GHz (with no need of CH;CHO)). and we identfied two transitions of CoH. with energies of the upper state of 483 K. The spectrum observed in A5142-MM? is essentially the same as that of À5]42-MMI. with smaller fluxes.," On the other hand, for A5142-MM1, no deuterated species were detected, was found to dominate the line at 230.317 GHz (with no need of ), and we identfied two transitions of $_6$ H, with energies of the upper state of 483 K. The spectrum observed in A5142-MM2 is essentially the same as that of A5142-MM1, with smaller fluxes." +" Among the strongest detected transitions we have chosen four to be representative of different excitation conditions, and computed the zero-order (integrated intensity) and first-order (velocity) maps (Figures |-b-e and 2-b-e)."," Among the strongest detected transitions we have chosen four to be representative of different excitation conditions, and computed the zero-order (integrated intensity) and first-order (velocity) maps (Figures 1-b–e and 2-b–e)." + From the figure it is seen that in 122198 the COM emission is restricted to MM?2 without extending to MM2-S. and that this emission is elongated for almost all the molecules in the southeast-northwest direction (the only unresolved emission is that fromCH3iCOCHh;.. às in Orion-KL. FFriedel 22005).," From the figure it is seen that in I22198 the COM emission is restricted to MM2 without extending to MM2-S, and that this emission is elongated for almost all the molecules in the southeast-northwest direction (the only unresolved emission is that from, as in Orion-KL, Friedel 2005)." + The deconvolved size and PA. of the average emission of the four transitions shown in Fig., The deconvolved size and P.A. of the average emission of the four transitions shown in Fig. + I-b-e ts listed in Table |., 1-b–e is listed in Table 1. + It is interesting to note that the first-order moment map of the three resolved COM transitions of 122198 shows a velocity gradient in the direction perpendicular to outflow A (Fig., It is interesting to note that the first-order moment map of the three resolved COM transitions of I22198 shows a velocity gradient in the direction perpendicular to outflow A (Fig. + le)., 1e). + Concerning A5142. COM emission ts found in both millimeter continuum sources MM1 and MM2. with the first-order moment showingthat there is a shift in. velocities between the two sources of ~3kms7!.. as found by Zhang ((2007). and with hints of an elongation in the east-west direction for MMI. and in the southeast-northwest direction for MM2 (Table 1).," Concerning A5142, COM emission is found in both millimeter continuum sources MM1 and MM2, with the first-order moment showingthat there is a shift in velocities between the two sources of $\sim3$, as found by Zhang (2007), and with hints of an elongation in the east-west direction for MM1, and in the southeast-northwest direction for MM2 (Table 1)." + What is more. the emission from MMI reveals an extension to the southwest. apparent mainly inCH;OH.. which is following the CO redshifted emission shown in Fig.," What is more, the emission from MM1 reveals an extension to the southwest, apparent mainly in, which is following the CO redshifted emission shown in Fig." + 2-8. The set of detected molecules in the mtermediate-mass hot cores of 122198 and A5142 does not include CN-bearing species., 2-e. The set of detected molecules in the intermediate-mass hot cores of I22198 and A5142 does not include CN-bearing species. + We inspected the observed frequency range and found that at least two transitions of sshould have been detected (at 230.488 and 230.739 GHz) with the same intensity. from synthetic spectra at rotational temperature in the range 100-600 K and column densities ~10 em? (Table 1).," We inspected the observed frequency range and found that at least two transitions of should have been detected (at 230.488 and 230.739 GHz) with the same intensity, from synthetic spectra at rotational temperature in the range 100–600 K and column densities $\sim10^{15}$ $^{-2}$ (Table 1)." + Thus. the set of detected molecules is similar to the sets of the hot corino 16293-2422. whereO'°CS..CH:iCHO.. and are also detected (Bottinelli 22007; Caux 22011).," Thus, the set of detected molecules is similar to the sets of the hot corino $-$ 2422, where, and are also detected (Bottinelli 2007; Caux 2011)." +" However. 116293-2422 Is dominated by simple O-rich and HCO-rich species. like H»CO. SOs.CH;OH..CH;CHO.. and CH;OCHO.. while in 122198 and A5]42 we detected more CH>,3-rich molecules. such as CH;CH:OH.. (CH2OH):.. and CH;COCH;."," However, $-$ 2422 is dominated by simple O-rich and HCO-rich species like $_2$ CO, $_2$, and , while in I22198 and A5142 we detected more $_{2/3}$ -rich molecules, such as , , and ." +. On the other hand. massive hot cores. such as Orion-KL (Caselli," On the other hand, massive hot cores, such as Orion-KL (Caselli" +temperatures using the colour-temperature relation of Kenyon Hartmann (1995).,temperatures using the colour-temperature relation of Kenyon Hartmann (1995). + The EWs (shown in oon the RH axis) are sealed to match the K3 standard at the blue end of the plot., The EWs (shown in on the RH axis) are scaled to match the K3 standard at the blue end of the plot. + The results show a similar upper bound to the previous results. indicating that the variation in scaling constant with colour is closely related to the changes in the underlying EW of the CaT absorption line with spectral type.," The results show a similar upper bound to the previous results, indicating that the variation in scaling constant with colour is closely related to the changes in the underlying EW of the CaT absorption line with spectral type." + The results in Fig., The results in Fig. + 5 were used to detine a semi-empirical reference spectrum. #(A). as a function of colour. which represents chromospherically inactive stars.," 5 were used to define a semi-empirical reference spectrum, $R(\lambda)$, as a function of colour, which represents chromospherically inactive stars." +" Using the normalised spectrum of the K3 reference star local to the first two CaT lines /Z?456À) and a scaling constant. 5,. we detine We modelled S, using a simple by-eye three-part linear function to represent the upper boundary of the points in Fig."," Using the normalised spectrum of the K3 reference star local to the first two CaT lines $R_{K3}(\lambda)$ and a scaling constant, $S_c$, we define We modelled $S_c$ using a simple by-eye three-part linear function to represent the upper boundary of the points in Fig." + 3. which we assume represents the CaT line depths for chromospherically inactive stars. where S.= Hfor(V—/)o3.4$ $\simeq$ M5)." + Ihe EWs of the first two CaT emission lines were measured by comparing a section of the the target spectrum local to the CaT line centre. S(À). with the reference spectrum. /?(A) (see Fig.," The EWs of the first two CaT emission lines were measured by comparing a section of the the target spectrum local to the CaT line centre, $S(\lambda)$, with the reference spectrum, $R(\lambda +)$ (see Fig." + 6)., 6). + The reference spectrum was aligned in wavelength and convolved with a broadening kernel. according to the RV and esin? of the target.," The reference spectrum was aligned in wavelength and convolved with a broadening kernel, according to the RV and $v\sin i$ of the target." + The target and reference spectra were then normalised to their average levels either side of the CaT line centres over the wavelength ranges indicated in Fig., The target and reference spectra were then normalised to their average levels either side of the CaT line centres over the wavelength ranges indicated in Fig. + 6., 6. + The reference spectrum was subtracted from the target spectrum to produce a difference spectrum The EW of the CaT features in AfA) gave a measure of chromospheric activity.," The reference spectrum was subtracted from the target spectrum to produce a difference spectrum The EW of the CaT features in $\Delta(\lambda +)$ gave a measure of chromospheric activity." + In practice the difference spectra can be noisy and the width of the residual chromospheric component depends on the esin? of the target.," In practice the difference spectra can be noisy and the width of the residual chromospheric component depends on the $v \sin +i$ of the target." + Integrating under ACA) would give different estimates of EW depending on the integration limits., Integrating under $\Delta(\lambda )$ would give different estimates of EW depending on the integration limits. +" This problem was circumvented using an “optimal extraction"" technique — i.e. multiplying the difference spectrum by a Gaussian profile of unit area. which represents the expected protile of the difference spectrum produced by a chromospheric emission line."," This problem was circumvented using an “optimal extraction” technique – i.e. multiplying the difference spectrum by a Gaussian profile of unit area, which represents the expected profile of the difference spectrum produced by a chromospheric emission line." + The width of the Gaussian profile for slowly rotating stars was found by fitting a Gaussian to the difference spectra of 25 long-period stars which showed signiticant CaT emission lines., The width of the Gaussian profile for slowly rotating stars was found by fitting a Gaussian to the difference spectra of 25 long-period stars which showed significant CaT emission lines. + This gave a width ay=0.30+0.02À., This gave a width $\sigma_0 = 0.30\pm 0.02$. +. A Gaussian profile. re-centred according to the target RV and broadened beyond συ according to esin7. gave a function 20). which was used to determine the EW as: Examples of 2?(A) are shown in Fig.," A Gaussian profile, re-centred according to the target RV and broadened beyond $\sigma_0$ according to $v\sin i$, gave a function $P(\lambda)$, which was used to determine the EW as: Examples of $P(\lambda)$ are shown in Fig." + 6 as dotted lines centred at the expected emission line wavelength., 6 as dotted lines centred at the expected emission line wavelength. + The uncertainty in the EWs due to noise in the spectrum was estimated as the rms value of the EWs measured using the same /?(À) centred at five wavelengths either side of the emission line., The uncertainty in the EWs due to noise in the spectrum was estimated as the rms value of the EWs measured using the same $P(\lambda)$ centred at five wavelengths either side of the emission line. +" We define the activity index R,,, us the fraction of a stür's bolometric luminosity emitted from the chromosphere in a CaT line.", We define the activity index $R^{'}_{Ca}$ as the fraction of a star's bolometric luminosity emitted from the chromosphere in a CaT line. + The conversion between the EW of the chromospheric component of the CaT line and the flux (in 7 4) was established by measuring the continuum flux densities in our defined continuum windows (see Fig., The conversion between the EW of the chromospheric component of the CaT line and the flux (in $^{-2}$ $^{-1}$ ) was established by measuring the continuum flux densities in our defined continuum windows (see Fig. + 6) in K- and M-dwarfs from he standard spectral library of Pickles (1998)., 6) in K- and M-dwarfs from the standard spectral library of Pickles (1998). + Using the V/ colours tabulated by Pickles for these stars and their V -band fluxes we fitted the following relationship where {0 is the intrinsic Cousins /-band magnitude and EW. is the EW of either of the CaT lines (the difference in continuum evels is ddex or less)., Using the $V-I$ colours tabulated by Pickles for these stars and their $V$ -band fluxes we fitted the following relationship where $I_0$ is the intrinsic Cousins $I$ -band magnitude and $_{Ca}$ is the EW of either of the CaT lines (the difference in continuum levels is dex or less). + The bolometric flux is given by where BC' is the V -band bolometric correction (Allen 1973)., The bolometric flux is given by where $BC$ is the $V$ -band bolometric correction (Allen 1973). + The difference in these expressions defines the activity index, The difference in these expressions defines the activity index +unresolved binaries. although in the case of an open cluster. it 1s expected to be less frequent. owing to the lower density of stars.,"unresolved binaries, although in the case of an open cluster, it is expected to be less frequent, owing to the lower density of stars." + To quantify this. we distributed 900 synthetic white dwarfs (the observed number of stars) in the field of view of the HST CCD (4052x4052 pixels) and we evaluated the probability of chance superposition.," To quantify this, we distributed 900 synthetic white dwarfs (the observed number of stars) in the field of view of the HST CCD $4052\times +4052$ pixels) and we evaluated the probability of chance superposition." + We found that this probability ts ~0.8% if the distance necessary to resolve two stars is ~10 pixels., We found that this probability is $\sim 0.8$ if the distance necessary to resolve two stars is $\sim 10$ pixels. + Thus. for the case of NGC 6791 this possibility is quite unlikely. and the unresolved binary white dwarfs are most probably real systems.," Thus, for the case of NGC 6791 this possibility is quite unlikely, and the unresolved binary white dwarfs are most probably real systems." + We used four different models for the distribution of secondary masses in the progenitor bynary system. under the assumption — the same as in Bedin et al. (," We used four different models for the distribution of secondary masses in the progenitor bynary system, under the assumption – the same as in Bedin et al. (" +2008b) — that binary white dwarts are produced by a primordial binary system.,2008b) – that binary white dwarfs are produced by a primordial binary system. + Our first distribution is that already used by Bedin et al. (, Our first distribution is that already used by Bedin et al. ( +"2008b). mg)=0.0 for g<0.5 and ng)=1.0 otherwise. where g=M2/M,. being M, and M» the mass of the primary and of the secondary. respectively.","2008b), $n(q)=0.0$ for $q<0.5$ and $n(q)=1.0$ otherwise, where $q=M_2/M_1$, being $M_1$ and $M_2$ the mass of the primary and of the secondary, respectively." + We refer to this distribution as model I., We refer to this distribution as model 1. + In model 2 we assume z(q)=1.0. independently of the mass ratio.," In model 2 we assume $n(q)=1.0$, independently of the mass ratio." + For model 3 we adopted n(q)«q.," For model 3 we adopted $n(q)\propto +q$." + Finally. for our last set of simulations. corresponding to model 4. we adopted n(q)ox q-!. We display the results of this set of simulations in Fig. 2..," Finally, for our last set of simulations, corresponding to model 4, we adopted $n(q)\propto q^{-1}$ We display the results of this set of simulations in Fig. \ref{m1m2}." + Evidently. the corresponding white-dwarf luminosity functions show dramatic differences.," Evidently, the corresponding white-dwarf luminosity functions show dramatic differences." + The distribution of secondary masses of Bedin et al. (, The distribution of secondary masses of Bedin et al. ( +2008b). top left panel. perfectly matches the observational white-dwarf luminosity function of NGC 679].,"2008b), top left panel, perfectly matches the observational white-dwarf luminosity function of NGC 6791." + When model 2 is adopted. the secondary peak of the simulated luminosity function. does not match the observational data. and the amplitude of the faintest peak is very much increased.," When model 2 is adopted, the secondary peak of the simulated luminosity function does not match the observational data, and the amplitude of the faintest peak is very much increased." + It might be argued that this incongruence could be fixed by simply changing the fraction of binary white dwarfs. and indeed this could be done. but then one would need à present total percentage of binary stars well above60%.. which is probably unrealistic.," It might be argued that this incongruence could be fixed by simply changing the fraction of binary white dwarfs, and indeed this could be done, but then one would need a present total percentage of binary stars well above, which is probably unrealistic." + Thus. we conclude that a flat distributor of secondary masses can be discarded.," Thus, we conclude that a flat distribution of secondary masses can be discarded." + When the third distribution of secondary masses is used. we obtain a good fit to the observational data. although the quality of the fit is not as good as that of model 1.," When the third distribution of secondary masses is used, we obtain a good fit to the observational data, although the quality of the fit is not as good as that of model 1." + This is not surprising. since both distributions of secondary masses increase for increasing values of q.," This is not surprising, since both distributions of secondary masses increase for increasing values of $q$." + Finally. when model 4 is employed. the simulated white-dwarf luminosity function is totally Incompatible with the observational data.," Finally, when model 4 is employed, the simulated white-dwarf luminosity function is totally incompatible with the observational data." + The same arguments used when discussing the flat distribution of secondary masses apply here. and thus we can safely discard this distribution.," The same arguments used when discussing the flat distribution of secondary masses apply here, and thus we can safely discard this distribution." + We conclude that most likely only distributions of secondary masses that increase as the mass ratio of the two components of the binary increases are compatible with the existing observational data for NGC 6791., We conclude that most likely only distributions of secondary masses that increase as the mass ratio of the two components of the binary increases are compatible with the existing observational data for NGC 6791. +In the 1989. 1991. and 1993 observations. data were recorded at two simultaneous frequencies. 1385 1652 MHz. within the 20-cm band.,"In the 1989, 1991, and 1993 observations, data were recorded at two simultaneous frequencies, 1385 1652 MHz, within the 20-cm band." + Each frequency consisted of 15 channels spread across a 23.5 MHz bandwidth with a sampling time of 10 seconds. resulting in a useable field-of-view of radius ~10 centered on the pulsar.," Each frequency consisted of 15 channels spread across a 23.5 MHz bandwidth with a sampling time of 10 seconds, resulting in a useable field-of-view of radius $\sim10'$ centered on the pulsar." + For the 2000-epoch observations. we also incorporated data from the Pie Town antenna of the VLBA. which doubled the resolution of the array primarily in. one dimension.," For the 2000-epoch observations, we also incorporated data from the Pie Town antenna of the VLBA, which doubled the resolution of the array primarily in one dimension." + The observations for that epoch were conducted at 1385 1516 MHz. and consisted of 15 channels across a 12.5 MHz bandwidth with 5-sec sampling. again resulting in a 10-aremin field-of-view.," The observations for that epoch were conducted at 1385 1516 MHz, and consisted of 15 channels across a 12.5 MHz bandwidth with 5-sec sampling, again resulting in a 10-arcmin field-of-view." + The flux density scale of our observations was determined using observations of 3C 286. while the time-varying gains for each antenna were measured using regular observations of PKS B1923+210 or TXS 20134370.," The flux density scale of our observations was determined using observations of 3C 286, while the time-varying gains for each antenna were measured using regular observations of PKS B1923+210 or TXS 2013+370." +" After standard editing and calibration. we produced images of the pulsar field for each epoch and frequency. using multi-frequency synthesis to mitigate bandwidth smearing. and discarding all baselines shorter than 10 km (corresponding to spatial scales larger than 4"")."," After standard editing and calibration, we produced images of the pulsar field for each epoch and frequency, using multi-frequency synthesis to mitigate bandwidth smearing, and discarding all baselines shorter than 10 km (corresponding to spatial scales larger than $4''$ )." + By removing these shorter baselines. we ensured that emission from SNR aand from the compact wind-driven nebula surrounding the pulsar were not detected.," By removing these shorter baselines, we ensured that emission from SNR and from the compact wind-driven nebula surrounding the pulsar were not detected." +" The only emission seen in our images was the pulsar itself. the ""hot-spot seen immediately adjacent= (Strom 1987)). and various other point sources spread throughout the field."," The only emission seen in our images was the pulsar itself, the “hot-spot” seen immediately adjacent \cite{str87}) ), and various other point sources spread throughout the field." + We have identified seven such sources within 10° of the pulsar. as listed in Table l..," We have identified seven such sources within $10'$ of the pulsar, as listed in Table \ref{tab_pos}." + After deconvolving each image using the algorithm. we applied a gaussian fit to the pulsar and to each of these seven sources to measure their position and extent at each epoch and frequency.," After deconvolving each image using the algorithm, we applied a gaussian fit to the pulsar and to each of these seven sources to measure their position and extent at each epoch and frequency." + In order to accurately measure the pulsar proper motion. we adopted six of the field sources as reference sources. reserving the nearest source to the pulsar (source | in Table 1)) as a check on our measurements.," In order to accurately measure the pulsar proper motion, we adopted six of the field sources as reference sources, reserving the nearest source to the pulsar (source 1 in Table \ref{tab_pos}) ) as a check on our measurements." + The reference sources are approximately evenly distributed throughout the field., The reference sources are approximately evenly distributed throughout the field. + The quality of each source as an astrometric reference was determined by measuring the vector separation between all possible pairs of sources. and then verifying that no source showed trends or significant changes in the magnitude and direction of these vectors.," The quality of each source as an astrometric reference was determined by measuring the vector separation between all possible pairs of sources, and then verifying that no source showed trends or significant changes in the magnitude and direction of these vectors." + We also verified that in all cases the dimensions of the fitted gaussian matched those of the synthesized beam. confirming that seatter broadening and bandwidth smearing (in the case of background sources) or scintillation (in the case of the pulsar) were not affecting our positional determinations.," We also verified that in all cases the dimensions of the fitted gaussian matched those of the synthesized beam, confirming that scatter broadening and bandwidth smearing (in the case of background sources) or scintillation (in the case of the pulsar) were not affecting our positional determinations." + The ionosphere can potentially distort the measured positions. producing a frequency-dependent angular displacement A@=ΚΑ. where 7 is the angular separation between a source and the field center. A is the observing wavelength. and & is a constant.," The ionosphere can potentially distort the measured positions, producing a frequency-dependent angular displacement $\Delta\theta=k \theta \lambda^2$, where $\theta$ is the angular separation between a source and the field center, $\lambda$ is the observing wavelength, and $k$ is a constant." + By measuring () for each source and each frequency. we found that & had a value consistent with zero. demonstrating that any ionospheric effects were dominated by other uncertanties in our measurements.," By measuring $\theta$ for each source and each frequency, we found that $k$ had a value consistent with zero, demonstrating that any ionospheric effects were dominated by other uncertanties in our measurements." + MeGary ((2001)) used the VLA to measure pulsar proper motions an order of magnitude smaller than that expected here. and found a variety of other ways in. which the positions of reference sources can be distorted. including relativistic effects due to the Earth’s motion. errors introduced by the VLA correlator and additional empirical corrections which had no. simple explanation.," McGary \nocite{mbf+01}) ) used the VLA to measure pulsar proper motions an order of magnitude smaller than that expected here, and found a variety of other ways in which the positions of reference sources can be distorted, including relativistic effects due to the Earth's motion, errors introduced by the VLA correlator and additional empirical corrections which had no simple explanation." + At the lower precision required here. we have accounted for all these effects simply by measuring the scatter in the position of each reference source between epochs.," At the lower precision required here, we have accounted for all these effects simply by measuring the scatter in the position of each reference source between epochs." + We began by determiniig the vector distances between all possible pairings of the six reference sources., We began by determining the vector distances between all possible pairings of the six reference sources. + The standare deviations of the componerts of each vector in Right Ascensior and Declination were computed for the four epochs: these were taken as the uncertainty for a particular pairing., The standard deviations of the components of each vector in Right Ascension and Declination were computed for the four epochs; these were taken as the uncertainty for a particular pairing. + This uncertainty was then decomposed between the two sources 11 that pair. the relative contributions of the two sources to the joint error being weighted inversely by each sources signal-to-noise ratio.," This uncertainty was then decomposed between the two sources in that pair, the relative contributions of the two sources to the joint error being weighted inversely by each source's signal-to-noise ratio." + We were thus able to derive an uncertainty η the position of each source for each pairing: these uncertainties were averaged over the five possible pairings to determine the best measurement of the true uncertainty in each coordinate for each source., We were thus able to derive an uncertainty in the position of each source for each pairing; these uncertainties were averaged over the five possible pairings to determine the best measurement of the true uncertainty in each coordinate for each source. + This analysis was performed separately for observations at 1385 MHz and at 1516/1652 MHz., This analysis was performed separately for observations at 1385 MHz and at 1516/1652 MHz. + A mean reference position for each epoch and frequency was then determined. by averaging together the positions of the six reference sources. Weighting the contribution from each source inversely by its distance from the field center.," A mean reference position for each epoch and frequency was then determined by averaging together the positions of the six reference sources, weighting the contribution from each source inversely by its distance from the field center." + The separation between the pulsar's position and this mean reference position was then measured for each epoch and frequency. combining in quadrature the calculated uncertainties in the pulsar position. with those determined for the reference position.," The separation between the pulsar's position and this mean reference position was then measured for each epoch and frequency, combining in quadrature the calculated uncertainties in the pulsar position with those determined for the reference position." + The results of these measurements are plotted in Figure .. and show a clear motion of the pulsar to the south-," The results of these measurements are plotted in Figure \ref{fig_motion}, and show a clear motion of the pulsar to the south-west." + The flux density of the pulsar was higher during the 1993 observations than at other epochs. resulting in smaller uncertainties m the pulsar position for this measurement.," The flux density of the pulsar was higher during the 1993 observations than at other epochs, resulting in smaller uncertainties in the pulsar position for this measurement." + Note that the position of the pulsar listed in Table 1. 1s consistent with previous determinations (Fosteretal. 1994)). but with larger errors due to the systematic errors discussed above.," Note that the position of the pulsar listed in Table \ref{tab_pos} is consistent with previous determinations \cite{flsb94}) ), but with larger errors due to the systematic errors discussed above." + Such uncertainties in the absolute astrometry do not affect our proper motion measurement. which has been determined based on astrometry relative to nearby background sources.," Such uncertainties in the absolute astrometry do not affect our proper motion measurement, which has been determined based on astrometry relative to nearby background sources." + As an independent test of our approach. we have similarly measured the proper motion for source ].," As an independent test of our approach, we have similarly measured the proper motion for source 1." + As is shown in Figure no change in position is seen for this source. demonstrating that the motion measured for the pulsar 1s real and that the uncertainties have been realistically assessed.," As is shown in Figure \ref{fig_motion}, no change in position is seen for this source, demonstrating that the motion measured for the pulsar is real and that the uncertainties have been realistically assessed." + By applying a weighted least squares fit to the pulsar's position at each epoch. we find a proper motion at 1385 MHz of ΗΞΔΙES mas |. at PA =250777. and at 1516/1652 MHz of gf2266 mas yr! at PA =240°+10°.," By applying a weighted least squares fit to the pulsar's position at each epoch, we find a proper motion at 1385 MHz of $\mu = +31\pm5$ mas $^{-1}$, at PA $=250^\circ \pm7^\circ$, and at 1516/1652 MHz of $\mu = 26\pm6$ mas $^{-1}$ at PA $=240^\circ \pm +10^\circ$." + These two measurements are consistent with each other within their uncertainties., These two measurements are consistent with each other within their uncertainties. + After taking into account apparent motion of the pulsar at the level of 5 mas yr! due to differential Galactic the combination of our two measurements yields a motion j=25+4 mas yr! at PA =252°t£T.," After taking into account apparent motion of the pulsar at the level of 5 mas $^{-1}$ due to differential Galactic the combination of our two measurements yields a motion $\mu = +25\pm4$ mas $^{-1}$ at PA $=252^\circ \pm 7^\circ$." +" The corresponding projected velocity is V,=(240+40)d» ffor a distance 2d» kpe.", The corresponding projected velocity is $V_t = (240\pm40)d_2$ for a distance $2d_2$ kpc. +" The transverse velocity we have inferred for PSR iis in agreement with the value V,~300 implied by seintillation in its dynamic spectrum. (Fruchter 1988)).", The transverse velocity we have inferred for PSR is in agreement with the value $V_t \sim 300$ implied by scintillation in its dynamic spectrum \cite{ftb+88}) ). + Furthermore. as shown in Figure 3. the measured," Furthermore, as shown in Figure \ref{fig_ctb80} the measured" +provide maps of the Galactic free-free emission and the Galactic synchrotron emission both in total and polarized intensity.,provide maps of the Galactic free-free emission and the Galactic synchrotron emission both in total and polarized intensity. +" The maps are 10°x in size, with ~1arcmin resolution and cover the frequency range between 115 and 180 MHz pertaining to the LOFAR-EoR experiment."," The maps are $10^\circ\times10^\circ$ in size, with $\sim1~{\rm arcmin}$ resolution and cover the frequency range between 115 and 180 MHz pertaining to the LOFAR-EoR experiment." + The code however is flexible as can provide simulation over any scale with any spatial and frequency resolution., The code however is flexible as can provide simulation over any scale with any spatial and frequency resolution. +" The Galactic emission is calculated from a 3D distribution of cosmic ray and thermal electrons, and the Galactic magnetic field."," The Galactic emission is calculated from a 3D distribution of cosmic ray and thermal electrons, and the Galactic magnetic field." + The model assumes two magnetic field components: regular and random., The model assumes two magnetic field components: regular and random. + The latter magnetic field and the thermal electron density are simulated as Gaussian random fields with power law power spectra., The latter magnetic field and the thermal electron density are simulated as Gaussian random fields with power law power spectra. +" In addition, the spatial variations of the energy spectral index p of the cosmic ray electrons are introduced to mimic the observed fluctuations of the brightness temperature spectral index B."," In addition, the spatial variations of the energy spectral index $p$ of the cosmic ray electrons are introduced to mimic the observed fluctuations of the brightness temperature spectral index $\beta$." + Note that all parameters of the simulation can be tuned to any desired value and this allows to explore the whole parameter space., Note that all parameters of the simulation can be tuned to any desired value and this allows to explore the whole parameter space. + The total and polarized Galactic maps are obtained for four different models of Galactic emission (see Fig., The total and polarized Galactic maps are obtained for four different models of Galactic emission (see Fig. + 3 4))., \ref{fig:synff}~ \ref{fig:PImodels}) ). +" The first assumes that synchrotron and free-free emitters are spatially separated, such that thermal plasma acts as a ""Faraday screen""."," The first assumes that synchrotron and free-free emitters are spatially separated, such that thermal plasma acts as a “Faraday screen”." +" The amplitude of the polarized emission is unchanged, while the polarization angles Faraday rotate."," The amplitude of the polarized emission is unchanged, while the polarization angles Faraday rotate." + Other three simulation have regions where both types of emitters are mixed in different ways., Other three simulation have regions where both types of emitters are mixed in different ways. + The synchrotron emission is differentially Faraday rotated and depolarization occurs (see Table 1))., The synchrotron emission is differentially Faraday rotated and depolarization occurs (see Table \ref{tab:maps}) ). +" The main result of our simulations is that we are able to produce realistic Galactic polarized emission that is comparable to observations, i.e., presence of the structures at different scales, spatial and frequency variations of the brightness temperature and its spectral index, complex Faraday structures, and depolarization."," The main result of our simulations is that we are able to produce realistic Galactic polarized emission that is comparable to observations, i.e., presence of the structures at different scales, spatial and frequency variations of the brightness temperature and its spectral index, complex Faraday structures, and depolarization." + The importance of this result comes from the fact that the planned EoR radio arrays have a polarized response and the extraction of the EoR signal from the foregrounds is usually performed along the frequency direction., The importance of this result comes from the fact that the planned EoR radio arrays have a polarized response and the extraction of the EoR signal from the foregrounds is usually performed along the frequency direction. + The Galactic foreground is a smooth function of frequency in a total intensity and it can show fluctuations in polarized intensity., The Galactic foreground is a smooth function of frequency in a total intensity and it can show fluctuations in polarized intensity. + The EoR signal is expected to be unpolarized and to show fluctuations along the frequency direction., The EoR signal is expected to be unpolarized and to show fluctuations along the frequency direction. +" Therefore, an imperfect calibration of the instrumental polarized response can transfer a fraction of the polarized signal into a total intensity."," Therefore, an imperfect calibration of the instrumental polarized response can transfer a fraction of the polarized signal into a total intensity." +" As a result, the leaked polarized emission can mimic the cosmological signal and make its extraction almost impossible (see Fig. 7))."," As a result, the leaked polarized emission can mimic the cosmological signal and make its extraction almost impossible (see Fig. \ref{fig:losEOR}) )." +" Based on our simulations, we conclude that the EoR observational windows need to be in regions with a very low polarized foreground emission, in order to minimize ‘leaked’ foregrounds."," Based on our simulations, we conclude that the EoR observational windows need to be in regions with a very low polarized foreground emission, in order to minimize `leaked' foregrounds." +" Faraday rotation measure synthesis, polarization surveys obtained by different radio telescopes, and a multiple EoR observations will help in mitigating the polarization leakages."," Faraday rotation measure synthesis, polarization surveys obtained by different radio telescopes, and a multiple EoR observations will help in mitigating the polarization leakages." +" However, further simulations and observations are necessary to pin point the best strategy for the EoR detection."," However, further simulations and observations are necessary to pin point the best strategy for the EoR detection." + We acknowledge discussion with the LOFAR-EoR key project members., We acknowledge discussion with the LOFAR-EoR key project members. + We are also thankful to the anonymous referee for his illustrative and constructive comments., We are also thankful to the anonymous referee for his illustrative and constructive comments. +" As LOFAR members authors are partly funded by the European Union, European Regional Development Fund, and by 'Samenwerkingsverband Noord-Nederland’, EZ/KOMPAS."," As LOFAR members authors are partly funded by the European Union, European Regional Development Fund, and by `Samenwerkingsverband Noord-Nederland', EZ/KOMPAS." +sub-Keplerian accretion affect the results of?.,sub-Keplerian accretion affect the results of. +. As shown in and 5.. we obtain smaller fractions of crystalline silicates throughout the disk.," As shown in \\ref{fig:cryst} and \ref{fig:cryst3-15}, we obtain smaller fractions of crystalline silicates throughout the disk." + This is an improvement over the old model. which was noted to overpredict crystallinity compared with observations.," This is an improvement over the old model, which was noted to overpredict crystallinity compared with observations." + A detailed parameter study is required to judge how well our current model reproduces all available observations., A detailed parameter study is required to judge how well our current model reproduces all available observations. + One complicating factor in such a procedure ts the observed lack of correlation between crystallinity and other systemic properties such as the stellar luminosity. the accretion rate and the masses of the star and the disk (?).," One complicating factor in such a procedure is the observed lack of correlation between crystallinity and other systemic properties such as the stellar luminosity, the accretion rate and the masses of the star and the disk \citep{watson09a}." + The observed absence of a correlation between two observables usually translates to a lack of a physical correlation. but this is not always the case.," The observed absence of a correlation between two observables usually translates to a lack of a physical correlation, but this is not always the case." + For example. ? showed why the crystallinity is not observed to be correlated with the stellar luminosity.," For example, \citet{kessler07a} showed why the crystallinity is not observed to be correlated with the stellar luminosity." + The disk around a brighter protostar is warmer throughout. so the region from which most of the silicate emission originates lies at a larger distance from the star. where the crystallinity 1s lower.," The disk around a brighter protostar is warmer throughout, so the region from which most of the silicate emission originates lies at a larger distance from the star, where the crystallinity is lower." + At the same time. though. the higher temperatures mean that more material can be thermally annealed. so the crystallinity at all radii goes up.," At the same time, though, the higher temperatures mean that more material can be thermally annealed, so the crystallinity at all radii goes up." + The two effects cancel each other. so the observed crystalline fraction 1s not correlated with the stellar luminosity.," The two effects cancel each other, so the observed crystalline fraction is not correlated with the stellar luminosity." + Likewise. care must be taken when interpreting other observed non-correlations or correlations.," Likewise, care must be taken when interpreting other observed non-correlations or correlations." + The best starting point for a more detailed comparison between model and observations appears to be the observed radial dependence of the relative abundances of specific types of crystalline silicates. such as enstatite and forsterite.," The best starting point for a more detailed comparison between model and observations appears to be the observed radial dependence of the relative abundances of specific types of crystalline silicates, such as enstatite and forsterite." + Our model can be expanded to track multiple types of silicates. each with their own formation temperature and mechanism.," Our model can be expanded to track multiple types of silicates, each with their own formation temperature and mechanism." + First of all. this may help in explaining the “erystallinity paradox” identified by ? (?:: see also refsubsec:oldres)).," First of all, this may help in explaining the “crystallinity paradox” identified by \citeauthor{olofsson09a} \citeyear{olofsson09a}; see also \\ref{subsec:oldres}) )." + Second. it can address the question whether crystalline silicates are predominantly formed by condensation from hot gas («1200 K). by thermal annealing at slightly lower temperatures (~800 K). or by shock waves outside the hot inner disk.," Second, it can address the question whether crystalline silicates are predominantly formed by condensation from hot gas $\sim$ 1200 K), by thermal annealing at slightly lower temperatures $\sim$ 800 K), or by shock waves outside the hot inner disk." + At the moment. neither the observations nor the models can rule out any of these mechanisms.," At the moment, neither the observations nor the models can rule out any of these mechanisms." + The crystalline fractions obtained with our model suggest. that thermal annealing followed by radial mixing must be taking place and must therefore be responsible for part of the observed crystalline silicates., The crystalline fractions obtained with our model suggest that thermal annealing followed by radial mixing must be taking place and must therefore be responsible for part of the observed crystalline silicates. + A scenario in which crystalline material is formed where it is observed. according to the model of ?.. appears unlikely.," A scenario in which crystalline material is formed where it is observed, according to the model of \citet{bouwman08a}, appears unlikely." + In addition to tracking multiple types of silicates. it may be worthwhile to investigate different collapse scenarios.," In addition to tracking multiple types of silicates, it may be worthwhile to investigate different collapse scenarios." + The ? collapse starts with a cloud core with an 77 density profile. but observations of pre-stellar cores usually show an ο density profile instead (2222?)..," The \citet{shu77a} collapse starts with a cloud core with an $r^{-2}$ density profile, but observations of pre-stellar cores usually show an $r^{-1.5}$ density profile instead \citep{alves01a,motte01a,harvey03a,andre04a,kandori05a}." + Bonnor-Ebert (BE) spheres have such a density profile (?2).. so they have been proposed as an alternative starting point for collapse models (?)..," Bonnor-Ebert (BE) spheres have such a density profile \citep{ebert55a,bonnor56a}, so they have been proposed as an alternative starting point for collapse models \citep{whitworth96a}." + The collapse of a BE sphere results in different densities. velocities and temperatures than those obtained with the ? collapse (????).. leading in turn to different crystalline. silicate abundances.," The collapse of a BE sphere results in different densities, velocities and temperatures than those obtained with the \citeauthor{shu77a} collapse \citep{foster93a,matsumoto03a,banerjee04a,walch09a}, leading in turn to different crystalline silicate abundances." + However. no analytical solutions currently exist for the collapse of a rotating BE sphere. so we are unable to pursue this point in any more detail.," However, no analytical solutions currently exist for the collapse of a rotating BE sphere, so we are unable to pursue this point in any more detail." + This paper presents a new method of correcting for the Keplerian velocity of envelope material accreting onto an ssymmetric. two-dimensional. circumstellar disk., This paper presents a new method of correcting for the sub-Keplerian velocity of envelope material accreting onto an symmetric two-dimensional circumstellar disk. + Unlike the previous corrections of ? and ?.. this new method properly conserves angular momentum and produces infall trajectories without discontinuities.," Unlike the previous corrections of \citet{hueso05a} and \citet{visser09a}, this new method properly conserves angular momentum and produces infall trajectories without discontinuities." + The latter is important for tracing changes in the chemical contents and dust properties during the evolution of the envelope and disk., The latter is important for tracing changes in the chemical contents and dust properties during the evolution of the envelope and disk. + The disks produced with the new method are smaller than those produced with the old method by up to a factor of ten., The disks produced with the new method are smaller than those produced with the old method by up to a factor of ten. + Depending on the initial conditions. the disk masses are between 100 and of previously computed values refsec:diskprop)).," Depending on the initial conditions, the disk masses are between 100 and of previously computed values \\ref{sec:diskprop}) )." + The new disks are a few degrees colder in the inner regions and a few degrees warmer in the outer regions. resulting in lower abundances of CO ice refsec:gasice)).," The new disks are a few degrees colder in the inner regions and a few degrees warmer in the outer regions, resulting in lower abundances of CO ice \\ref{sec:gasice}) )." + By the time the system reaches the classical T Tauri stage. at about | Myr. the global ice abundances still agree well with observations.," By the time the system reaches the classical T Tauri stage, at about 1 Myr, the global ice abundances still agree well with observations." + Overall. there are no major changes in the gas-1ce ratios compared with ?..," Overall, there are no major changes in the gas-ice ratios compared with \citet{visser09a}." + The disk was treated as geometrically flat by ?.., The disk was treated as geometrically flat by \citet{dullemond06a}. + As in ?.. we now also take into account the vertical structure when computing the infall trajectories.," As in \citet{visser09a}, we now also take into account the vertical structure when computing the infall trajectories." + This results in the bulk of the accretion occuring at larger radi., This results in the bulk of the accretion occuring at larger radii. + A smaller fraction of the infalling material now comes close enough to the star to be heated above 800 K. the temperature required for thermal annealing of amorphous silicates into crystalline form.," A smaller fraction of the infalling material now comes close enough to the star to be heated above 800 K, the temperature required for thermal annealing of amorphous silicates into crystalline form." + Therefore. the new method produces crystalline abundances that are lower by a few per cent to more than a factor of five compared to the old model.," Therefore, the new method produces crystalline abundances that are lower by a few per cent to more than a factor of five compared to the old model." + We now obtain a better match with observations and we argue that thermal annealing followed by radial mixing is responsible for at least part of, We now obtain a better match with observations and we argue that thermal annealing followed by radial mixing is responsible for at least part of +of the Dufouretal.(2007) sample.,of the \cite{Dufour.Bergeron.ea07} sample. + It is also the upper limit in our spectra with higher signal-to-noise ratios. and a further reduction does not change the models anymore. since the electrons come predominantly from the metals.," It is also the upper limit in our spectra with higher signal-to-noise ratios, and a further reduction does not change the models anymore, since the electrons come predominantly from the metals." + As the next step we used thetheoretical ugriz nagnitudes for both sequences (with nominal broadening constants) to estimate an effective temperature for all objects in the sample using à y minimization., As the next step we used thetheoretical $ugriz$ magnitudes for both sequences (with nominal broadening constants) to estimate an effective temperature for all objects in the sample using a $\chi^2$ minimization. + The second parameter in the fitting procedure was a number set to | for one sequence and 0 for the other., The second parameter in the fitting procedure was a number set to 1 for one sequence and 0 for the other. + This allowed for an approximate interpolation between the two sets of abundances., This allowed for an approximate interpolation between the two sets of abundances. + The resulting temperature is given in Table 3. as (phot) in the second column., The resulting temperature is given in Table \ref{tabresults} as (phot) in the second column. + Assuming that = 8. this fitting procedure also gives a photometric distance.," Assuming that = 8, this fitting procedure also gives a photometric distance." + than half of our sample are closer than 100. pe. and all closer than 200 pe.," More than half of our sample are closer than 100 pc, and all closer than 200 pc." + Interstellar reddening should not be important. compared to the other sources of uncertainty. and was neglected in our fits.," Interstellar reddening should not be important, compared to the other sources of uncertainty, and was neglected in our fits." + We used the temperature of the grid point closest to the best-fit photometric temperature as a starting value in the analysis of the individual objects., We used the temperature of the grid point closest to the best-fit photometric temperature as a starting value in the analysis of the individual objects. + The abundances were varied. following a visual comparison of observed and theoretical spectrum.," The abundances were varied, following a visual comparison of observed and theoretical spectrum." + A small grid with 1100-300 K above and below the current best value was calculated and theoretical SDSS colors for these models compared to the observed ones., A small grid with 100-300 K above and below the current best value was calculated and theoretical SDSS colors for these models compared to the observed ones. + Most weight was given to the most accurate colors. Le. e—r and r—i.," Most weight was given to the most accurate colors, i.e. $g-r$ and $r-i$." +" This procedure was iterated. until a reasonable fit was achieved to the spectrum and the colors. €—r. r—i,"," This procedure was iterated, until a reasonable fit was achieved to the spectrum and the colors. $g-r$, $r-i$," + and ;—z were usually reproduced by the final model within 1-2 c; for 4—e the error was often (not always) larger (see Table 4)). because of missing absorption in the w region.," and $i-z$ were usually reproduced by the final model within 1-2 $\sigma$; for $u-g$ the error was often (not always) larger (see Table \ref{compcol}) ), because of missing absorption in the $u$ region." + In the higher quality spectra we could additionally use the ionization equilibrium of calcium to determine the temperature., In the higher quality spectra we could additionally use the ionization equilibrium of calcium to determine the temperature. + In a few cases the final temperature differs by several 100 K from the photometrie starting value. because two objects with sinilar colors in the intermediate range of Fig.," In a few cases the final temperature differs by several 100 K from the photometric starting value, because two objects with similar colors in the intermediate range of Fig." + 3 can have very different temperatures. depending on the details of the metal contamination.," \ref{ugr1} can have very different temperatures, depending on the details of the metal contamination." + Figures for all spectra with the fits are displayed in Fig.4 and Fig.5.., Figures for all spectra with the fits are displayed in \ref{fitplota} and \ref{fitplotb}. + The results for aand the abundances of the observed elements are given in Table 3.., The results for and the abundances of the observed elements are given in Table \ref{tabresults}. . + The objects of our sample form a natural extension of the DZ temperature sequence studied by, The objects of our sample form a natural extension of the DZ temperature sequence studied by + , +The motion of Nix (bottom panel of etre 2)) appears more imegular than that of IEvdra.,The motion of Nix (bottom panel of figure \ref{figRNixHydra}) ) appears more irregular than that of Hydra. + We flud the position of Nix to be well-described by a model of three epicveles with different frequencies: e(f)=ry(1|»»poatCkcositui).," We find the position of Nix to be well-described by a model of three epicycles with different frequencies: $r(t)=r_0(1+\sum_{k=1,2,3} e_k \cos (\kappa_k t + +\omega_k))$." + The best fit values are priuted iu table 1., The best fit values are printed in table 1. + We distinguish the cause of each epievele by its period., We distinguish the cause of each epicycle by its period. + The combined poteutial of Pluto aud Charon oscillates with frequency of Ὁμμ—Oxi: motion being forced by this potential should occur ou integer niultiples of this frequency., The combined potential of Pluto and Charon oscillates with frequency of $\Omega_{\rm Charon}-\Omega_{\rm Nix}$; motion being forced by this potential should occur on integer multiples of this frequency. + Usine tl1ο ος iu table 1.. we see that 2x2z/(Oxi;|he)=2zx/(Oxi2883/2)26.39 davs.," Using the numbers in table \ref{tabFitResults}, , we see that $2 \pi/(\Omega_{\rm Nix}+\kappa_2) = 2\pi/(\Omega_{\rm Nix}+\kappa_3/2)= +6.39$ days." + The secoud aud third epievcles in our fit correspoud to motion at the first aud second =harimouic of Nixs relative orbital frequency., The second and third epicycles in our fit correspond to motion at the first and second harmonic of Nix's relative orbital frequency. + We therefore interpret the first ter with a size of eq=3:«10.P and a period close to Nix's orbital period. as analogous to the two-body ecceutricity.," We therefore interpret the first term, with a size of $e_1=3 \times 10^{-3}$ and a period close to Nix's orbital period, as analogous to the two-body eccentricity." + We perform another iutegration of the best ft initial coiitious from ? to investigate the secular effects between Nix aud Uvdra., We perform another integration of the best fit initial conditions from \citet{TBGE07} to investigate the secular effects between Nix and Hydra. + We use the best fit masses from ? for the twe» outer satellites., We use the best fit masses from \citet{TBGE07} for the two outer satellites. + Since the motion of Uvdra is dominated by a single epicvelie frequency. the variation in the size of 1s epievele is apparent ou the timescale of several vears.," Since the motion of Hydra is dominated by a single epicyclic frequency, the variation in the size of its epicycle is apparent on the timescale of several years." + To determine the effect of secular variations on Nix. we fit he same three-component epievelie model to five orbits at fo5 vears.," To determine the effect of secular variations on Nix, we fit the same three-component epicyclic model to five orbits at $t \sim 5$ years." +" In the best-fit model to these later orbits. tl' only difference compared to the model of table Ἰ is iu ey. the epievcle with a frequency close to Πάνταs orbital fiquency,"," In the best-fit model to these later orbits, the only difference compared to the model of table \ref{tabFitResults} is in $e_1$, the epicycle with a frequency close to Hydra's orbital frequency." + This is further confirmation that the degree of freedom represeuted by e4 is analogous to the two-body eccetricity., This is further confirmation that the degree of freedom represented by $e_1$ is analogous to the two-body eccentricity. + To compute the distribution of eccentricities aud inclinaions expected of Pluto's moous. we solve equation for each of the moons. Oogiven the imteraction frequencies| svecitied by equations 19. and 20.," To compute the distribution of eccentricities and inclinations expected of Pluto's moons, we solve equation \ref{eqDiffeoftgeneral} + for each of the moons, given the interaction frequencies specified by equations \ref{eqPintermediate} and \ref{eqPofIintermediate}." + The ouly remaiming paralucters to evaluate are the damping timescales for the ecceutricity and inclinations of cach satellite., The only remaining parameters to evaluate are the damping timescales for the eccentricity and inclinations of each satellite. + We use the standard formula for the damping of eccentricity due to the tidal force of the primary acting on a secondary that is i svuchronous rotation ολη where Qo is the dissipation function of the secondary. aud fo=194072/(2pGino) is its effective rigidity. a ratio between the material streneth of the secondary. aud its ποgravitv.," We use the standard formula for the damping of eccentricity due to the tidal force of the primary acting on a secondary that is in synchronous rotation \citep{YP81,MD99}: where $Q_2$ is the dissipation function of the secondary, and ${\tilde \mu_2} = 19 \mu r_2 / (2 \rho G m_2)$ is its effective rigidity, a ratio between the material strength of the secondary and its self-gravity." + The damping rate of eccentricity duc to tides of the primary acting on the secondary. 754. if the primary is also rotating svuchronously with the orbit of the satellite. is eiven by equation 25 with the quantities specific to the primary switched with those of the secondary aud vice versa.," The damping rate of eccentricity due to tides of the primary acting on the secondary, $\tau_{d,1}$, if the primary is also rotating synchronously with the orbit of the satellite, is given by equation \ref{eqTidalDamping} with the quantities specific to the primary switched with those of the secondary and vice versa." + Pluto aud Charon are known to be in a double-svuchronous state of rotation. where the spin period of each body is equal tothe 6.1 dav orbital period.," Pluto and Charon are known to be in a double-synchronous state of rotation, where the spin period of each body is equal tothe 6.4 day orbital period." + Iu many binaries. only the spin of the secondary is svuchronous with the," In many binaries, only the spin of the secondary is synchronous with the" +~38x107I7 erg em™ for the broad-line region and ~3.0x1077xE? erg em? for the infrared torus (see Ghisellini Taveechio 2009).,$\sim 3.8\times 10^{-2}\times \Gamma^2$ erg $^{-3}$ for the broad-line region and $\sim 3.0\times 10^{-4}\times \Gamma^2$ erg $^{-3}$ for the infrared torus (see Ghisellini Tavecchio 2009). + The values calculated by using Eq. (25) , The values calculated by using Eq. \ref{eq:cooling}) ) +have to be compared with the characteristic times observed during the declining phases of the outbursts (see the D values of the last column in the Table 1)., have to be compared with the characteristic times observed during the declining phases of the outbursts (see the D values of the last column in the Table \ref{tab:timescales}) ). + By assuming the typical value of Γ~610 (e.g. Ghisellini et al., By assuming the typical value of $\Gamma \sim \delta \sim 10$ (e.g. Ghisellini et al. + 2010). Eq. (2))," 2010), Eq. \ref{eq:cooling}) )" + becomes: By substituting the redshifts of the sources. the observed cooling times span from a bit less than one hour in the case of the broad-line region and more than 10 hours for the torus.," becomes: By substituting the redshifts of the sources, the observed cooling times span from a bit less than one hour in the case of the broad-line region and more than 10 hours for the torus." + Therefore. the observed upper limits of a few hours (see |r| in Table 1)) of the characteristic time scales favor the BLR parsec) location of the dissipation zone.," Therefore, the observed upper limits of a few hours (see $|\tau|$ in Table \ref{tab:timescales}) ) of the characteristic time scales favor the BLR (sub-parsec) location of the dissipation zone." + It would be possible to reconcile the cooling time of EC based on the infrared seed photons from the molecular torus if assuming a large bulk Lorentz factor., It would be possible to reconcile the cooling time of EC based on the infrared seed photons from the molecular torus if assuming a large bulk Lorentz factor. + For example. if 30. then Eq. (4))," For example, if $\Gamma \sim \delta \sim 30$ , then Eq. \ref{eq:cooltorus}) )" + becomes: However. this is an unlikely hypothesis. in conflict with the values of the jet apparent speed as measured with high-resolution radio observations.," becomes: However, this is an unlikely hypothesis, in conflict with the values of the jet apparent speed as measured with high-resolution radio observations." + Lister et al. (, Lister et al. ( +2009). by analyzing a large set of data obtained with high-resolution VLBA observations at 15 GHz in the period 1994-2007. have reported that the greatest values of the apparent speed are generally measured at positions very close to the core. at the limit of the angular resolution of the instrument (~| mas).,"2009), by analyzing a large set of data obtained with high-resolution VLBA observations at 15 GHz in the period $-$ 2007, have reported that the greatest values of the apparent speed are generally measured at positions very close to the core, at the limit of the angular resolution of the instrument $\sim 1$ mas)." + In the cases of the three sources studied in the present work. they reported the values of Bay=21.13.14 for PKS B1222+216. 3C 273 and 3C 454.3. respectively. which corresponds to Doppler factors roughly in the range 6~9—15 (calculated by assuming Pap ΨΟΟΓ).," In the cases of the three sources studied in the present work, they reported the values of $\beta_{\rm app}^{\rm max}=21,13,14$ for PKS $+$ 216, 3C 273 and 3C 454.3, respectively, which corresponds to Doppler factors roughly in the range $\delta \sim 9-15$ (calculated by assuming $\beta_{\rm app} \sim \sqrt{2\delta\Gamma}$ )." + The locations of the features used to perform these measurements are at ~5—15 pe. which are the typical distances of the infrared torus.," The locations of the features used to perform these measurements are at $\sim 5-15$ pc, which are the typical distances of the infrared torus." + A Doppler factor greater by more than a factor 2 seems to be unlikely. although it cannot be excludedpriori: we are studying outstanding high fluxes at y rays and. therefore. we cannot avoid thinking that also radio observations (1f any) following these strong outburst could result in exceptional values of Bapp.," A Doppler factor greater by more than a factor 2 seems to be unlikely, although it cannot be excluded: we are studying outstanding high fluxes at $\gamma$ rays and, therefore, we cannot avoid thinking that also radio observations (if any) following these strong outburst could result in exceptional values of $\beta_{\rm app}$." + We have searched for the shorter time scale in the high-energy y-ray emission from FSRQs., We have searched for the shorter time scale in the high-energy $\gamma$ -ray emission from FSRQs. + To have the best trade off between the smallest time bins and sufficient statistics for a significant detection. we have analyzed the Fermi//LAT data of three FSRQs. whose flux above 100 MeV has exceeded the threshold of 107 ph em7? s7!.," To have the best trade off between the smallest time bins and sufficient statistics for a significant detection, we have analyzed the /LAT data of three FSRQs, whose flux above 100 MeV has exceeded the threshold of $10^{-5}$ ph $^{-2}$ $^{-1}$." + We have found three sources: PKS BI2224216. 3C 273. and 3C 454.3.," We have found three sources: PKS $+$ 216, 3C 273, and 3C 454.3." + We were able to set the tightest upper limit on the observed characteristic time scale to date. which were of the order of «2—3 hours. depending on the source.," We were able to set the tightest upper limit on the observed characteristic time scale to date, which were of the order of $<2-3$ hours, depending on the source." + This. in turn. suggests that the location. of the y-ray emission region could be constrained as within the broad-line region. thus disfavoring the other possibility of a dissipation zone beyond the infrared torus.," This, in turn, suggests that the location of the $\gamma$ -ray emission region could be constrained as within the broad-line region, thus disfavoring the other possibility of a dissipation zone beyond the infrared torus." + These upper limits are not conclusive yet. because it is still possible to invoke exceptionally great values of the Doppler factor to reconcile the observations with the hypothesis of the dissipation zone being located at parsec scale.," These upper limits are not conclusive yet, because it is still possible to invoke exceptionally great values of the Doppler factor to reconcile the observations with the hypothesis of the dissipation zone being located at parsec scale." + Incidentally. we have noted that the shortest upper limit measured in this work (7«2.3 hours) can be set in the case of PKS B1222+216. which was also recently detected above 100 GeV by MAGIC (70-400 GeV. Mariotti et al.," Incidentally, we have noted that the shortest upper limit measured in this work $\tau < 2.3$ hours) can be set in the case of PKS $+$ 216, which was also recently detected above 100 GeV by MAGIC $-$ 400 GeV, Mariotti et al." + 2010. Aleksié et al.," 2010, Aleksić et al." + 2011) and Fermi//LAT (Neronov et al., 2011) and /LAT (Neronov et al. + 2010). the latter by integrating the data collected over several days.," 2010), the latter by integrating the data collected over several days." + The GeV flux resulted to be also extremely variable. with doubling time scale of the order of 10 minutes. which is now the shortest time scale ever detected in à FSRQ (Aleksié et al.," The GeV flux resulted to be also extremely variable, with doubling time scale of the order of 10 minutes, which is now the shortest time scale ever detected in a FSRQ (Aleksić et al." + 2011)., 2011). + The upper limit estimated in the present work is in agreement with the findings of the MAGIC Collaboration. although the latter work refers to an observation performed on 2010 June 17. at the end of the time period analyzed in the present work (see Fig. 2.. panel).," The upper limit estimated in the present work is in agreement with the findings of the MAGIC Collaboration, although the latter work refers to an observation performed on 2010 June 17, at the end of the time period analyzed in the present work (see Fig. \ref{fig:curva1222}, )," + while the shortest variability measured by Fermi//LAT reported here refers to the end of 2010 April. at the beginning of the light curve shown in Fig. 2..," while the shortest variability measured by /LAT reported here refers to the end of 2010 April, at the beginning of the light curve shown in Fig. \ref{fig:curva1222}." + The detection at hundreds of GeV. together with fast flux variability. poses new problems.," The detection at hundreds of GeV, together with fast flux variability, poses new problems." + As known. the BLR in FSRQs is à rich. environment of soft photons. which m turn can severely limit the escape of y rays with energies above tens of GeV because of pair production (e.g. Liu Bai 2006).," As known, the BLR in FSRQs is a rich environment of soft photons, which in turn can severely limit the escape of $\gamma$ rays with energies above tens of GeV because of pair production (e.g. Liu Bai 2006)." + Therefore. these photons of hundreds of GeV should come from zones outside the BLR. possibly around the molecular torus as suggested by Tanaka et al. (," Therefore, these photons of hundreds of GeV should come from zones outside the BLR, possibly around the molecular torus as suggested by Tanaka et al. (" +2011) on the basis of the analysis of y-ray spectra. but at such distances from the central black hole. it is expected that the blob — if linearly expanding with a constant ratio r/R~0.1—0.25 — has reached à size so large to exclude the possibility of changes over hours time scales or less.,"2011) on the basis of the analysis of $\gamma$ -ray spectra, but at such distances from the central black hole, it is expected that the blob – if linearly expanding with a constant ratio $r/R\sim 0.1-0.25$ – has reached a size so large to exclude the possibility of changes over hours time scales or less." + A possible solution has been recently suggested by Tavecchio et al. (, A possible solution has been recently suggested by Tavecchio et al. ( +2011). who proposed to explain these observation with something similar to the structured jet proposed for BL Laes.,"2011), who proposed to explain these observation with something similar to the structured jet proposed for BL Lacs." + LF thanks C. D. Dermer for useful discussions on his model., LF thanks C. D. Dermer for useful discussions on his model. + This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC). provided by NASA's Goddard Space Flight Center.," This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center." + This work has been partially supported by Agenzia Spaziale Italiana (ASI) Grant [/009/10/0., This work has been partially supported by Agenzia Spaziale Italiana (ASI) Grant I/009/10/0. +structure in the universe induces. peculiar motions which distorts the clustering pattern measured. in redshift space on all scales.,structure in the universe induces peculiar motions which distorts the clustering pattern measured in redshift space on all scales. + This cllect must be taken into account when analvzing three dimensional datasets. which use recshilt as the radial coordinate., This effect must be taken into account when analyzing three dimensional datasets which use redshift as the radial coordinate. + Redshift space effects alter the appearance of the clustering of matter. and together with non-linear evolution and bias. lead the power spectrum to depart [rom simple linear perturbation theory predictions.," Redshift space effects alter the appearance of the clustering of matter, and together with non-linear evolution and bias, lead the power spectrum to depart from simple linear perturbation theory predictions." + On small scales. randomised. velocities associated. with viralised: structures decrease the power.," On small scales, randomised velocities associated with viralised structures decrease the power." +" The dense central regions of galaxy clusters look elongated. along the line of sight in redshift space. which produces ""fingers of (7) in redshift survey cone plots."," The dense central regions of galaxy clusters look elongated along the line of sight in redshift space, which produces fingers of \citep{Jackson} in redshift survey cone plots." + On large scales. coherent. bulk Hows cistort clustering statistics. (seeὃνforareviewofredshiftspace distortions)..," On large scales, coherent bulk flows distort clustering statistics, \citep[see][for a review of redshift space distortions]{1998ASSL..231..185H}." + For growing perturbations on large scales. the overall ellect of redshift space distortions is to enhance the clustering amplitude.," For growing perturbations on large scales, the overall effect of redshift space distortions is to enhance the clustering amplitude." +" Any difference in the velocity field due to mass Dowing from underdense regions (ο high density regions will alter the volume clement. causing an enhancement of the apparent density contrast in redshift space. 6.07). compared to that in real space. 0,7)."," Any difference in the velocity field due to mass flowing from underdense regions to high density regions will alter the volume element, causing an enhancement of the apparent density contrast in redshift space, $\delta_s(\vec{r})$, compared to that in real space, $\delta_r(\vec{r})$." + “Phis οσοι was first analvzed by 2 and. can be approximated by where j£ is the cosine of the angle between the waveveetor. &. and the line of sight. 9=f/b and the bias. b—1 for dark matter.," This effect was first analyzed by \citet{Kaiser:1987qv} and can be approximated by where $\mu$ is the cosine of the angle between the wavevector, $\vec{k}$, and the line of sight, $\beta = f/b$ and the bias, $b=1$ for dark matter." + The Ixaiser formula (eq. 3)), The Kaiser formula (Eq. \ref{k}) ) + relates the overdensity in redshift space to the corresponding value in real space using several approximations: 1., relates the overdensity in redshift space to the corresponding value in real space using several approximations: 1. + The small scale velocity dispersion can be neglected., The small scale velocity dispersion can be neglected. + 2., 2. + Phe velocity gradient. απ/ατ]σ1., The velocity gradient $|\rm{d}\vec{u}/\rm{d}r| \ll 1$. + 3., 3. + The velocity ancl density. perturbations satisfy the linear continuity equation., The velocity and density perturbations satisfy the linear continuity equation. + 4., 4. + The real space density perturbation is assumed. to be small. |ó(r)]«1. so that higher order ternis can be neglected.," The real space density perturbation is assumed to be small, $|\delta(r)| \ll 1$, so that higher order terms can be neglected." + All of these assumptions are valid on scales that are well within the linear regime anc will break down on cilferent scales as the density Uuctuations grow., All of these assumptions are valid on scales that are well within the linear regime and will break down on different scales as the density fluctuations grow. + The linear regine is therefore defined over a dillercnt range of scales for each ellect., The linear regime is therefore defined over a different range of scales for each effect. + The matter power spectrum in redshift. space can be decomposed into multipole moments using Legendre polvnonials. Ly) The anisotropy in PP(&) is symmetric in fi. as PCA. qp). so onlv even values of/ are summed. over.," The matter power spectrum in redshift space can be decomposed into multipole moments using Legendre polynomials, $L_l(\mu)$, The anisotropy in $P( \vec{k} )$ is symmetric in $\mu$, as $P(k,\mu)=P(k,-\mu)$ , so only even values of $l$ are summed over." + Each multipole moment is given by where the first two non-zero moments have Leeendre polvnomials. Lo(ji)=1 and Loy)=05471)/2.," Each multipole moment is given by where the first two non-zero moments have Legendre polynomials, $L_0(\mu) = 1$ and $L_2(\mu) = (3\mu^2 - 1)/2$." + Using the redshift space density contrast. Eq.," Using the redshift space density contrast, Eq." + 3. can be used to form D(h.pi) and then integrating over the cosine of the angle ji gives the spherically averaged monopole power spectrum in redshift space. £5(&). where P(&) denotes the matter power spectrum in real space.," \ref{k} can be used to form $P(k,\mu)$ and then integrating over the cosine of the angle $\mu$ gives the spherically averaged monopole power spectrum in redshift space, $P^s_0(k)$, where $P^r(k)$ denotes the matter power spectrum in real space." + In practice. P(4) cannot be obtained directly for a real survey without making approximations (c.g.?).. ," In practice, $P^r(k)$ cannot be obtained directly for a real survey without making approximations \citep[e.g.][]{1994MNRAS.270..183B}. ." +In this paper we also consider the estimator for f suggested. by 2.. which is the ratio of quadrupole to monopole moments of the redshift space power spectrum. PAVSG).," In this paper we also consider the estimator for $f$ suggested by \citet{Cole:1993kh}, which is the ratio of quadrupole to monopole moments of the redshift space power spectrum, $P_2^s(k)/P_0^s(k)$." + From Eq., From Eq. + 3. and after spherically averaging. the estimator for f is then which is independent of the real space power spectrum.," \ref{k} and after spherically averaging, the estimator for $f$ is then which is independent of the real space power spectrum." + Llere. as before. f=o/b. with b=1 for dark matter.," Here, as before, $f = \beta/b$, with $b=1$ for dark matter." +" Assuming the lineof sight component is along the z-axis. the fully non-linear relation between the real and. recshilt space power spectrum can be written as (7) where A=fhy s. is the comoving peculiar velocity along the line of sight. Aw,=(x)w(x’) p=xx' and the only approximation made is the plane parallel approximation."," Assuming the lineof sight component is along the $z$ -axis, the fully non-linear relation between the real and redshift space power spectrum can be written as \citep{Scoccimarro:1999ed} + where $\lambda = f k \mu$, $u_z$ is the comoving peculiar velocity along the line of sight, $\Delta u_z = u_z({\bf{x}}) - u_z(\bf{x'})$, $\bf{r} = \bf{x} -\bf{x'}$ and the only approximation made is the plane parallel approximation." + This expression is the Fourier analog of the ‘streaming first suggested by ο and πιο]ος by ? o take into account the densitv-velocity coupling., This expression is the Fourier analog of the streaming first suggested by \citet{1980:Peebles} and modified by \citet{1995ApJ...448..494F} to take into account the density-velocity coupling. + At small scales (as & increases) the exponential component clamps he power. representing the impact of randomised velocities inside gravitationally bound structures.," At small scales (as $k$ increases) the exponential component damps the power, representing the impact of randomised velocities inside gravitationally bound structures." + Simplified mocdels. for redshift space. distortions are requenthy used., Simplified models for redshift space distortions are frequently used. + Examples include multiplving Eq., Examples include multiplying Eq. + 6 by a actor which attempts to take into account small scale effects and is either a Gaussian or an exponential (?).., \ref{mr} by a factor which attempts to take into account small scale effects and is either a Gaussian or an exponential \citep{Peacock:1993xg}. +" A popular ohenomenological example of this which incorporates the damping effect of velocity dispersion on small scales is the so called ""dispersion (?) where a, is the pairwise velocity dispersion along the line of sight. which is treated as à parameter to be fitted to the data."," A popular phenomenological example of this which incorporates the damping effect of velocity dispersion on small scales is the so called dispersion \citep{Peacock:1993xg}, where $\sigma_p$ is the pairwise velocity dispersion along the line of sight, which is treated as a parameter to be fitted to the data." +" Using numerical simulations. ?. found a fit to the quacrupole to monopole ratio ἐν=GIWui2) to mimic damping and non-linear ellects. where (P/I5), is the linear theory prediction given by Iq. "," Using numerical simulations, \citet{1999MNRAS.310.1137H} + found a fit to the quadrupole to monopole ratio $P^s_2/P^s_0=(P^s_2/P^s_0)_{\tiny \mbox{lin}}(1-x^{1.22}) $ to mimic damping and non-linear effects, where $(P^s_2/P^s_0)_{\tiny \mbox{lin}}$ is the linear theory prediction given by Eq. \ref{dmm}," +7.0=Αι and Ay ds a free parameter., $x=k/k_1$ and $k_1$ is a free parameter. + Γον extended the dvnamic range of simulations. to replicate the elect of a larger box. using the approximate method for addinglong wavelength: power suggested by 2.. ," They extended the dynamic range of simulations, to replicate the effect of a larger box, using the approximate method for addinglong wavelength power suggested by \citet{1997MNRAS.286...38C}. ." +The velocity divergence auto power spectrum is the emscmble average. Poe=(9) where @=VdH is the velocity. divergence.," The velocity divergence auto power spectrum is the emsemble average, $P_{\theta \theta} = \langle |\theta|^2 \rangle $ where $\theta = \vec{\nabla}\cdot \vec{u}$ is the velocity divergence." + The cross power spectrum of the velocity divergence and matter density is Psy= (dé).," The cross power spectrum of the velocity divergence and matter density is $P_{\delta \theta}= \langle |\delta \theta| \rangle$ ," +coincident magnetic and spin axes of the central object and take this axis as the z axis of evlindrical coordinates (17.6.2).,"coincident magnetic and spin axes of the central object and take this axis as the $z$ axis of cylindrical coordinates $(r,\phi,z)$." +" The magnetic torque per unit. volume of. plasma in the inner ring of the disk that is threaded by the intrinsic magnetic field. of the central object. can be approximated bv DEMtesrkSraOB,NaeB.H,. where 2, is the average azimuthal magnetic field component."," The magnetic torque per unit volume of plasma in the inner ring of the disk that is threaded by the intrinsic magnetic field of the central object, can be approximated by $\tau_v=rF_{v\phi} = +r \frac{B_z}{4\pi} \frac{\partial B_{\phi}}{\partial z} +\sim r \frac{B_zB_{\phi}}{4\pi H}$, where $B_{\phi}$ is the average azimuthal magnetic field component." + We stress that 23... as used here. is an average toroidal magnetic field component.," We stress that $B_{\phi}$, as used here, is an average toroidal magnetic field component." + The toroidal component Likely varies cpisocically between reconnection events (Goodson Winglee 1999. Matt et al.," The toroidal component likely varies episodically between reconnection events (Goodson Winglee 1999, Matt et al." + 2002. Ixato. Havashi Matsumato 2004. Uzclensky 2002).," 2002, Kato, Hayashi Matsumato 2004, Uzdensky 2002)." +" The average How of disk angular momentum entering the inner ring is Mores. where Mods mass accretion rate and c, ds the Weplerian speed. in the disk."," The average flow of disk angular momentum entering the inner ring is $\dot{M}r v_k$, where $\dot{M}$ is mass accretion rate and $v_k$ is the Keplerian speed in the disk." +" This angular momentum must be extracted by the magnetic torque. 7. hence: In order to proceed further. we assume that £2, AD.. D.=ftmu anduse c4=VICEμαr where A is. a constant. presumed to be of order unity. ye is the magnetic dipole moment of the central object M. its mass. and C. the Newtonian gravitational force constant."," This angular momentum must be extracted by the magnetic torque, $\tau$, hence: In order to proceed further, we assume that $B_{\phi} = \lambda B_z$ , $B_z=\mu/r^3$, anduse $v_k=\sqrt{GM/r}$, where $\lambda$ is a constant, presumed to be of order unity, $\mu$ is the magnetic dipole moment of the central object $M$ its mass, and $G$, the Newtonian gravitational force constant." +" With these assumptions we obtain where wy=rpfr and the magnetopause radius. r7, is eiven by We scale the accretion rate to that needed το produce luminosity at the Eddington limit for a central object. of mass M. and define and using ry,=CAL/C and eq."," With these assumptions we obtain where $\omega_k = v_k/r$ and the magnetopause radius, $r_m$ is given by We scale the accretion rate to that needed to produce luminosity at the Eddington limit for a central object of mass $M$ , and define and using $r_g=GM/c^2$ and eq." + 3. we deline In order to estimate the size of the boundary. region. (δν we normalize this cdisk-magnetosphere mocdel to an average atoll NS (Table 1. RLO2) of mass AJ= 1.42M..," 3, we define In order to estimate the size of the boundary region, $(\delta r /r)$, we normalize this disk-magnetosphere model to an average atoll NS (Table 1, RL02) of mass $M = 1.4 M_{\odot}$ ." + The average rate of spin is 450 Lz. the co-rotation radius is ~30 km. and the maximum luminosity for the low state is GAIAL/2r~2Q7 cre T prom this we find ΑΙ=⋅⊥ ⊥⊳∖ ⋅ .," The average rate of spin is $\sim 450$ Hz, the co-rotation radius is $\sim 30$ km, and the maximum luminosity for the low state is $GM\dot{M}/2r ~\sim 2 \times 10^{36}$ erg $^{-1}$ From this we find $\dot{M} = 6.4 \times 10^{16} g s^{-1}$ ." +" ≼≻⋅≟↓∪⊔∙↙∣⋅↔⊽⋡∐↥≺⊾⊔⇂∪↓⋅⋜⋯⋜↧∖⇁≺⋅↓⋅⋜↧⋏∙≟⋖⋅⊔↓⋜↧⋏∙≟⊔≺⊾∣⊔∼⊔↓∪⊔↓⋖⋅⊔∣∪⇂ ∿↓⋅⋅↱≻↓∪⊁−∣⋏∙≟⋜⋯⊳∖⊳∖≼↛⊔↓⇝⊳∖∖⋎⋖⊾∐⊔∠⊓↓⋯↿ (Amy""0.8."," Then for an average magnetic moment of $\sim 1.5 \times 10^{27}$ gauss $^3$ , we find that $\frac{\lambda \delta r}{r})^{2/7} \sim 0.3$." + Thus f=Mn0.015: Le.. the boundary region is suitably small. though likely larger than the scale height of the trailing cisk.," Thus $\xi = \frac{\lambda \delta r}{r} \sim 0.015$; i.e., the boundary region is suitably small, though likely larger than the scale height of the trailing disk." +" For later convenience. we define parameters απ £ asThen in terms of the variables defined so far. we can express the (reprocessed) disk Luminosity as At the co-rotation radius we reach the maximum. luminosity. L.. of the lowhare state. with Keplerian angular speed wy,=wy. the angular speed of the magnetosphere. and ry=(GALEI). Phos ↾↓∖∖∖⋎∪⋜↧∠"," For later convenience, we define parameters $\beta$ and $\xi$ asThen in terms of the variables defined so far, we can express the (reprocessed) disk luminosity as At the co-rotation radius we reach the maximum luminosity, $L_c$, of the low/hard state, with Keplerian angular speed $\omega_k = \omega_s$, the angular speed of the magnetosphere, and $r_m=(GM/\omega_s^2)^{1/3}$." +⇂∠⇂↕⇂↕⋖⋟↓↥⋜↧↓⊏↥⇂⇂⋜↧↓↕⇂↕⇂↕∢⋅≻⊔⋖⊾⋖⊾∠⇂∢⊾∠⊔⋅∪↓⋅↿↓↥⋖⋅⋜↧↓↥⋜↧↓∙∖⇁≻↕≻∪⇂⋅↿↓∐⋅ How into the base of a jet are the scaling parameters for the poloidalmagnetic field and the inner clisk density., Thus Two additional quantities needed for the analysis of the flow into the base of a jet are the scaling parameters for the poloidalmagnetic field and the inner disk density. +" The magnetic field at the base of the jet is simply For p. the density in the disk. we assume a standard ""alpha disk. for which AJ=perdes"," The magnetic field at the base of the jet is simply For $\rho$, the density in the disk, we assume a standard `alpha' disk, for which $\dot{M} = \rho 4 \pi r H v_r$." +" The radial inllow speed. ος is proportional to e£ἐν, where es is sound speed in the disk."," The radial inflow speed, $v_r$ is proportional to $v_s H/r$, where $v_s$ is sound speed in the disk." + Using ἐνxe;/ey. taking ezxD?p and solving the mass Low rate equation for p vields: The radio luminosity of a jet is a function of the rate at which the magnetosphere can do work on the inner ring of the disk.," Using $H/r \propto v_s/v_k$, taking $v_s^2 \propto B^2/\rho$ and solving the mass flow rate equation for $\rho$ yields: The radio luminosity of a jet is a function of the rate at which the magnetosphere can do work on the inner ring of the disk." + This depends on the relative speed. between the magnetosphere ancl the inner disk: i.e. 42=τίωςwy). or Disk mass. spiraling in quasi-leplerian orbits [rom negligible speed: at racial infinity must regain at least as much energy as was radiated away in order to escape.," This depends on the relative speed between the magnetosphere and the inner disk; i.e., $\dot{E} =\tau (\omega_s - \omega_k)$, or Disk mass, spiraling in quasi-Keplerian orbits from negligible speed at radial infinity must regain at least as much energy as was radiated away in order to escape." + For this to be provided. by the magnetosphere requires E=GMAL/2r. from which wp<δα.," For this to be provided by the magnetosphere requires $\dot{E} \geq GM\dot{M}/2r$, from which $\omega_k \leq 2\omega_s/3$." + Thus the magnetosphere alone is incapable of completely ejecting all of the acercting matter once the inner disk reaches this limit and the radio luminosity will be commmensurately reduced and ultimately eut off., Thus the magnetosphere alone is incapable of completely ejecting all of the accreting matter once the inner disk reaches this limit and the radio luminosity will be commensurately reduced and ultimately cut off. + The radio Hux. £5. of jet sources has a power law dependence on frequency of the form. The spectral energy. distributions of GBILC and ACN in racio-infrared show very Little. if any. evolution in the low state during outbursts: Le. à is essentially constant (azm— (0.5. radio: 0.15.IR. see e.g.. Chatyct al.," The radio flux, $F_{\nu}$, of jet sources has a power law dependence on frequency of the form The spectral energy distributions of GBHC and AGN in radio-infrared show very little, if any, evolution in the low state during outbursts; i.e., $\alpha$ is essentially constant $\alpha \approx -0.5$ , radio; $-0.15$ ,IR, see e.g., Chatyet al." + 2003)., 2003). + ‘Lo determinethe dependence of radio (uson po AZ and in. we use the model aad methods of H803.," To determinethe dependence of radio fluxon $\mu$ , $M$ and $\dot{m}$ , we use the model and methods of HS03." + Their analysis was based on a radiation transfer equation (Rabicki Lightman, Their analysis was based on a radiation transfer equation (Rybicki Lightman +spectra.,spectra. +" The 3-0 upper limits are calculated following Seacquist. Ivison Hall (1995) where σ is the channel-to-channel rms noise. 9v the velocity resolution and Ae, the line width."," The $\sigma$ upper limits are calculated following Seaquist, Ivison Hall (1995) where $\sigma$ is the channel-to-channel rms noise, $\delta v$ the velocity resolution and $\Delta v_{\mbox{\tiny{fwhm}}}$ the line width." + The spectra were binned to a velocity resolution of '., The spectra were binned to a velocity resolution of $^{-1}$. + We set. the TCN(1—0) line widths equal to that of the CO lines see Greve el ((2005)., We set the $(1-0)$ line widths equal to that of the CO lines – see Greve et (2005). + This is probably a conservative estimate since in local ULIRGs. the ICN line widths are rarely larger (han those of CO (Solomon et 11992: Gao Solomon 2004a).," This is probably a conservative estimate since in local ULIRGs, the HCN line widths are rarely larger than those of CO (Solomon et 1992; Gao Solomon 2004a)." + The resulting upper line flux limits are 0.08 and ss.! for J02399 and J16359. respectively.," The resulting upper line flux limits are 0.08 and $^{-1}$ for J02399 and J16359, respectively." + From these flux limits we derive upper limits on the apparent WCN(1—0) line Iluminosities of οι<50xLOM and <6.6xLOM !pc? for J02399 and J16359. respectively.," From these flux limits we derive upper limits on the apparent $(1-0)$ line luminosities of $L'_{\mbox{\tiny{HCN(1-0)}}}\le 5.0\times 10^{10}$ and $\le 6.6\times 10^{10}$ $^{-1}$ $^2$ for J02399 and J16359, respectively." +" Correcting for gravitational lensing we find intrinsic line Iuminosities of Lt,«2.0xLol and <0.3xLOM tpe?.", Correcting for gravitational lensing we find intrinsic line luminosities of $L'_{\mbox{\tiny{HCN(1-0)}}}\le 2.0\times 10^{10}$ and $\le 0.3 \times 10^{10}$ $^{-1}$ $^2$. + These upper limits on the ICN line luminosity are similar to those achieved towards high-z QSOs using the Verv Large Array Hsaak et 22004: Carili et 22005)., These upper limits on the HCN line luminosity are similar to those achieved towards $z$ QSOs using the Very Large Array Isaak et 2004; Carilli et 2005). + Table 1. lists our findings along with all high-z HCN observations published in the literature al the time of writing., Table \ref{table:results} lists our findings along with all $z$ HCN observations published in the literature at the time of writing. + It is seen that of 10 sources observed to date only 4 have been detected — (he remainder being upper limits., It is seen that of 10 sources observed to date only 4 have been detected – the remainder being upper limits. +" In order to determine the star formation elliciency per dense gas mass. and the dense gas fraction. as gauged by the Zi/Ly. and Lt,/L5, ratio. respectively (Gao Solomon 2004a.b). we need accurate estimates of the FIR. and CO(1-0) The FIR. luminosities of SMGs are generally difficult to estimate accurately. largely due to (he poor sampling of their EI/subnun/radio spectral energy distributions."," In order to determine the star formation efficiency per dense gas mass, and the dense gas fraction, as gauged by the $L_{\mbox{\tiny{FIR}}}/L'_{\mbox{\tiny{HCN}}}$ and $L'_{\mbox{\tiny{HCN}}}/L'_{\mbox{\tiny{CO}}}$ ratio, respectively (Gao Solomon 2004a,b), we need accurate estimates of the FIR and CO(1-0) The FIR luminosities of SMGs are generally difficult to estimate accurately, largely due to the poor sampling of their FIR/submm/radio spectral energy distributions." + Furthermore. in our case (he situation is complicated by the fact that most. if not all. of the sources in Table |. contain AGN. which max be at least partly responsible for heating the dust and thus powering the FIR emission.," Furthermore, in our case the situation is complicated by the fact that most, if not all, of the sources in Table \ref{table:results} contain AGN, which may be at least partly responsible for heating the dust and thus powering the FIR emission." +" Unfortunately. FUR/subimi data from the literature do not allow for a detailed modelling of a hot (z100 IXIN) dust component (heated bv the ACN), and we are therefore unable to correct for any AGN contamination."," Unfortunately, FIR/submm data from the literature do not allow for a detailed modelling of a hot $\gs 100$ K) dust component (heated by the AGN), and we are therefore unable to correct for any AGN contamination." +" The one exception is the z=3.9 BAL quasar. 00827945255. where the separate AGN sstarburst contributions to the FIR: luminosity have been determined by Rowan-Robinson (2000) who find an apparent FIR luminosity of Lu,©1.0x10!LE. for the starburst (corrected to the cosmology adopted here)."," The one exception is the $z=3.9$ BAL quasar, $+$ 5255, where the separate AGN starburst contributions to the FIR luminosity have been determined by Rowan-Robinson (2000) who find an apparent FIR luminosity of $L_{\mbox{\tiny{FIR}}}\simeq 1.0\times 10^{14}\,\Lsolar$ for the starburst (corrected to the cosmology adopted here)." + In the case of SMGs. extremely deep A-ray observations strongly sugeest that while every SAIG probably harbours an AGN. it is the starburst which in almost all cases powers the bulk (70-90 percent) of the FIR huninosity (Alexander et 22005). and anv AGN contamination would therefore not dramatically affect our conclusions.," In the case of SMGs, extremely deep X-ray observations strongly suggest that while every SMG probably harbours an AGN, it is the starburst which in almost all cases powers the bulk (70-90 percent) of the FIR luminosity (Alexander et 2005), and any AGN contamination would therefore not dramatically affect our conclusions." + While optical spectroscopy of J16359 shows no evidence {ο suggest the presence of strong nuclear aclivily in Chis source (Ixneib et 22004). this is not the case in J02399. which appears to," While optical spectroscopy of J16359 shows no evidence to suggest the presence of strong nuclear activity in this source (Kneib et 2004), this is not the case in J02399, which appears to" +observations to the emission from both components.,observations to disentangle the emission from both components. +" For a mass disentangleratio logr=-1 at 5x10° years, the young population accounts for at least of the flux, the minimum being in the H band."," For a mass ratio $\log r=-1$ at $5\times10^6$ years, the young population accounts for at least of the flux, the minimum being in the H band." +" Yet, for the systems in which there is clearly an evolved stellar population, its emission in the near-infrared is similar to the error bars for the currently available data."," Yet, for the systems in which there is clearly an evolved stellar population, its emission in the near-infrared is similar to the error bars for the currently available data." +" Thus, for a given age, the detectability limit depends on the error bars in the near-infrared."," Thus, for a given age, the detectability limit depends on the error bars in the near-infrared." +" In the present case, for a 5x106 years old burst, it is about10%."," In the present case, for a $5\times10^6$ years old burst, it is about." +". The recent, in-situ, star formation history in collisional debris may be be inferred comparing various tracers of star formation: ultraviolet, Ho or mid-/far-infrared."," The recent, in-situ, star formation history in collisional debris may be be inferred comparing various tracers of star formation: ultraviolet, $\alpha$ or mid-/far-infrared." + Each tracer has its own characteristics., Each tracer has its own characteristics. +" Ultraviolet is sensitive to the photospheric emission of massive stars over a timescale of a few 100x10° years, Ha to the ionized gas surrounded star forming regions over a timescale of about 10x10° years and finally infrared is a result of the radiation of dust absorbing emission from massive young stars."," Ultraviolet is sensitive to the photospheric emission of massive stars over a timescale of a few $100\times10^6$ years, $\alpha$ to the ionized gas surrounded star forming regions over a timescale of about $10\times10^6$ years and finally infrared is a result of the radiation of dust absorbing emission from massive young stars." + The availability of several bands permits not only to constrain the recent star formation history but also to obtain a more precise estimate of the star formation rates., The availability of several bands permits not only to constrain the recent star formation history but also to obtain a more precise estimate of the star formation rates. +" However they are still sensitive to some degeneracies, depending on the observations available, and thus the fits must be cautiously "," However they are still sensitive to some degeneracies, depending on the observations available, and thus the fits must be cautiously interpreted." +"We compare the SFR obtained from the SED fitting, interpreted.presented in Table 5.1.0 to the ones published in which use the conversion factors published by for the UV and the Ha emission and by for the 8 wm. The SFR"," We compare the SFR obtained from the SED fitting, presented in Table \ref{tab:fit-parameters} to the ones published in which use the conversion factors published by for the UV and the $\alpha$ emission and by for the 8 $\mu$ m. The SFR" +the case of the MOS. data we used. the response files aalL115.rsp.,the case of the MOS data we used the response files 15.rsp. +. The OAL data were analysed in a similar way using and (this latter task was not incorporated in SAS v5.2 but will be in a later version)., The OM data were analysed in a similar way using and (this latter task was not incorporated in SAS v5.2 but will be in a later version). + Data were backeround subtracted and corrected for coincidence losses (Mason et al 2001)., Data were background subtracted and corrected for coincidence losses (Mason et al 2001). + The Optical Monitor cata shows that CIZ Cru hac a mean brightness of V=17.9 and a maximum 1 —17.5., The Optical Monitor data shows that CE Gru had a mean brightness of $V$ =17.9 and a maximum $V$ =17.5. + Since the V band observations started at the descent. fron maximum its likely that its true maximum was brighter than this., Since the $V$ band observations started at the descent from maximum its likely that its true maximum was brighter than this. + Assuming a similar colour to that found by Tuohy et al (1988) (D.V —0.53) this places Cl Cru in a high accretion state at the time of theXMAI-Newton observations and a similar brightness to observed by “Tuohy ct al (15)., Assuming a similar colour to that found by Tuohy et al (1988) $B-V$ =0.53) this places CE Gru in a high accretion state at the time of the observations and a similar brightness to observed by Tuohy et al $V\sim$ 18). + The length. of the observation in the EPIC MOS detectors Covered Just over 1 orbital evele., The length of the observation in the EPIC MOS detectors covered just over 1 orbital cycle. + The flux in the UV filters. corresponds to: UVWMI ~45510DPΑ.Ε ΝΑΟΣ to.10077A. (based on OAL observations of. isolated white dwarls).," The flux in the UV filters corresponds to: UVW1 $\sim~4.5\times10^{-16}$, UVW2 $\sim~4.0\times10^{-16}$, (based on OM observations of isolated white dwarfs)." + The mean Hux in the V. filter corresponds to ~25.10 aat. 5000A., The mean flux in the $V$ filter corresponds to $\sim~2.5\times10^{-16}$ at 5000. +.. We show in Figure 1. the light curve of CIS Cru in various enerev bands using EPIC pn and EPIC MOS data (where he MOSI and MOS2 data have been co-adcded) folded on he orbital period of “Tuohy ct al (1988)., We show in Figure \ref{light} the light curve of CE Gru in various energy bands using EPIC pn and EPIC MOS data (where the MOS1 and MOS2 data have been co-added) folded on the orbital period of Tuohy et al (1988). + We also show the OAL data: CE Gru was detected in all three filters (it is also he first time that it has been detected in the near-UV)., We also show the OM data: CE Gru was detected in all three filters (it is also the first time that it has been detected in the near-UV). + There are two distinct. parts to the orbital light. curve: a faint phase lasting ~0.6 orbital eveles. and a brighter yhase lasting 0.4 orbital eveles.," There are two distinct parts to the orbital light curve: a faint phase lasting $\sim 0.6$ orbital cycles, and a brighter phase lasting $\sim +0.4$ orbital cycles." + These relative clurations are similar to those in the optical light curves seen. by Cropper et al (1990)., These relative durations are similar to those in the optical light curves seen by Cropper et al (1990). + The bright phase is also of à similar duration to that of the red. pole seen by Tuohy et al (1955) when the svstenm was at a similar brightness compared to our observations., The bright phase is also of a similar duration to that of the red pole seen by Tuohy et al (1988) when the system was at a similar brightness compared to our observations. + We therefore assign the bright phase. X-rav emission to the pole in the lower hemisphere. and. the fainter phase emission to the pole in the upper hemisphere.," We therefore assign the bright phase X-ray emission to the pole in the lower hemisphere, and the fainter phase emission to the pole in the upper hemisphere." +" Although there maybe some ambiguity in this assignment. the fact the we observe decreasing emission in the VY band at the end of the bright phase provides supporting evidence for this assignment since the ""blue. pole does not show such a rapid cop in V."," Although there maybe some ambiguity in this assignment, the fact the we observe decreasing emission in the $V$ band at the end of the bright phase provides supporting evidence for this assignment since the `blue' pole does not show such a rapid drop in $V$." + In the bright phase. a «cip is seen in the soft. N-rav light curve. but not at higher¢nergies.," In the bright phase, a dip is seen in the soft X-ray light curve, but not at higher energies." + This is characteristic of photo-clectric absorption. and is seen in other polars (ος Watson et al 1989).," This is characteristic of photo-electric absorption, and is seen in other polars (eg Watson et al 1989)." + It is thought to result. from the accretion stream crossing our line of sight to the accretion region. thereby absorbing the soft. N-ravs.," It is thought to result from the accretion stream crossing our line of sight to the accretion region, thereby absorbing the soft X-rays." + This is consistent with the model of Wickramasinghe et al (1991) for CL Cru in which the two aceretion regions lie near the magnetic poles. approximately at the. foot-points of the field. lines xwsinge througho the regionὃν where the stream threads onto the magnetic field.," This is consistent with the model of Wickramasinghe et al (1991) for CE Gru in which the two accretion regions lie near the magnetic poles, approximately at the foot-points of the field lines passing through the region where the stream threads onto the magnetic field." + It is most likely that the dip is caused bv the aceretion stream to theupper pole absorbing the emission from the lower pole: there is clear. evidence. [or accretion at the upper pole and. it is inevitable that the stream crosses our line of sight., It is most likely that the dip is caused by the accretion stream to the pole absorbing the emission from the lower pole: there is clear evidence for accretion at the upper pole and it is inevitable that the stream crosses our line of sight. + Ht is possible for the ballistic stream or the stream to the lower pole to be the cause of the absorption. but this requires a high inclination and the ballistic stream to penetrate very. close to the white dwarf before threading.," It is possible for the ballistic stream or the stream to the lower pole to be the cause of the absorption, but this requires a high inclination and the ballistic stream to penetrate very close to the white dwarf before threading." + These are special conditions. and in the absence of even a grazing eclipse we consider this to be unlikely.," These are special conditions, and in the absence of even a grazing eclipse we consider this to be unlikely." + At energies greater than 2keV. there is no evidence for the dip seen at lower energies.," At energies greater than 2keV, there is no evidence for the dip seen at lower energies." + Using the spectral moclel described. below we can estimate the absorbing column, Using the spectral model described below we can estimate the absorbing column +It is well-known that the sunspot penumbra (the outer part of sunspots) has a very complicate filamentary structure and a strong non-stationary outflow.,It is well-known that the sunspot penumbra (the outer part of sunspots) has a very complicate filamentary structure and a strong non-stationary outflow. + This outflow is responsible for the so-called IEvershed effect. à Doppler shift of the spectral lines emerging [rom sunspots (Evershed1909).," This outflow is responsible for the so-called Evershed effect, a Doppler shift of the spectral lines emerging from sunspots \citep{evershed1909}." +. The magnetic structure of the penumbra can be represented as a mixture of two magnetic field components with different inclinations ancl strengths (e.8..DegenhlidiBellotRubioetal.2004:SánchezAlmeida2005:BorreroBeek 2008).," The magnetic structure of the penumbra can be represented as a mixture of two magnetic field components with different inclinations and strengths \citep[e.g.,][]{degenhardt91,schmidt92,title93,lites93, +stanchfield97,bellot04,sanchez05,borrero05,beck08}." +. Llowever. the radial Evershed flow (in particular. the high-speed “Evershed coluds) is associated with ihe more strongly inclined. almost horizontal field (e.g.Titleetal.1993:BellotRubioetal. 2003).," However, the radial Evershed flow (in particular, the high-speed 'Evershed coluds') is associated with the more strongly inclined, almost horizontal field \citep[e.g.][]{title93,shine1994,bellot03}." +. Recently. significant progress in our understaxding of (he Evershed effect was made by nunmerical simulations (Ileinemannetal.2007;Scharmer2008:Rempel]xitüiashvilietal. 2009a).," Recently, significant progress in our understanding of the Evershed effect was made by numerical simulations \citep{heinemann2007, +scharmer2008,rempel2009,rempel_sci09,kiti09a}." +. These studies suggested (hat the Evershed flow is a consequence of overturnng magnetoconvection in (he presence of inclined magnetic fields. ancl that the diving mechanism is associated with (raveling convective waves (hat propagate in the direction of the magnetic field inclination. (HIurlburtetal.2000:IXitiashvili20092)..," These studies suggested that the Evershed flow is a consequence of overturning magnetoconvection in the presence of inclined magnetic fields, and that the driving mechanism is associated with traveling convective waves that propagate in the direction of the magnetic field inclination \citep{hurlburt2000,kiti09a}." + The issue is not resolved ancl other interpretations are possible (seeSchlichenmaier2009)., The issue is not resolved and other interpretations are possible \citep[see][]{schliche09}. +. Thus. it is important to confront the simulations with as many observations as possible.," Thus, it is important to confront the simulations with as many observations as possible." + In this Letter. we examine tlie idea that the sea-serpent penunibral field lines detected by SainzDalda&BellotRubio(2008) in high-resolution Hinode measurements are related to (he same mechanism of overturning convection and (raveling convective waves in a strong inclined magnetic field.," In this Letter, we examine the idea that the sea-serpent penumbral field lines detected by \cite{dalda08} in high-resolution Hinode measurements are related to the same mechanism of overturning convection and traveling convective waves in a strong inclined magnetic field." + Our analysis is based on (he radiative MIID simulations of Ixitiashvili (2009a)., Our analysis is based on the radiative MHD simulations of \citet{kiti09a}. +. Analvses of visible and near-infrared spectro-polarimetrie observations from the ground revealed (hat in the mid and outer penumbra the Evershecl flows are directed. downwad and have magnetic polarities opposite to Chat of the spot (WestendorpPlazaetal.1997.seeBellotRubio2009[oradetailed description)...," Analyses of visible and near-infrared spectro-polarimetric observations from the ground revealed that in the mid and outer penumbra the Evershed flows are directed downward and have magnetic polarities opposite to that of the spot \citep[][see Be\-llot Rubio 2009 +for a detailed description]{westend97}." + The spectro-polarimeter aboard Linocle (IXosugietal.2007:Tsuneta2008) made il possible to identilv isolated magnetic patches of opposite polarity associated with strong. even supersonic. Evershed. downllows (Ichimotoetal.2007:BellotRubio2009:S&nehezAlmeida&Ichimoto 2009)..," The spectro-polarimeter aboard Hinode \citep{kosugi07,tsuneta2008} made it possible to identify isolated magnetic patches of opposite polarity associated with strong, even supersonic, Evershed downflows \citep{ichimoto07, bellot09, sanchez09}. ." + This provided, This provided + The study of the statistical properties of Large Scale Structure (LSS) in the Universe and their evolution with redshift is one the major tools in observational cosmology., The study of the statistical properties of Large Scale Structure (LSS) in the Universe and their evolution with redshift is one the major tools in observational cosmology. + These structures are usually mapped through optical observation of galaxies which are used as a tracer of the underlying matter distribution., These structures are usually mapped through optical observation of galaxies which are used as a tracer of the underlying matter distribution. + An alternative and elegant approach for mapping the matter distribution. using neutral atomic hydrogen )) as a tracer with intensity mapping. has been proposed in recent years (Petersonetal.(2006)) (Changetal.(2008)).," An alternative and elegant approach for mapping the matter distribution, using neutral atomic hydrogen ) as a tracer with intensity mapping, has been proposed in recent years \citep{peterson.06} \citep{chang.08}." +. Mapping. the matter distribution using HI 21 em emission as a tracer has been extensively discussed in Iterature (Furlanettoetal.(2006)) (Tegmark&Zaldarriaga(2009)) and is being used in projects such as LOFAR (Rotteringetal.(2006)) or MWA (Bowmanetal.(2009)) to observe reionisation at redshifts z - 10., Mapping the matter distribution using HI 21 cm emission as a tracer has been extensively discussed in literature \citep{furlanetto.06} \citep{tegmark.09} and is being used in projects such as LOFAR \citep{rottgering.06} or MWA \citep{bowman.07} to observe reionisation at redshifts z $\sim$ 10. + Evidence in favor of the acceleration. of the expansion of the universe have been accumulated over the last twelve years. thanks to the observation of distant supernovae. CMB anisotropies and detailed analysis of the LSS.," Evidence in favor of the acceleration of the expansion of the universe have been accumulated over the last twelve years, thanks to the observation of distant supernovae, CMB anisotropies and detailed analysis of the LSS." + A cosmological Constant (A) or new cosmological energy density called has been advocated as the origin of this acceleration., A cosmological Constant $\Lambda$ ) or new cosmological energy density called has been advocated as the origin of this acceleration. + Dark Energy is considered as one of the most intriguing puzzles in Physics and Cosmology., Dark Energy is considered as one of the most intriguing puzzles in Physics and Cosmology. + Several cosmological probes can be used to constrain the properties of this new cosmic fluid. more precisely its equation of state: The Hubble Diagram. or luminosity distance as a function of redshift of supernovae as standard candles. galaxy clusters. weak shear observations and Baryon Acoustic Oscillations (BAO).," Several cosmological probes can be used to constrain the properties of this new cosmic fluid, more precisely its equation of state: The Hubble Diagram, or luminosity distance as a function of redshift of supernovae as standard candles, galaxy clusters, weak shear observations and Baryon Acoustic Oscillations (BAO)." + BAO are features imprinted in the distribution of galaxies. due to the frozen sound waves which were present in the photon-baryon plasma prior to recombination at z ~ 1100.," BAO are features imprinted in the distribution of galaxies, due to the frozen sound waves which were present in the photon-baryon plasma prior to recombination at z $\sim$ 1100." + This scale can be considered as à standard ruler with a comoving length of ~I50Mpe., This scale can be considered as a standard ruler with a comoving length of $\sim 150 \mathrm{Mpc}$. + These features have been first observed in the CMB anisotropies and are usually referred to às (Mauskopfetal.(2000).. Larsonetal.(201 D))).," These features have been first observed in the CMB anisotropies and are usually referred to as \cite{mauskopf.00}, \cite{larson.11}) )." + The BAO modulation has been subsequently observed in the distribution of galaxies at low redshift ες «1) in the galaxy-galaxy correlation function by the SDSS (Eisensteinetal.(2005)) (Percivaletal.(2007) (Percivaletal.(2010)).. 24GFRS (Coleetal.(2005)) as well as WiggleZ (Blakeetal.(2011)) optical galaxy surveys.," The BAO modulation has been subsequently observed in the distribution of galaxies at low redshift ( $z < 1$ ) in the galaxy-galaxy correlation function by the SDSS \citep{eisenstein.05} \citep{percival.07} \citep{percival.10}, 2dGFRS \citep{cole.05} as well as WiggleZ \citep{blake.11} optical galaxy surveys." + Ongoing (Eisensteinetal.(2011))— or. future. surveys (LSST.Science) plan to measure precisely the BAO scale in the redshift range O.."," Therefore, when comparing $\alpha_{\rm cool}$ with $\alpha_{\rm total}$, two quantities are considered: $\alpha_{\rm cool}$, using the midplane values of $t_{\rm cool}$, $\Omega$ and $\gamma$, and $\alpha_{\rm cool}$ calculated using vertically averaged values of $\bar{t}_{\rm cool}$, $\bar{\Omega}$, and $\bar{\gamma}$." + We calculate fc... by first averaging the specitic internal energy η and its rate of change ἡ separately. giving This distinction between midplane and vertically averaged. values is important.," We calculate $\bar{t}_{\rm cool}$ by first averaging the specific internal energy $u$ and its rate of change $\dot{u}$ separately, giving This distinction between midplane and vertically averaged values is important." + Using the midplane values of foo. allows us to determine the validity of recent ID semi-analytic models. such us ? and ?. that calculate transport properties based on the midplane temperature.," Using the midplane values of $t_{\rm cool}$ allows us to determine the validity of recent 1D semi-analytic models, such as \citet{Clarke_09} and \citet{Rice_and_Armitage_09}, that calculate transport properties based on the midplane temperature." + The vertically averaged quantities. however. give a more accurate estimate of the rate at which the dise loses energy and allows us to establish if local heating and cooling is in balance.," The vertically averaged quantities, however, give a more accurate estimate of the rate at which the disc loses energy and allows us to establish if local heating and cooling is in balance." + This will then determine if the local a-approximation is still appropriate. even if using midplane values is not.," This will then determine if the local $\alpha$ -approximation is still appropriate, even if using midplane values is not." +" To study the effect of increasing dise mass on angular momentum transport. Simulations |. 2. 3 4. which share the same stellar mass CA,=LA. ) are analysed together."," To study the effect of increasing disc mass on angular momentum transport, Simulations 1, 2, 3 4, which share the same stellar mass $M_* = 1 M_\odot$ ) are analysed together." + These dises have initial masses of 0.25. 0.5. 1.10 and 1.5 Al. respectively.," These discs have initial masses of 0.25, 0.5, 1.0 and 1.5 $M_{\rm \odot}$ respectively." + Despite all four simulations beginning with a wide range of disc masses. their surface density profiles do not differ greatly between rocὃς60 au. as ean be seen in Figure 2..," Despite all four simulations beginning with a wide range of disc masses, their surface density profiles do not differ greatly between $r \sim 20 - 60$ au, as can be seen in Figure \ref{fig:Ms1}." + The higher mass dises (fiui=1 diui= 1.5) are in general much denser between roc]O—20 au. indicating mass build-up in the inner regions as suggested and seen by other authors (222)..," The higher mass discs $q_{\rm init}=1$ $q_{\rm init}=1.5$ ) are in general much denser between $r \sim 10 - 20$ au, indicating mass build-up in the inner regions as suggested and seen by other authors \citep{Armitage_et_al_01,Zhu_et_al_09,Rice2010}." +" The lower-mass disces (diui=0.25 diui= 0.5) undergo a period of quiescent settling lasting approximately 2000 years. adjusting themselves by accretion onto the central star. spreading in radius (see Figure 13) and by cooling towards marginal instability. ultimately settling into quasi-steady, self-regulated states (2).."," The lower-mass discs $q_{\rm init}=0.25$ $q_{\rm init}=0.5$ ) undergo a period of quiescent settling lasting approximately 2000 years, adjusting themselves by accretion onto the central star, spreading in radius (see Figure \ref{fig:Ms1discs}) ) and by cooling towards marginal instability, ultimately settling into quasi-steady, self-regulated states \citep{Lodato_and_Rice_04}." + The higher mass dises (diui=1 diui= 1.5) undergo several transient burst events. marked by persistently strong nz=2 spiral activity (see Figure 13).," The higher mass discs $q_{\rm init}=1$ $q_{\rm init}=1.$ 5) undergo several transient burst events, marked by persistently strong $m=2$ spiral activity (see Figure \ref{fig:Ms1discs}) )." + They also adjust their q more rapidly compared to the two lower mass discs. with reductions between over approximately 10 ORPs.," They also adjust their $q$ more rapidly compared to the two lower mass discs, with reductions between over approximately 10 ORPs." + This is due to significant accretion. with the central star accreting a total of O.234/. for Gui= Land O.38Al. for qui=1.5.and is consistent with the suggestion (22). that the mass accretion rate has a verystrong dependence on surface density or. equivalently. disc mass.," This is due to significant accretion, with the central star accreting a total of $0.23 M_\odot$ for $q_{\rm init}=1$ and $0.38 M_\odot$ for $q_{\rm init}=1.5$,and is consistent with the suggestion \citep{Rice_and_Armitage_09, Clarke_09} that the mass accretion rate has a verystrong dependence on surface density or, equivalently, disc mass." + The dises with diui0.5 also spread to a much larger radius than the diui<0.5 dises (which is clear in Figure 13). with signiticant fractions of mass outside 60 au.," The discs with $q_{\rm init} >0.5$ also spread to a much larger radius than the $q_{\rm init} <0.5$ discs (which is clear in Figure \ref{fig:Ms1discs}) ), with significant fractions of mass outside 60 au." + All the discs in Figure 2. are stable against fragmentation. with ;j=/o4>3 QU 0.06) at all radit (22)...," All the discs in Figure \ref{fig:Ms1} are stable against fragmentation, with $\beta = t_{\rm cool} \Omega >>3$ $\alpha_{\rm cool} < 0.06$ ) at all radii \citep{Gammie,Ken_1}. ." + The values of .7 as a function of opacity regime are also in good agreement with those predicted by ?.., The values of $\beta$ as a function of opacity regime are also in good agreement with those predicted by \citet{Cossins2010}. . +of the N66 complex (except one) have the same age. Le. 3411 Myr. Sabbietal. (2007,"of the N66 complex (except one) have the same age, i.e. $\pm$ 1 Myr. \citet[][]{Sabbi07}'" +")""s subcluster Se 10 overlaps N664A. in which they count a total of 61 low-mass PMS objects in an area 1.6 pe in radius."," 's subcluster Sc 10 overlaps N66A, in which they count a total of 61 low-mass PMS objects in an area 1.6 pc in radius." + To estimate the ages. they fit the color-magnitude diagrams of the subclusters(4S7 ACS images F555W and F814W) with Padua isochrones etal. 1994).," To estimate the ages, they fit the color-magnitude diagrams of the subclusters ACS images F555W and F814W) with Padua isochrones \citep[][]{Bertelli94}." +. They also use PMS isochrones (Stessetal..2000) to evaluate the ages of the various subclusters., They also use PMS isochrones \citep[][]{Siess00} to evaluate the ages of the various subclusters. + They note that compared to other subclusters. Sc 10 appears redder. suggesting either that it is a few million years older or that it is coeval with the others but affected by higher extinction.," They note that compared to other subclusters, Sc 10 appears redder, suggesting either that it is a few million years older or that it is coeval with the others but affected by higher extinction." + They maintain that the magnitudes and colors of the PMS stars in Se 10 appear too bright and red to be compatible with a stellar population older than 4 Myr., They maintain that the magnitudes and colors of the PMS stars in Sc 10 appear too bright and red to be compatible with a stellar population older than 4 Myr. + They therefore attribute an age of 34 11 Myr to this subcluster. as for others. and do not consider a younger age.," They therefore attribute an age of $\pm$ 1 Myr to this subcluster, as for others, and do not consider a younger age." +" At the same time. they note that ""Some of these associations (ie.. Se 10 and 12) appear still embedded in dust and fuzzy nebulosities and are probably sites of recent or even still ongoing star formation.”"," At the same time, they note that “Some of these associations (i.e., Sc 10 and 12) appear still embedded in dust and fuzzy nebulosities and are probably sites of recent or even still ongoing star formation.”" + This means that they do not preclude the possibility of à younger age., This means that they do not preclude the possibility of a younger age. + Once again. one should be cautious when interpreting the color-magnitude diagrams of objects lying in the face of a very bright rregion. because the colors may be contamiated by nebular emission.," Once again, one should be cautious when interpreting the color-magnitude diagrams of objects lying in the face of a very bright region, because the colors may be contaminated by nebular emission." + Our suggestion of a younger age for the exciting stars of N66A. however agrees perfectly with other studies of this region.," Our suggestion of a younger age for the exciting stars of N66A, however agrees perfectly with other studies of this region." + In particular. Gouliermisetal.(2008) argue that the entire N66 region may host younger star formation events induced from the east. where the SNR B0057-724 lies al.. 2004).," In particular, \citet[][]{Gouliermis08} argue that the entire N66 region may host younger star formation events induced from the east, where the SNR B0057-724 lies \citep[][]{Reid06,Naze02,Danforth03,Naze04}." +. There is indeed a large hhole there. which is offset from the central parts of N66. and interesting enough. N66A lies on the triggered formation arc suggested to be associated with a shock wave coming from the direction of the SNR (their Fig.," There is indeed a large hole there, which is offset from the central parts of N66, and interesting enough, N66A lies on the triggered formation arc suggested to be associated with a shock wave coming from the direction of the SNR (their Fig." + 1)., 1). + An expanding rregion or à bubble blown by the winds of the massive progenitor of the SNR B0057-724 and possibly the W-R binary 55980 and the O7 laf- star 880 (Walborn&Fitzpatrick.1990) may be the stimulating agent., An expanding region or a bubble blown by the winds of the massive progenitor of the SNR B0057-724 and possibly the W-R binary 5980 and the O7 Iaf+ star 80 \citep[][]{Walborn90} may be the stimulating agent. + There are therefore stars of a range of ages in the N66 complex. 55980 and 880 being older than the 3346 cluster. which has not yet produced any WN stars.," There are therefore stars of a range of ages in the N66 complex, 5980 and 80 being older than the 346 cluster, which has not yet produced any WN stars." + We have used imaging and spectroscopy in the optical with the ESO NTT as wellHST ACS and Spitzer archive data to study N66A. This compact rregion is quite a distinctive. object in. N66. 3346). the pre-eminent starburst region of the SMC.," We have used imaging and spectroscopy in the optical with the ESO NTT as well ACS and Spitzer archive data to study N66A. This compact region is quite a distinctive object in N66 346), the pre-eminent starburst region of the SMC." + We have presented a global view of the whole region and emphasized the importance of N66A. We derived a number of the physical characteristics of NOGA. and for the first time using spectroscopy the spectral classification of the main exciting star of N66A. It is a dwarf massive star of type earlier than O8.," We have presented a global view of the whole region and emphasized the importance of N66A. We derived a number of the physical characteristics of N66A, and for the first time using spectroscopy the spectral classification of the main exciting star of N66A. It is a dwarf massive star of type earlier than O8." + We have argued that N66A is probably produced by a recent massive star formation in N66., We have argued that N66A is probably produced by a recent massive star formation in N66. + Its exciting stars are most likely to have been triggered by the action of shocks caused by a previous generation of massive stars., Its exciting stars are most likely to have been triggered by the action of shocks caused by a previous generation of massive stars. + Moreover. N66À belongs to a rare class of compact rregions i the MCs. called HEBs (High-Excitation Blobs).," Moreover, N66A belongs to a rare class of compact regions in the MCs, called HEBs (High-Excitation Blobs)." + Only two other HEBs have so far been detected in the MCs., Only two other HEBs have so far been detected in the MCs. +between the measurements and the [fitting formula of Scoccimarro&Couchman(2001).,between the measurements and the fitting formula of \citet{ScoccimarroCouchman2001}. +. To assess the agreement between PE. and N-bocdy measurements as a function of scale and. triangle shape. we will consider five sets of configurations.," To assess the agreement between PT and N-body measurements as a function of scale and triangle shape, we will consider five sets of configurations." + We will present results as a function of & for equilateral configurations Dk.hk. hk). isosceles configurations (2k.2h.k) as well as increasingly “squeezed” configurations. Lh.A.AA) with fixed AA.," We will present results as a function of $k$ for equilateral configurations $B(k,k,k)$ , isosceles configurations $B(2k,2k,k)$ as well as increasingly “squeezed” configurations $B(k,k,\D k)$ with fixed $\Delta k$." +" To further explore the shape dependence. we will also show the result of measuring the matter bispectrum for two sets of generic configurations for which the magnitude of two sides of the triangle (A, and. fe) is fixed. while the angle 8 between them is varied."," To further explore the shape dependence, we will also show the result of measuring the matter bispectrum for two sets of generic configurations for which the magnitude of two sides of the triangle $k_1$ and $k_2$ ) is fixed while the angle $\theta$ between them is varied." + For each of these sets. in each of the following figures. de Upper two panels show measurements of the matter jspectrum. D. or thereduced bispectrum ϐ. see. below. for initial conditions. as well as 10 ratio to the corresponding tree-level expression in. PT where the acoustic oscillations are removed by means of the Lgmooth transfer function of Eisenstein&Lu(1998).," For each of these sets, in each of the following figures, the upper two panels show measurements of the matter bispectrum $B$, or the bispectrum $Q$, see below, for initial conditions, as well as the ratio to the corresponding tree-level expression in PT where the acoustic oscillations are removed by means of the smooth transfer function of \citet{EisensteinHu1998}." +". Recall wt there is no ""linear"" matter bispectrum for Gaussian initial conditions (but there is an initial bispectrum in )0 presence of primordial non-CGaussianity).", Recall that there is no “linear” matter bispectrum for Gaussian initial conditions (but there is an initial bispectrum in the presence of primordial non-Gaussianity). + Lor sake of comparison. we take the treccIevel prediction as a reference since it is most directly. related. to the linear. bispectrum. which is generically DτοPr.," For sake of comparison, we take the tree-level prediction as a reference since it is most directly related to the linear bispectrum, which is generically $B^{tree}\sim P_L^2$." + The last three rows in the plots focus on the clfect of primordial non-CGaussianity., The last three rows in the plots focus on the effect of primordial non-Gaussianity. + We show. in particular. the ratlo the cillercnce with respect to the Gaussian case. and the combination -2 00)] to highlight the elfects proportional to νε.," We show, in particular, the ratio, the difference with respect to the Gaussian case, and the combination -2 0)]/2 to highlight the effects proportional to $\fNL^2$." + La all cases. the N-body results indicate the mean over eight realizations of the specific combination (ratio. cillerence. ete.)," In all cases, the N-body results indicate the mean over eight realizations of the specific combination (ratio, difference, etc.)" + performed with Gaussian ancl non-Gaussian initial conditions drawn from the same random seed field ὁ (see section 3))., performed with Gaussian and non-Gaussian initial conditions drawn from the same random seed field $\phi$ (see section \ref{sec:sims}) ). + In this way. we can study the elect of non-Gaussianity without the additional sampling variance allecting. for instance. the dillerence Dye;Bey obtained as the between the Dye;and the De; over the eight. realizations.," In this way, we can study the effect of non-Gaussianity without the additional sampling variance affecting, for instance, the difference $B_{NG}-B_G$ obtained as the between the $B_{NG}$and the $B_G$ over the eight realizations." + Finally. the three. columns. correspond. to the results at redshift z=0. 1 and 2.," Finally, the three columns correspond to the results at redshift $z=0$, $1$ and $2$." + In all the plots. the numerical results are compared to the tree-level lines) and one-loop predictions lines) in PV.," In all the plots, the numerical results are compared to the tree-level ) and one-loop predictions ) in PT." + In3.. we show the matter bispectrum BCA.A.A) for equilateral configurations.," In, we show the matter bispectrum $B(k,k,k)$ for equilateral configurations." +" As can be seen. non-linearities are xuticularly severe. consisting in a almost 300% correction relative. to the tree-level prediction.. for⋅ &20.2./Alpe"" and z=0 for instance."," As can be seen, non-linearities are particularly severe, consisting in a almost $\sim 300\%$ correction relative to the tree-level prediction for $k\simeq 0.2\kMpc$ and $z=0$ for instance." + The bispectrum measured. [from a otal simulation volume of ~33.Cpe? presents errors of he order of at this scale for equilateral configurations., The bispectrum measured from a total simulation volume of $\sim 33\cGpc$ presents errors of the order of at this scale for equilateral configurations. + otice that this specifie triangle shape sullers. unlike other configurations close in shape and scale. from a relatively arge variance (up to a factor of six).," Notice that this specific triangle shape suffers, unlike other configurations close in shape and scale, from a relatively large variance (up to a factor of six)." + This ellect originates xwilv from the symmetry factor sg in and from the large contribution of higher-order correlation unctions to the bispectrum variance.," This effect originates partly from the symmetry factor $s_B$ in, and from the large contribution of higher-order correlation functions to the bispectrum variance." + The one-loop prediction appears to be well within our errors up to &O.15hAlpe and. describes reasonably well the behavior at smaller scales., The one-loop prediction appears to be well within our errors up to $k\sim 0.15\kMpc$ and describes reasonably well the behavior at smaller scales. + For As0.15hMpe.+. the one-loop prediction. behaves better. than the fitting formula of Scoccimarro&Couchman(2001). (in theplots C01). which under-predicts. the data. points at. mildly non-linear scales.," For $k\lesssim 0.15\kMpc$, the one-loop prediction behaves better than the fitting formula of \citet{ScoccimarroCouchman2001} (in theplots SC01), which under-predicts the data points at mildly non-linear scales." + This ~20% discrepancy. unsurprising eiven the size of the simulation box used for the Lit (240fh! Mpe). has already been noted by Panοal.," This $\sim 20\%$ discrepancy, unsurprising given the size of the simulation box used for the fit $240\Mpc$ ), has already been noted by \citet{PanColesSzapudi2007}." + It should be remarked that the SCOL formula aimed ab describing the nonlinear. bispectrum at smaller. scales. xwiieulalelv. for weak lensing applications. and did not acldressed specifically the issue of the acoustic features.," It should be remarked that the SC01 formula aimed at describing the nonlinear bispectrum at smaller scales, particulalrly for weak lensing applications, and did not addressed specifically the issue of the acoustic features." + Panetal.(2007). also. proposed a phenomenological mocel for he matter bispectrum based on a rescaling argument similar o the one explored. in Hamiltonetal.(1991):Peacock&Docds (1996).," \citet{PanColesSzapudi2007} also proposed a phenomenological model for the matter bispectrum based on a rescaling argument similar to the one explored in \citet{HamiltonEtal1991, PeacockDodds1996}." +".. We also compared this prescription to our measurcments and find that it agrees better than the fitting ""unction. of Scoccimarro&Couchman(2001).", We also compared this prescription to our measurements and find that it agrees better than the fitting function of \citet{ScoccimarroCouchman2001}. +.. However. he rescaling induces an large and unphysical shift in the acoustic oscillations that should. be properly accounted. for (inPanetal.2007.comparisonsareshownwithsimulationsoffeaturelessmatterpower spectra).," However, the rescaling induces an large and unphysical shift in the acoustic oscillations that should be properly accounted for \citep[in][comparisons are shown with simulations of featureless matter power spectra]{PanColesSzapudi2007}." + The third. row of shows the ellect of »imorcdial non-Gaussianity in terms of the ratio D(fvj= 0) , The third row of shows the effect of primordial non-Gaussianity in terms of the ratio $B(\fNL=100)/B(\fNL=0)$ . +Lt is interesting to notice that. the additional non-linear contributions due to. non-Ciaussian initial conditions correspond. for these set of configurations. toa ~5% correction regardless of redshift.," It is interesting to notice that the additional non-linear contributions due to non-Gaussian initial conditions correspond, for these set of configurations, to a $\sim 5\%$ correction regardless of redshift." + In. fact. the contribution of the initial bispectrum By to this elfect is alreacly subclominant at &Ο.��ήAlpe* and z=0. while one-loop corrections themselves fail to account for it at slightly smaller scales.," In fact, the contribution of the initial bispectrum $B_0$ to this effect is already subdominant at $k\sim 0.1\kMpc$ and $z=0$, while one-loop corrections themselves fail to account for it at slightly smaller scales." + “Phis is also apparent in the dillerence D(fxy—100).νι0) which. in the PP picture. arises rom the one-loop contributions depending on the initial jispectrum and trispectrum.," This is also apparent in the difference $B(\fNL=100) - B(\fNL=0)$ which, in the PT picture, arises from the one-loop contributions depending on the initial bispectrum and trispectrum." + At redshift zero. these provide an accurate description of (νι=100)—0) up ok0.15hMpe. +.," At redshift zero, these provide an accurate description of $B(\fNL=100) - B(\fNL=0)$ up to $k~0.15\kMpc$ ." + Finally. in the last row we compare the combination μεν=1100)|B(fx;100)2νιO)/2 o Bie which. in the one-loopapproximation. is the sole erm depencding on the initial trispectrum and. therefore. on νι ," Finally, in the last row we compare the combination $[B(\fNL=+100)+B(\fNL=-100)-2~B(\fNL=0)]/2$ to $B_{112}^{II}$ which, in the one-loopapproximation, is the sole term depending on the initial trispectrum and, therefore, on $\fNL^2$ ." +Vhis term appears to underestimate by about 50% (at yest) the simulation results., This term appears to underestimate by about $50\%$ (at best) the simulation results. + One shouldnonetheless keep in mind these contributions represent a0.154 correction to the matter bispectrum., One shouldnonetheless keep in mind these contributions represent a$0.1\%$ correction to the matter bispectrum. + In 4.. we show the matter bispectrum for the," In , we show the matter bispectrum for the" +Dwarf Novae (DN) systems a white dwarf (WD) accreting matter at time-averaged rates (M5contain«10M..vr! from a low-mass (<1.. typically) stellar companion (see Osaki 1996 for an overview).,Dwarf Novae (DN) systems contain a white dwarf (WD) accreting matter at time-averaged rates $\timav<10^{-9}M_\odot \ {\rm yr}^{-1}$ from a low-mass $<0.5M_\odot$ typically) stellar companion (see Osaki 1996 for an overview). + At these (M;'s. the accretion disk is subject to a thermal causes it to rapidly transfer matter onto the WD (at instabilityM>> (M) which fora few days to a week once every month to year.," At these $\timav$ 's, the accretion disk is subject to a thermal instability which causes it to rapidly transfer matter onto the WD (at $\dot M \gg +\timav$ ) for a few days to a week once every month to year." + The orbital periods of these binaries are usually less than 2 hours (below the period gap). but there arealso DN above the period gap. > 3 hours (see Shafter 1992).," The orbital periods of these binaries are usually less than 2 hours (below the period gap), but there arealso DN above the period gap, $>$ 3 hours (see Shafter 1992)." + The M onto the WD ts often low enough between outbursts that the UV emission is dominated by the internal luminosity of the WD., The $\dot M$ onto the WD is often low enough between outbursts that the UV emission is dominated by the internal luminosity of the WD. + Indeed recent spectroscopy has resolved the WD's contribution to the quiescent light and found effective temperatures 10.000—40.000K (see Sion 1999).," Indeed recent spectroscopy has resolved the WD's contribution to the quiescent light and found effective temperatures $T_{\rm eff}\sim +10,000-40,000 \ {\rm K}$ (see Sion 1999)." + The measured internal WD luminosity i5 larger than expected from an isolated WD of similar age ( Gyr). indicating that it has been heated by accretion (Sion 1985).," The measured internal WD luminosity is larger than expected from an isolated WD of similar age $\approx$ Gyr), indicating that it has been heated by accretion (Sion 1985)." + Compressional heating (1.9. internal gravitational energy release) appears to be the main driver for this re-heatine (Sion 1995)., Compressional heating (i.e. internal gravitational energy release) appears to be the main driver for this re-heating (Sion 1995). + Sion's (1995) estimate for internal eravitational enerev release within the WD (of mass M and radius R) was Lz0.15GM(MD/R.," Sion's (1995) estimate for internal gravitational energy release within the WD (of mass $M$ and radius $R$ ) was $L\approx 0.15 +GM\timav/R$." +" However. we show in. $2. that the energy release actually depends on the thermal state of the WD interior and that the dominant enerey is in ⊽the accreted outer envelope. giving.. {τεrT 2ΚΤΟahr4M,/2.puny. where j(z0.6 is the mean molecular weight of the accreted material. 7. is the WD core temperature. 5/7, is the baryon mass. and & is Boltzmann's constant."," However, we show in \ref{sec:physics} that the energy release actually depends on the thermal state of the WD interior and that the dominant energy release is in the accreted outer envelope, giving $L\approx +3kT_c \timav/\mu m_p$ , where $\mu\approx 0.6$ is the mean molecular weight of the accreted material, $T_c$ is the WD core temperature, $m_p$ is the baryon mass, and $k$ is Boltzmann's constant." + The theoretical challenge that we address in $3. is how to calculate 7. as a function of and thus find 7.4.," The theoretical challenge that we address in \ref{sec:Tcmethod} is how to calculate $T_c$ as a function of $\timav$, and thus find $T_{\rm eff}$." + Because of unstable nuclear burning and the iM).resulting classical novae cycle. the H/He envelope mass changes with time. allowing the core to cool at low accumulated masses and be heated prior to unstable ignition.," Because of unstable nuclear burning and the resulting classical novae cycle, the H/He envelope mass changes with time, allowing the core to cool at low accumulated masses and be heated prior to unstable ignition." + We use nova ignition to determine the maximum mass of the overlying freshly accreted shell. and find the steady-state (1.e. cooling equals heating throughout the classical novae cycle) core temperature. 7... as a function of (M) and M.," We use nova ignition to determine the maximum mass of the overlying freshly accreted shell, and find the steady-state (i.e. cooling equals heating throughout the classical novae cycle) core temperature, $T_c$, as a function of $\timav$ and $M$." + We compare our calculations to HST/STIS observations and infer (M on the timescale of 10° years., We compare our calculations to HST/STIS observations and infer $\timav$ on the timescale of $10^6$ years. + We find that DN above the period gap have (Mjz00?M.yr. while those below have (Mjz1077M..ye!. consistent with that expected from traditional CV evolution (e.g. Howell. Nelson. Rappaport 2001). even those that involve some “hibernation” (Shara et 11986: Kolb et ," We find that DN above the period gap have $\timav\approx 10^{-9}M_\odot \ {\rm +yr^{-1}}$, while those below have $\timav\approx 10^{-10} M_\odot \ {\rm +yr^{-1}}$, consistent with that expected from traditional CV evolution (e.g. Howell, Nelson, Rappaport 2001), even those that involve some “hibernation” (Shara et 1986; Kolb et 2001)." +The result more surprising if the much weaker magnetic 22001).braking laws of isAndronov. Pinsonneault. Sills (2001) are correct.," The result is more surprising if the much weaker magnetic braking laws of Andronov, Pinsonneault, Sills (2001) are correct." + We also predict the minimum light (My) of CVs in quiescence for a range of (Mj. WD mass. and companion mass.," We also predict the minimum light $M_V$ ) of CVs in quiescence for a range of $\timav$, WD mass, and companion mass." + This assists the search for the predicted large population of CVs with very low mass companions (<0.1M ..) that are near. or past. the period minimum (Howell. Rappaport. Politano. 1997).," This assists the search for the predicted large population of CVs with very low mass companions $<0.1M_\odot$ ) that are near, or past, the period minimum (Howell, Rappaport, Politano 1997)." +" Observations. already show that the WD OUfixes the quiescent colors of these CVs and our calculations are useful for CV surveys in the field (e.g. 2DF. SDSS. see Marsh et 2200122 and; SzkodyS7eody et 22002) 220023:and globular"" areclusters."," Observations already show that the WD fixes the quiescent colors of these CVs and our calculations are useful for CV surveys in the field (e.g. 2DF, SDSS, see Marsh et 2001 and Szkody et 2002) and globular clusters." +- Compressional heating is the energy released by fluid elements as they are compressed by further accretion., Compressional heating is the energy released by fluid elements as they are compressed by further accretion. + The important feature of this heating mechanism ts that the heat is released in the WD interior.. and thus is radiated on a timescale which tslonger than the time between DN outbursts.," The important feature of this heating mechanism is that the heat is released in the WD , and thus is radiated on a timescale which islonger than the time between DN outbursts." + Contrast this to the gravitational potential energy released by the infalling matter. (GM/R per," Contrast this to the gravitational potential energy released by the infalling matter, $GMm_p/R$ per" +noisy ab Ryο and the break becomes less well defined.,noisy at $R_{v} > 3.3h^{-1}_{70}Mpc$ and the break becomes less well defined. + It is interesting (hat the N-body simulations of Wang et al. (, It is interesting that the N-body simulations of Wang et al. ( +2009) show (their Fig.,2009) show (their Fig. +" 6) that for host halo masses ereater than LOMA1M. ejected sub-halos fall back while for host halo masses lower than this ejected sub-halos are likely to reach the region bevond /2,.", 6) that for host halo masses greater than $10^{13}h^{-1} M_{\odot}$ ejected sub-halos fall back while for host halo masses lower than this ejected sub-halos are likely to reach the region beyond $R_{v}$. + The data in this higher Nass range are (oo sparse lo determine whether (his same phenomenon is responsible [or the break becoming less well defined., The data in this higher mass range are too sparse to determine whether this same phenomenon is responsible for the break becoming less well defined. +" Plots for higher and lower values of Qy are similar with the statistic among the red points between the dashed lines in (he 2/22,<2 plots asvimptoting at lower aud higher values.", Plots for higher and lower values of $\Omega_{\Lambda}$ are similar with the statistic among the red points between the dashed lines in the $R/R_{v} < 2$ plots asymptoting at lower and higher values. +" The results for 2/2,>2 (black points) for a range in vacuun energy are very similar (to those shown in the middle panel.", The results for $R/R_{v} > 2$ (black points) for a range in vacuum energy are very similar to those shown in the middle panel. +" It is not clear what is responsible for the [all-olf below 42,~2h.)Alpe in these plots especially given that TOS found their result at. 2,~L3h41Mpe."," It is not clear what is responsible for the fall-off below $R_{v} \sim 2h^{-1}_{70}Mpc$ in these plots especially given that T08 found their result at $R_{v} \sim 1.3h^{-1}_{70} +Mpc$." +" A possible explanation comes from the observation that the galaxies (hat are supposed to be expanding at the Hubble rate (those plotted in the middle panel) also show large deviations from unity in (he same low range of δὲ, suggesting that the field galaxies surrounding these low mass groups may not be uniformly distributed.", A possible explanation comes from the observation that the galaxies that are supposed to be expanding at the Hubble rate (those plotted in the middle panel) also show large deviations from unity in the same low range of $R_{v}$ suggesting that the field galaxies surrounding these low mass groups may not be uniformly distributed. + A sub-sample of more isolated groups was analvsed in order to measure the ellect of eroup clustering on the result., A sub-sample of more isolated groups was analysed in order to measure the effect of group clustering on the result. + This sub-saumple included only those 3894 groups of the original 12620 without a neighbor within 44pe., This sub-sample included only those 3894 groups of the original 12620 without a neighbor within $4h^{-1}_ {70}Mpc$. + The results are shown in the bottom panel of Fig., The results are shown in the bottom panel of Fig. + 4 and can be compared to the top panel., 4 and can be compared to the top panel. + The previous results shown in Figs 3 5 remain unchanged but with larger uncertainty., The previous results shown in Figs 3 5 remain unchanged but with larger uncertainty. +" In addition the fall-off below H,—hatMpe noted above is still present.", In addition the fall-off below $R_{v} \sim 2h^{-1}_{70}Mpc$ noted above is still present. + This region should show the most change if the effect of clustering is à dominaüine influence., This region should show the most change if the effect of clustering is a dominating influence. + Increasing (he isolation criterion above leaves too few groups ancl very poor stalistics., Increasing the isolation criterion above leaves too few groups and very poor statistics. + Asa further check on the results another sub-sample consistinge of only those 1835 eeroups with more than 5 members was analvsed., As a further check on the results another sub-sample consisting of only those 1835 groups with more than 5 members was analysed. + These results have larger uncertainties but there are no svstematic differences from those shown in Figs 3 4., These results have larger uncertainties but there are no systematic differences from those shown in Figs 3 4. + The main results of this work are summarized in Fig., The main results of this work are summarized in Fig. + 5 which shows how the solutions varv as a [function Qy or degree of sub-IIubble expansion., 5 which shows how the solutions vary as a function $\Omega_{\Lambda}$ or degree of sub-Hubble expansion. + The statistic in (he individual panels in Fig., The statistic in the individual panels in Fig. + 5 was determined in exactly the same manner as (hat in the simulation in Fig., 5 was determined in exactly the same manner as that in the simulation in Fig. + 2., 2. +" Red points represent 3Y'(77,) and black points Y(//(2,).", Red points represent $Y(H_{v})$ and black points $Y(H(z_{g})$. +" To the left of the break al R/BR,~2 these ordinates are plotted against RU)/i2, while to the right. against ΠΠτρ)...", To the left of the break at $R/R_{v} \sim 2$ these ordinates are plotted against $R(H_{v})/R_{v}$ while to the right against $R(H(z_{g})/R_{v}$. + The same groups were used to construct each panel., The same groups were used to construct each panel. + These included. those with 2.6 4 +\times 10^{-8}$ ph ${\rm cm}^{-2} {\rm s}^{-1}$ ), with the names and X-ray fluxes of some of the more interesting counterpart candidates, and the $\gamma-$ ray fluxes, spectral indices, and the $\tau$ variability statistic where available." + In the cases where there is a bright. thermal SNR in the field. we first fit the spectrum using a thermal plasina moclel. aud then added a power law component with a spectral iudex of 2.0 to see if the fit inproved aud to provide upper limits on any non-thermal component.," In the cases where there is a bright, thermal SNR in the field, we first fit the spectrum using a thermal plasma model, and then added a power law component with a spectral index of 2.0 to see if the fit improved and to provide upper limits on any non-thermal component." + Only. the non-thermal [Lax limit is listed in Table 2.., Only the non-thermal flux limit is listed in Table \ref{MULtab}. + In cases where there was uo obvious source. the same fittiug process was used to provide lo upper limits on the flux.," In cases where there was no obvious source, the same fitting process was used to provide $1 \sigma$ upper limits on the flux." + In some cases of previously known objects. we quote values from the literature.," In some cases of previously known objects, we quote values from the literature." +" In order to compare the different. sources. we calculated an N-ray to 5—ray energy ""spectral index” ay,=1+logF,/Ax)/6 where £4 is the photon flux above 1GeV. which correspouds to the flux deusity at 1GeV if a photon index of 2.0 is assumed. aud Ay is the X-ray. power law normalization in photous GeVbem ο. corresponding to the uuabsorbed flux density at LkeV. This value is also listed in Table 2.."," In order to compare the different sources, we calculated an X-ray to $\gamma-$ ray energy “spectral index"" $\alpha_{X\gamma}= +1+log(F_{\gamma}/A_X)/6$ where $F_{\gamma}$ is the photon flux above 1GeV, which corresponds to the flux density at 1GeV if a photon index of 2.0 is assumed, and $A_X$ is the X-ray power law normalization in photons ${\rm GeV}^{-1}\,{\rm cm}^{-2}$ , corresponding to the unabsorbed flux density at 1keV. This value is also listed in Table \ref{MULtab}. ." + The RAIS level σι of. the timing+ residual. power isB definedd to be oRD=fySuCFMf.," The RMS level $\sigma_{\rm R}$ of the timing residual power is defined to be $\sigma_{\rm R}^2 =\int_{0}^{\infty} S_{\rm R}(f) +df$." + The spectra of CAV backerounds generated by various astrophysical processes are usually sunmiarized as power-law spectra with power iudex a. ie. the characteristic strain of GWs is ο=AGfy).," The spectra of GW backgrounds generated by various astrophysical processes are usually summarized as power-law spectra with power index $\alpha$, i.e. the characteristic strain of GWs is $h_{\rm c}=A_{\rm c} (f/f_{0})^{\alpha}$." + For such power-law spectra. the RAIS level of correspoucding pulsar timing residuals Is the constants 44...75 take following values y=H3.27TS the fp =Max[Tlfos]is the larger of the following two frequencies: (1) the frequency cut-off (P 1)due to the finite leneth time span T. of observation: (2) the iutzimsic frequency cut-off feu =wag/(2x)due to eraviton nass.," For such power-law spectra, the RMS level of corresponding pulsar timing residuals is where the constants $\beta_1 \dots \beta_{5}$ take following values and the $f_{\rm L}={\rm Max}[T^{-1},f_{\rm cut}]$ is the larger of the following two frequencies: (1) the frequency cut-off $T^{-1}$ ) due to the finite length time span $T$ of observation; (2) the intrinsic frequency cut-off $f_{\rm +cut}=\wc/(2\pi)$ due to graviton mass." + One can derive an upper lanit for the CAV velocity using single pulsar timing data. because of the surfing effect (Baskaranetal.2008b):: but it is unlikely that oue can use single pulsar timing data to constrain the eraviton mass (Daskaranetal.2008a).," One can derive an upper limit for the GW velocity using single pulsar timing data, because of the surfing effect \citep{BPPP08}; but it is unlikely that one can use single pulsar timing data to constrain the graviton mass \citep{BPPP08b}." +. Because of the correction factor gCf.) (see Fig. 1)).," Because of the correction factor $\eta(f_{\rm g})$ (see Fig. \ref{fig:eta}) )," + the exaviton mass reduces the CAV induced pulsar timing residuals., the graviton mass reduces the GW induced pulsar timing residuals. + This prevents us from coustrainig the graviton mass using the amplitude of single pulsar timing residuals., This prevents us from constraining the graviton mass using the amplitude of single pulsar timing residuals. + However. as explained in the next section. the cross correlation between pulsar timing residuals from different directions will help us in detecting the eraviton mass.," However, as explained in the next section, the cross correlation between pulsar timing residuals from different directions will help us in detecting the graviton mass." + A stochastic CAV backeround leaves a correlation between timing residuals of pulsars pairs 2008).," A stochastic GW background leaves a correlation between timing residuals of pulsars pairs \citep{HD83, LJR08}." +. Such a correlatio1 C(O). depends on the angular distance 0 between two pulsars.," Such a correlation, $C(\theta)$, depends on the angular distance $\theta$ between two pulsars." + It turus out that the eravitou nass changes the shape of this correlation fiction., It turns out that the graviton mass changes the shape of this correlation function. + One can therefore detect a massive eraviton by exaiuiuiug the shapes of pulsar tiuius correl:ion fictions., One can therefore detect a massive graviton by examining the shapes of pulsar timing correlation functions. + As shown in Appendix D.. the pulsar timing cross-correclation function for a massive CAV backeround depends ou the graviton mass. specific power spectra of CAV vackerouncd. aud observation schedule.," As shown in Appendix \ref{app:hel}, the pulsar timing cross-correlation function for a massive GW background depends on the graviton mass, specific power spectra of GW background, and observation schedule." + Iu this wav. an analytical expression for the cross-correlation fuiction would uot be xossible.," In this way, an analytical expression for the cross-correlation function would not be possible." + We use Monte-Carlo sinmlations iun this paper to determiue the shape of the correlation function for CAV backgrounds with a power-law spectra., We use Monte-Carlo simulations in this paper to determine the shape of the correlation function for GW backgrounds with a power-law spectra. + Iu the Monte-Carlo siauulatious for C(0). we randomly chocoe pulsars from an isotropic distribution over sky positions.," In the Monte-Carlo simulations for $C(\theta)$, we randomly choose pulsars from an isotropic distribution over sky positions." + We then hold constant these pulsar positions and caculate the augular separation 0 between every pair of pulsars., We then hold constant these pulsar positions and calculate the angular separation $\theta$ between every pair of pulsars. + Next. to simulate the power-law CW backeround. we generate 104 monochromatic waves. choosing random phase. aud choosing the auuplitude from the power-law ο=X(fifoy. where we take a=2/3 (Phinney2001:απο&Dacser2003:Wryithe&Loeb2003:Enolaetal.200[:Sesanatal.2004:Wen 2009).," Next, to simulate the power-law GW background, we generate $10^{4}$ monochromatic waves, choosing random phase, and choosing the amplitude from the power-law $h_{\rm c}=A_{\rm c} (f/f_{0})^{\alpha}$, where we take $\alpha=-2/3$ \citep{Phinney01,JB03, WL03, EINS04, SHMV04, WLH09}." +. The timing residuals are calculated using Eq. (9)), The timing residuals are calculated using Eq. \ref{eq:z}) ) + and (10))., and \ref{eq:r}) ). +" Then. the cross-correlation ""unction. C(0). between pulsar pairs is calculated."," Then, the cross-correlation function, $C(\theta)$, between pulsar pairs is calculated." + We repeat stch processes aud average over the angular depeudent correlatiou function (0) uutil the change in C(0) is less than 0.1, We repeat such processes and average over the angular dependent correlation function $C(\theta)$ until the change in $C(\theta)$ is less than $0.1\%$. + The averaged correlationfunction is tien sinoothed by fitting an eighth order Legendre polvnonual (see Leeeta.(2008). for the details)., The averaged correlationfunction is then smoothed by fitting an eighth order Legendre polynomial (see \cite{LJR08} for the details). + This sincothec C(O) is the correlation function we need., This smoothed $C(\theta)$ is the correlation function we need. + The C(0) are plotted for various parameters iu Fig. 2.., The $C(\theta)$ are plotted for various parameters in Fig. \ref{fig:hel}. + We also check the results by choosing differeut sets of pulsars to male sure the ο(0) is no sensitive to the details of the random pulsar samples., We also check the results by choosing different sets of pulsars to make sure the $C(\theta)$ is not sensitive to the details of the random pulsar samples. + As the C(O) is the statistical expectation of the correlation function. we call it the 1n coutras with the defined in the jext section.," As the $C(\theta)$ is the statistical expectation of the correlation function, we call it the in contrast with the defined in the next section." + As one 1nay expect. the massive graviton has strongero effects for data frou long observing periods than from short periods.," As one may expect, the massive graviton has stronger effects for data from long observing periods than from short periods." +" One cau see this by compariie the 5-vear and 10-vear correlation functions given in Fie. ὃν,"," One can see this by comparing the 5-year and 10-year correlation functions given in Fig. \ref{fig:hel}," + where curves COLTCSPOlleΠιο to the same range of ex:witon nass show cousiderablv greater deviations frou the massless case in the lü-vear correlation function than iu tliο 5-vear one., where curves corresponding to the same range of graviton mass show considerably greater deviations from the massless case in the 10-year correlation function than in the 5-year one. + As we lewe explained. the massive eraviton reduces the pulsar timing response to CAVs through the correction factor (fe).," As we have explained, the massive graviton reduces the pulsar timing response to GWs through the correction factor $\eta(f_{\rm g})$." + IntUs way. a non-zero eravitou nass reduces the pulsar tine array seusitivitv for detecting a CAV background.," In this way, a non-zero graviton mass reduces the pulsar timing array sensitivity for detecting a GW background." + It is interesting to know how the scusiivity cranges. if the eraviton is massive.," It is interesting to know how the sensitivity changes, if the graviton is massive." + The stochastic CW backeromncd is detected by comparing the measured cross-correlation function e(0;) with the theoretica correlation C(0) calculated in previous section., The stochastic GW background is detected by comparing the measured cross-correlation function $c(\theta_{l})$ with the theoretical correlation $C(\theta)$ calculated in previous section. +" Tere. the measured cross-correlation function (7) is defined by where the (η) aud Ri(f;j) are the timime residuals of pulsar ""a aud ‘hb at time f; aud Nis the unmber of observations."," Here, the measured cross-correlation function $c(\theta_{l})$ is defined by where the $R_{a}(t_{l})$ and $R_{b}(t_{l})$ are the timing residuals of pulsar `a' and `b' at time $t_{l}$ and $N$ is the number of observations." +" The Πέ)=3nul aud Ruf)=ni""Rit) /N.", The $\overline{R_{b}(t_{l})}=\sum_{l=0}^{N-1} R_{b}(t_{l})/N$ and $\overline{R_{a}(t_{l})}=\sum_{l=0}^{N-1} R_{a}(t_{l})/N$ . +" The 0, is the angle between the direction", The $\theta_{m}$ is the angle between the direction + , +the Caussian some restrictions in parameter space were investigatect.,the Gaussian some restrictions in parameter space were investigated. + A κο of 282 hieh quality CCD frames was selected to sample the rauge in FWIIM and span the entire observing epoch ranec., A set of 282 high quality CCD frames was selected to sample the range in FWHM and span the entire observing epoch range. + All these frames have a large απνο of stars. but are not crowded.," All these frames have a large number of stars, but are not crowded." + For al frames the supersampling of the PSF was performed aud various nage profile fit moclels uu ou these. separately for cach CCD frame.," For all frames the supersampling of the PSF was performed and various image profile fit models run on these, separately for each CCD frame." + Results were sunmnuarzed ina table aud supplemented by observing log items., Results were summarized in a table and supplemented by observing log items. + Figure 5 shows the strongest correlation found for the various parameters investigated., Figure 5 shows the strongest correlation found for the various parameters investigated. + The shape paraletcrs (0.3) of the sxiunetrica Lorentz profile model 1 cau be predicted from the profile width of the Gaussian model 1 fit.," The shape parameters $\alpha, \beta$ ) of the symmetrical Lorentz profile model 4 can be predicted from the profile width of the Gaussian model 1 fit." + The profile width here is he radius (about FWIIM/2) with unt bin width (0.2 pixel) of the supersaupled xofile data., The profile width here is the radius (about FWHM/2) with unit bin width (0.2 pixel) of the supersampled profile data. + A linear term is sufficient to predict he 3 paramcter. while for the à paraimcter a secoud order polvuouual was adopted.," A linear term is sufficient to predict the $\beta$ parameter, while for the $\alpha$ parameter a second order polynomial was adopted." + Scaling o the actual pixel size these results were hniud-coded to preset both shape parameters in profile fit model 5. which is otherwise the same as model l.," Scaling to the actual pixel size these results were hard-coded to preset both shape parameters in profile fit model 5, which is otherwise the same as model 4." + This leaves oulv 5 free fit parameters. exactly he same as for the 2-dim Caussian model fiction (see above aud Table 1).," This leaves only 5 free fit parameters, exactly the same as for the 2-dim Gaussian model function (see above and Table 1)." + Tests were performed to determine any possible variatious of the à aud JJ parameters., Tests were performed to determine any possible variations of the $\alpha$ and $\beta$ parameters. + Supersaupled PSFs were generated as a function of 2 nagnitudoe bius. and in another tes the data were split iuto 1 quadrants ou the CCD frames.," Supersampled PSFs were generated as a function of 2 magnitude bins, and in another test the data were split into 4 quadrants on the CCD frames." + Consisteut results for the à aud Jj parameters were found. confirming the relationship with the profile width as before with very stall variation as a function of other selection criteria.," Consistent results for the $\alpha$ and $\beta$ parameters were found, confirming the relationship with the profile width as before with very small variation as a function of other selection criteria." + Tests were performed using elliptical. profile models (6.7.8).," Tests were performed using elliptical profile models (6,7,8)." + No significant advantage was found over circular. sviunetrie models.," No significant advantage was found over circular, symmetric models." + The residuals simular to those shown in Fig., The residuals similar to those shown in Fig. + did not generally decrease. unless the model was exteuded to include asvnuuetmne terms da addition.," 4 did not generally decrease, unless the model was extended to include asymmetric terms in addition." + Asvunuetric profiles were tested extensively ou the supersampled PSF data of the selected fraanes used previously., Asymmetric profiles were tested extensively on the supersampled PSF data of the selected frames used previously. + In particular. model 12 was used to probe parameter space aud look for dependencies.," In particular, model 12 was used to probe parameter space and look for dependencies." + Sinaller residuals than with aux svinnetric profile were found. however different paranieter values are needed for stellar images iu different locations ou the detector as well as for different CCD. frames.," Smaller residuals than with any symmetric profile were found, however different parameter values are needed for stellar images in different locations on the detector as well as for different CCD frames." + Figures 6 and 7 show some examples obtained with test ruus using models 9 aud 11. respectively.," Figures 6 and 7 show some examples obtained with test runs using models 9 and 11, respectively." +" The amplitude. e, (Eq."," The amplitude, $c_{x}$ (Eq." + 6). of the asviuuinetric term along the .-coordinate (right ascension) is approximated by a function linear with air temperature and c itself.," 6), of the asymmetric term along the $x$ -coordinate (right ascension) is approximated by a function linear with air temperature and $x$ itself." + huasge profiles are απλο] at low we and the largest asvuuuctry is seen atf large we., Image profiles are symmetric at low $x$ and the largest asymmetry is seen at large $x$. + Similarly the amplitude of the asviuuetrv along the y-coordinate was estimated as a linear function of temiperature and y., Similarly the amplitude of the asymmetry along the $y$ -coordinate was estimated as a linear function of temperature and $y$. +" Model 19 iuplenmieuts these preset values for ορ. and ey, leaving onlv 6 free paramcters. ποπιο the a.b profile widths aloug or aud gy. respectively (elliptical Loreutz base model)."," Model 13 implements these preset values for $c_{x}$, and $c_{y}$, leaving only 6 free parameters, including the $a, b$ profile widths along $x$ and $y$, respectively (elliptical Lorentz base model)." + Double star models solve simultancously for at least 3 more parameters: the center coordinates. a.y aud amplitude. A of the secondary component.," Double star models solve simultaneously for at least 3 more parameters: the center coordinates, $x,y$ and amplitude, $A$ of the secondary component." + Again. the goal is to minimize the number of free paraüneters as much as possible.," Again, the goal is to minimize the number of free parameters as much as possible." + Thus. for example. a single paraiecter for the background levelis used.," Thus, for example, a single parameter for the background level is used." + Some double star models also assiunie equal widths of the profiles of both components., Some double star models also assume equal widths of the profiles of both components. + Table 1 gives nore details ποσο» 20 to 23)., Table 1 gives more details (models 20 to 23). + Critical for handling of bleuded images is the identification of such cases and the determination of sufficieutly accurate starting parameters for the iterative. nou-Imuear double star profile fit routin," Critical for handling of blended images is the identification of such cases and the determination of sufficiently accurate starting parameters for the iterative, non-linear double star profile fit routine." +" This process can casily ""go astray due to the relatively large nuunber of parameters and the sunall umber of pixels available with the critically salpled UCAC data."," This process can easily “go astray"" due to the relatively large number of parameters and the small number of pixels available with the critically sampled UCAC data." + The adopted criterion for detecting au object on a dark aud Hat corrected CCD frame is to have at least 2 connected pixels above a specified S/N threshold level of 30 above mean backerounud., The adopted criterion for detecting an object on a dark and flat corrected CCD frame is to have at least 2 connected pixels above a specified S/N threshold level of $3 \sigma$ above mean background. + For cach such detected object à ceutroid position (center-of-light. Ist moments) is calculated as well as the 2ud moments.," For each such detected object a centroid position (center-of-light, 1st moments) is calculated as well as the 2nd moments." + The orientation ofthe major axis and nuage elongation. defined as the ratio of major to minor axis are derived frou these moments.," The orientation of the major axis and image elongation, defined as the ratio of major to minor axis are derived from these moments." +" An clongation of 1.0 means a circular. svunmuetre Πμαρο, otherwise the clongation is ereater than 1l."," An elongation of 1.0 means a circular, symmetric image, otherwise the elongation is greater than 1." + Au image profile fit with iuodel, An image profile fit with model +not siguificauthy distorted (as will be shown later). aud that the quadrupole moment of the primary is svuuuctric so that it can be deseribed by a single value.,"not significantly distorted (as will be shown later), and that the quadrupole moment of the primary is symmetric so that it can be described by a single value." + This potential results in a variation of Kepler law. so that the orbital angular frequency (2) aud orbital radius (à) are related by: Since the orbital radius is not directly measurable in gravitational radiation. the orbital angular frequency is the variable of iuterest.," This potential results in a variation of Kepler's law, so that the orbital angular frequency $\omega$ ) and orbital radius $a$ ) are related by: Since the orbital radius is not directly measurable in gravitational radiation, the orbital angular frequency is the variable of interest." + We will show later that the quadrupole correction will be less than SO WO can solve for & as a perturbation about the Keplerian solution. «y=(GALvy," We will show later that the quadrupole correction will be less than, so we can solve for $a$ as a perturbation about the Keplerian solution, $a_0 = \left(GM/\omega^2\right)^{1/3}$." + “We set a=ay(d|δααμ). and find the perturbation to be: We are now iu a position to calculate the gravitational wave strain and the eravitational wave power for a perturbed system," We set $a = a_0\left(1 + \delta a/a_0\right)$, and find the perturbation to be: We are now in a position to calculate the gravitational wave strain and the gravitational wave power for a perturbed system." + Assumiug point masses for the orbital configuration in order to caleulate the total quadrupole moment of the binary system followiug the method of Peters&Mathews(1963).. we fud that the power radiated through gravitational radiation is: The energy radiated by exavitational waves comes fron the orbital euergv of the svsteii and this manitests itself in a eradual shriukiusg of the orbit with in increase in the orbital frequency. kuown as the “chirp.”," Assuming point masses for the orbital configuration in order to calculate the total quadrupole moment of the binary system following the method of \citet{peters63}, we find that the power radiated through gravitational radiation is: The energy radiated by gravitational waves comes from the orbital energy of the system, and this manifests itself in a gradual shrinking of the orbit with an increase in the orbital frequency, known as the “chirp.”" + In the case of J0651. the tidal distortion of the compoucuts provides a torque that spins up the coniponents so that their rotations remain locked to the orbital period.," In the case of J0651, the tidal distortion of the components provides a torque that spins up the components so that their rotations remain locked to the orbital period." + The increase iu the rotational kinetic euergev of the components also comes from the orbital cucrey of the system. aud so the increase in orbital frequency will be lager than that solely due to the ciuission of eravitational radiation.," The increase in the rotational kinetic energy of the components also comes from the orbital energy of the system, and so the increase in orbital frequency will be larger than that solely due to the emission of gravitational radiation." + Tf the torques ou the tidal deformations couple to any internal inodes for cach component. additional energv can be lost to heating of the component stars.," If the torques on the tidal deformations couple to any internal modes for each component, additional energy can be lost to heating of the component stars." + However. the resonance condition for coupling the tidal deformations to these internal modes requires that the driving frequency of the distortion. be comparable to the natural frequency of oue of the modes.," However, the resonance condition for coupling the tidal deformations to these internal modes requires that the driving frequency of the distortion be comparable to the natural frequency of one of the modes." + The driving frequency is given by: where wis the orbital frequency and © is the spin frequency of the white dwarf (Fuller&Lai2011b)., The driving frequency is given by: where $\omega$ is the orbital frequency and $\Omega$ is the spin frequency of the white dwarf \citep{fuller11b}. +. Since the lowest normal modo frequency in a white dwart is on the order of a mlIz (Wiuset&Isepler2008).. aud the orbital frequency is 1.3 uillz. then οxw/2 in order for uw to be comparable to any normal mode frequency.," Since the lowest normal mode frequency in a white dwarf is on the order of a mHz \citep{winget08}, and the orbital frequency is 1.3 mHz, then $\Omega\le\omega/2$ in order for $\omega_{t}$ to be comparable to any normal mode frequency." + This would be clearly visible in the light curve. aud so we cau neglect coupling to the internal modes.," This would be clearly visible in the light curve, and so we can neglect coupling to the internal modes." + Au additional channel for cnerev loss in the svstem may be through heating without any direct coupling to normal nodes., An additional channel for energy loss in the system may be through heating without any direct coupling to normal modes. + Fuller&Lai(2011) have shown that the tidal heating rate can be compared to the tidal πριτή energy rate by: and so if O—w. then the energy loss due to heating can also be neglected.," \citet{fuller11b} have shown that the tidal heating rate can be compared to the tidal spin-up energy rate by: and so if $\Omega\sim\omega$, then the energy loss due to heating can also be neglected." + A more detailed treatineut of the effects of tidal heating on the spin evolution of J0651 and the implications of a non-ucelieible contribution to heating can be found in Piro(2011)., A more detailed treatment of the effects of tidal heating on the spin evolution of J0651 and the implications of a non-negligible contribution to heating can be found in \citet{piro11}. +" Tere. we obtain a lower bouud on the increase in the chirp by only considering the rotational kinetic enerev and ignoring any internal heating due to coupling with internal modes. thus the change in total energv of the svstem is equal to the power radiated through eravitational radiation. so: where J, aud J. are the iuomoeuts of tertia of the primary and the secondary. respectively,"," Here, we obtain a lower bound on the increase in the chirp by only considering the rotational kinetic energy and ignoring any internal heating due to coupling with internal modes, thus the change in total energy of the system is equal to the power radiated through gravitational radiation, so: where $I_p$ and $I_s$ are the moments of inertia of the primary and the secondary, respectively." + LInutroduciug the dimensionless quantities due to the quadrupole correction to the poteutial (A0) aud the spin-up of the colmponcnts (Ay). where: we find where wy is the value of the chirp in the absence of any tidal ceformatious: The chirp can be used in combination with the eravitational wave frequency Gee= 2w) to determine the “chirp mass’. a combination of the reduced mass and the total mass eiven by: MM=TM.," Introducing the dimensionless quantities due to the quadrupole correction to the potential $\Delta_{\rm Q}$ ) and the spin-up of the components $\Delta_{\rm I}$ ), where: we find where $\dot{\omega}_0$ is the value of the chirp in the absence of any tidal deformations: The chirp can be used in combination with the gravitational wave frequency $\omega_{\rm GW} = 2\omega$ ) to determine the “chirp mass”, a combination of the reduced mass and the total mass given by: ${\mathcal M}_c = \mu^{3/5}M^{2/5}$." + TE the corrections due to tidal deformation are not properly accounted for. the calewlated chirp mass (MG) will be ereater than the true chirp mass by: The amplitude of the two polarizations are given by (e.g:Cutler1998). as: where dois the distauce to the binary and / is the inclination.," If the corrections due to tidal deformation are not properly accounted for, the calculated chirp mass $\tilde{\mathcal M}_c$ ) will be greater than the true chirp mass by: The amplitude of the two polarizations are given by \citep[e.g.:][]{cutler98} as: where $d$ is the distance to the binary and $i$ is the inclination." + We note that the fact that J0651 is eclipsing inuplies cos{20.05 and so the «-polarization amplitude is near zero aud the | -polarization amplitude is near its minimuu., We note that the fact that J0651 is eclipsing implies $\cos{i} \simeq 0.05$ and so the $\times$ -polarization amplitude is near zero and the $+$ -polarization amplitude is near its minimum. +Thus the strain amplitude may be as uch as a factor of two lower than the value estimated iu," Thus, the strain amplitude may be as much as a factor of two lower than the value estimated in" +of LRGs means that the monopole redshift space power spectrum is nearly insensitive {ο the redshilt space nonlinearities in (hie halo density. field.,of LRGs means that the monopole redshift space power spectrum is nearly insensitive to the redshift space nonlinearities in the halo density field. +" The upper dotted curve shows {νοDanesXOF,>bz."," The upper dotted curve shows $P_{s,sat}/P_{real,cen}\times b^2_{cen}/b^2_{sat}$." + LThe increaseB inB power inB real space when the satellites. are included. is larger (han (he suppression of power in redshift space bv their FOGs. so Chat Che satellite monopole spectrum has more power at high 7 than the real space central This paper introduced. and tested our algorithin for using the halo density field to estimate (he underlving matter power spectrum.," The increase in power in real space when the satellites are included is larger than the suppression of power in redshift space by their FOGs, so that the satellite monopole spectrum has more power at high $k$ than the real space central This paper introduced and tested our algorithm for using the halo density field to estimate the underlying matter power spectrum." + We found the nonlinear correction between this field and the underlving matter clensity field to be both smaller and more robust to variations in (he effects of satellite galaxies (han both the EOG-conmpressed. density. field used in the analvsis of 2. and (he τούς space monopole power spectrum used in the analvsis of ?.., We found the nonlinear correction between this field and the underlying matter density field to be both smaller and more robust to variations in the effects of satellite galaxies than both the FOG-compressed density field used in the analysis of \citet{tegmark/etal:2006} and the redshift space monopole power spectrum used in the analysis of \citet{percival/etal:2007}. + The parameters of our simulation set were selected to provide accurate two point halo density and velocity statistics ο assure accurate representations of FOG features in our mock catalogs., The parameters of our simulation set were selected to provide accurate two point halo density and velocity statistics to assure accurate representations of FOG features in our mock catalogs. + To our knowledge. this is the first attempt (o study the detailed effects of FOG treatment on the LRG power spectrum.," To our knowledge, this is the first attempt to study the detailed effects of FOG treatment on the LRG power spectrum." + We find that the FOG treatment can allect handpowers even in the linear regime. <0.1.," We find that the FOG treatment can affect bandpowers even in the linear regime, $k \leq 0.1$." + We first examined (he nonlinear matter power spectrum of our 42 simulations., We first examined the nonlinear matter power spectrum of our 42 simulations. + The ratio of the nonlinear to input matter power spectra is well described by a smearing of the DAOs as modeled by ? and à smooth increase in power with & that ean be fit by a third order polynomial out to &=0.4\Mpe| or second order polynomial out to &=0.25hMpe+t., The ratio of the nonlinear to input matter power spectra is well described by a smearing of the BAOs as modeled by \citet{eisenstein/seo/white:2007} and a smooth increase in power with $k$ that can be fit by a third order polynomial out to $k =0.4 \; h \; {\rm Mpc}^{-1}$ or second order polynomial out to $k=0.2 \; h \; {\rm Mpc}^{-1}$. + We detect a substantial deviation [rom the predictions of halolit (?).., We detect a substantial deviation from the predictions of halofit \citep{smith/etal:2003}. + Fie., Fig. + T demonstrates (he main point of this work: satellite galaxies svstematically alter the shape of the power spectrum at k<0.1fhMpe||., \ref{fig:LRGratMIDall} demonstrates the main point of this work: satellite galaxies systematically alter the shape of the power spectrum at $k < 0.1 \; h \; {\rm Mpc}^{-1}$. + Extraction of cosmological inlormation from (he broadband shape of (ae power spectrum is already limited by svstematics (?) which we (and others) suggest can be attributed primarily to differences in the satellite contribution to the powerspectrin., Extraction of cosmological information from the broadband shape of the power spectrum is already limited by systematics \citep{sanchez/cole:2007} which we (and others) suggest can be attributed primarily to differences in the satellite contribution to the powerspectrum. + In (his paper we demonstrate that while the FOG compression scheme in? exacerbates (hese issues ancl requires a large nonlinear correction. ihe FOG features in the censitv field can be used (ο reconstruct the halo density field with high fidelity.," In this paper we demonstrate that while the FOG compression scheme in \citet{tegmark/etal:2006} exacerbates these issues and requires a large nonlinear correction, the FOG features in the density field can be used to reconstruct the halo density field with high fidelity." + The power spectrum of this field deviates from the dark matter power spectrum at the <4% level for κ.<0.2fhMpe land .," The RMS scatter about the best-fitting solution is 0.99 km $^{-1}$, whereas the mean formally-estimated uncertainty on an individual RV measurement is 0.8 km $^{-1}$." +" Lhe uncertainty in the measured radial-velocity. aniplitucde NKDolels aey ο pereentο upper iDlimit"" oft 41 Many foror (heB massz of companionen 5. so if the transits are genuinely caused by a body orbiting the host star. it has to be of planetary rather than stellar mass."," The uncertainty in the measured radial-velocity amplitude yields a 99.9 percent upper limit of 4.1 $_{Jup}$ for the mass of companion $b$, so if the transits are genuinely caused by a body orbiting the host star, it has to be of planetary rather than stellar mass." + However. the possibility. remained. that the transits could be caused by a faint. spatially-unresolyved eclipsing-binarycollNing-Aary companionο," However, the possibility remained that the transits could be caused by a faint, spatially-unresolved eclipsing-binary companion." +i. Grenieretal.(1999). classify LID 15082. as an ;A5niNSEA star. i.e. AS from the Ca11 A line. AS from the IH lines. and I4 from the metal lines.," \citet{grenier99} classify HD 15082 as an A5mA8F4 star, i.e. A5 from the Ca $K$ line, A8 from the H lines, and F4 from the metal lines." + This would suggest that 1D15082 is a classical Am star. with overabundances of iron-group metals anc underabundances of Ca and Se (Wolll1983)., This would suggest that HD15082 is a classical Am star with overabundances of iron-group metals and underabundances of Ca and Sc \citep{wolff83}. +. Stromeren-Crawlord obj? photometry (Hauck&liod1997) vields Zi;=7430 Ix. logg—421 and. via the calibration of Smalley(1993)... while Geneva photometey from. the General. Catalogue of Photometric vields Tipp=TATL£68 WK. log=435+0.07 and AL/L]=0.08£0.09 with the Ixunzlietal.(1997) calibration.," Stromgren-Crawford $uvby\beta$ photometry \citep{hauck97} yields $T_{\rm eff} = 7430$ K, $\log g = 4.21$ and via the calibration of \citet{smalley93}, while Geneva photometry from the General Catalogue of Photometric yields $T_{eff}=7471\pm 63$ K, $\log g = 4.35 \pm 0.07$ and $[M/H] = 0.08\pm 0.09$ with the \citet{kunzli97cal} calibration." + The templatei spectrum.: (laken(1: without the iodine cel) was analysed using. the spectral. synthesis. package (Smith1992:: Smalley.Smith.&Dworetsky 2001))., The template spectrum (taken without the iodine cell) was analysed using the spectral synthesis package \citealt{smith92uclsyn}; \citealt{smalley2001uclsyn}) ). + A reasonable fit to the spectrum is. obtained with Tipp=7400£200 K. logg=43X02 and ΔΕΗ]= 0.4402. in good agreement with the values derived.. from.. photometry.," A reasonable fit to the spectrum is obtained with $T_{eff} = 7400 \pm 200$ K, $\log g = 4.3 \pm 0.2$ and $[M/H] = 0.1 \pm 0.2$ , in good agreement with the values derived from photometry." + NoH obvious. Ani characteristics.2η are visible in this spectrum other than slightly weak IH &Ixlinesiadefiniliveanalysisoflhisissuewillrequircaspectrumwilhmuch TLhesle, No obvious Am characteristics are visible in this spectrum other than slightly weak $H$ $K$ lines; a definitive analysis of this issue will require a spectrum with much higher signal-to-noise. +llarproperlicsaresummarizedinTable 2..During a transit. a planet blocks a small part of the stellar," The stellar properties are summarized in Table \ref{wasp33-params}.During a transit, a planet blocks a small part of the stellar" + (Maroisetal.2008).. (Chauvinetal.2005).. (Schmidtetal.2008) 50.032 «10 (Scharf&Menou," \citep{lafreniere08b, lafreniere10}, \citep{marois08}, \citep{kalas08}, \citep{chauvin05b}, \citep{luhman07}, \citep{schmidt08} $\lesssim$ $<$ \citep{pollack96}. \citep[e.g.][]{vorobyov10}. \citep[e.g.][]{bate03}. \citep{scharf09, veras09}." + 23 ~700 sstar (spectral type B9V) in the Upper Scorpius young association., $\sim$ $\sim$ $\sim$ star (spectral type B9V) in the Upper Scorpius young association. + The separation. of this new companion. places it among the widest known substellar companions to stars and its extreme mass ratio — among the lowest currently known — is comparable to those of directly imaged planets. even though its mass is well above the deutertum-burning threshold.," The separation of this new companion places it among the widest known substellar companions to stars and its extreme mass ratio – among the lowest currently known – is comparable to those of directly imaged planets, even though its mass is well above the deuterium-burning threshold." + Together with the companions mentioned above. this new substellar companion presents a good challenge to all formation scenarios and contributes to blurring the distinction between giant planets and brown dwarfs even further.," Together with the companions mentioned above, this new substellar companion presents a good challenge to all formation scenarios and contributes to blurring the distinction between giant planets and brown dwarfs even further." + The discovery presented in this paper was made as part of a direct imaging search for new stellar and. substellar companions around about 90 stars in the Upper Scorpius region., The discovery presented in this paper was made as part of a direct imaging search for new stellar and substellar companions around about 90 stars in the Upper Scorpius region. + The overall target sample was built by randomly selecting. from the list of Upper Scorpius stars in Carpenteretal. (2006).. an equal number of stars in each of five equal logarithmic mass bins over the range —0.15-5M. the spectral types range from BO to M5.," The overall target sample was built by randomly selecting, from the list of Upper Scorpius stars in \citet{carpenter06}, an equal number of stars in each of five equal logarithmic mass bins over the range $\sim$ 0.15-5; the spectral types range from B0 to M5." + The observations were made using the NIRI camera (Hodappetal.2003). and the ALTAIR adaptive optics system (Herriotetal.2000). at the Gemini. North Telescope., The observations were made using the NIRI camera \citep{hodapp03} and the ALTAIR adaptive optics system \citep{herriot00} at the Gemini North Telescope. + Except for a few faint targets. the target stars themselves were used for wave front sensing.," Except for a few faint targets, the target stars themselves were used for wave front sensing." + The field lens of ALTAIR was used to reduce the effect of anisoplanatism., The field lens of ALTAIR was used to reduce the effect of anisoplanatism. + The first epoch imaging of wwas done on 2008 May 24 in the narrow band filter Keoninuun centered at 2.0975 jim. For sky subtraction we used 5 dither positions corresponding to the corner and center of à square of side10”., The first epoch imaging of was done on 2008 May 24 in the narrow band filter $K_{\rm continuum}$ centered at 2.0975 $\mu$ m. For sky subtraction we used 5 dither positions corresponding to the corner and center of a square of side. + At each position we obtained one co-addition of twelve 0.5 s integrations m fast. high read-noise mode. followed by one single 10 s integration in slow. low read-noise mode.," At each position we obtained one co-addition of twelve 0.5 s integrations in fast, high read-noise mode, followed by one single 10 s integration in slow, low read-noise mode." + At each positionthisprovides an unsaturated image of the target star anda much deeper image of the field that can be readily spatially registered and scaled in flux., At each positionthisprovides an unsaturated image of the target star anda much deeper image of the field that can be readily spatially registered and scaled in flux. + The, The +the mergers of two or more low-mass ALS stars since they are too massive to have been formed from mass transfer.,the mergers of two or more low-mass MS stars since they are too massive to have been formed from mass transfer. + In a few cases. this can also be argued for entire BS populations using photometry.," In a few cases, this can also be argued for entire BS populations using photometry." + For instance. Chen&Han(2008b). performed detailed: binary evolution calculations to study. dynamical stability during mass transfer from an evolving giant star onto a MS companion.," For instance, \citet{chen08b} performed detailed binary evolution calculations to study dynamical stability during mass transfer from an evolving giant star onto a MS companion." + Dased on their results. it can arguably be inferred. that most DSs in NGC ISS are. sulliciently bright that they probably could not have formed from mass transfer alone.," Based on their results, it can arguably be inferred that most BSs in NGC 188 are sufficiently bright that they probably could not have formed from mass transfer alone." + If true. this suggests that most of these BSs must be the products of stellar meregers.," If true, this suggests that most of these BSs must be the products of stellar meregers." + Reearcless of the dominant BS formation mechanism(s) operating in dense star clusters. clvnamical interactions should play at least some role.," Regardless of the dominant BS formation mechanism(s) operating in dense star clusters, dynamical interactions should play at least some role." + For example. even if blue stragelers are formed as a result of binary evolution processes such as mass transfer. the progenitor binaries themselves should have been alfected by at least one civnamical interaction over the course of their lifetime.," For example, even if blue stragglers are formed as a result of binary evolution processes such as mass transfer, the progenitor binaries themselves should have been affected by at least one dynamical interaction over the course of their lifetime." + Numerous scattering experiments have been performed to explore the outcomes of binary-binary and. in particular. sinele-hinary encounters (e.g.McMillan.1986:Sigurdsson&Phinney1993:Freeeauetal. 2004).," Numerous scattering experiments have been performed to explore the outcomes of binary-binary and, in particular, single-binary encounters \citep[e.g.][]{mcmillan86, sigurdsson93, fregeau04}." + Most of the earliest. of these. studies were performed in the point-particle limit. ignoring altogether the often non-neeligible implications of the stars’ finite sizes (ee.Hut.&Bah-call1983:Alikkola 1983).," Most of the earliest of these studies were performed in the point-particle limit, ignoring altogether the often non-negligible implications of the stars' finite sizes \citep[e.g.][]{hut83b, mikkola83}." +. Later. more realistic simulations clearly. demonstrated the importance of taking into account the dissipative cllects of tidal interactions and direct contact between stars (e.g.AleAlillanetal.LOST:Cleary&Alon-aghan 1990).," Later, more realistic simulations clearly demonstrated the importance of taking into account the dissipative effects of tidal interactions and direct contact between stars \citep[e.g.][]{mcmillan87, cleary90}." +. As a result of the increased number of free parameters for the encounters anc the longer integration times required to run the simulations to completion. [ew studies have been conducted: to explore the outcomes of binary-binary encounters or interactions involving triple πμο...," As a result of the increased number of free parameters for the encounters and the longer integration times required to run the simulations to completion, few studies have been conducted to explore the outcomes of binary-binary encounters or interactions involving triple systems." + In this paper. we introduce an analytic technique to constrain the most probable dynamical origin of an observed binary or triple svstem containing one or more merger products.," In this paper, we introduce an analytic technique to constrain the most probable dynamical origin of an observed binary or triple system containing one or more merger products." + Provided the observed system is found within a moderately dense cluster environment. with binary. and/or triple fractions of at least a few percent. the probability is often. high that it. formed from a merger. during an encounter involving one or more binary or triple stars.," Provided the observed system is found within a moderately dense cluster environment with binary and/or triple fractions of at least a few percent, the probability is often high that it formed from a merger during an encounter involving one or more binary or triple stars." + In Section 2.. we present an equation for energy. conservation during individual stellar encounters and outline the process for applving our technique.," In Section \ref{method}, we present an equation for energy conservation during individual stellar encounters and outline the process for applying our technique." + Specifically. we present a step-by-step methodology to esaluate whether or not an assunied dynamical history could have realistically produced. an observed. system. ancl describe how to determine the most probable dynamical formation scenario.," Specifically, we present a step-by-step methodology to evaluate whether or not an assumed dynamical history could have realistically produced an observed system and describe how to determine the most probable dynamical formation scenario." + In. Section. 3... we apply our technique to a few observed binary and: triple systems thought to contain merger products. in. particular a triple svstem that is thought to contain two BSs and the peculiar. period-eccentricity. distribution of the DS. binary population in NGC 158.," In Section \ref{results}, we apply our technique to a few observed binary and triple systems thought to contain merger products, in particular a triple system that is thought to contain two BSs and the peculiar period-eccentricity distribution of the BS binary population in NGC 188." + We discuss the implications of our results in Section 4.., We discuss the implications of our results in Section \ref{discussion}. + In this section. we present à general prescription for conservation of energv during stellar encounters.," In this section, we present a general prescription for conservation of energy during stellar encounters." + We will limit the discussion to tvpical interactions thought to occur in globular and old open clusters. although our technique can be generalized to any choice of parameter space.," We will limit the discussion to typical interactions thought to occur in globular and old open clusters, although our technique can be generalized to any choice of parameter space." + The types of encounters of interest in this paper will predominantIv involve low-mass MS stars with relative velocities at infinity ranging [rom *] km/s to 10 km/s (e.g.Leonard.1989:Sigurdsson&Phinney1993).," The types of encounters of interest in this paper will predominantly involve low-mass MS stars with relative velocities at infinity ranging from $\lesssim 1$ km/s to $\sim 10$ km/s \citep[e.g.][]{leonard89, sigurdsson93}." +. Our technique describes how ο isolate the most probable dynamical formation history for an observed binary or triple containing one or more merger »oducts by providing an estimate for the time required for a given interaction to occur in a realistic cluster environment., Our technique describes how to isolate the most probable dynamical formation history for an observed binary or triple containing one or more merger products by providing an estimate for the time required for a given interaction to occur in a realistic cluster environment. + We begin by assuming that an observed system was ormed directly from a dynamical interaction (or sequence of interactions)., We begin by assuming that an observed system was formed directly from a dynamical interaction (or sequence of interactions). + In this case. the observed: parameters. of he system provide the final distribution of energies for the system resulting [rom the interaction(s).," In this case, the observed parameters of the system provide the final distribution of energies for the system resulting from the interaction(s)." + After choosing an appropriate dynamical scenario (ie. whether the objects involved. in the interaction(s) are single. binary or triple stars). we can work backwards using energy conservation to constrain the initial energies going into the encounter.," After choosing an appropriate dynamical scenario (i.e. whether the objects involved in the interaction(s) are single, binary or triple stars), we can work backwards using energy conservation to constrain the initial energies going into the encounter." + This provides an estimate for the initial orbital energies and jerefore semi-major axes of any binaries or triples going into the interaction., This provides an estimate for the initial orbital energies and therefore semi-major axes of any binaries or triples going into the interaction. + This in turn gives the cross section for collision and hence the time required. for the hypothesized interaction(s) to occur., This in turn gives the cross section for collision and hence the time required for the hypothesized interaction(s) to occur. + Since the formation event must have happened in the ast Tes vers. where res ds the lifetime of the merger wocluct. a formation scenario is likely only if the derived encounter time-scale is shorter than the lifetime of the merger procluct(s).," Since the formation event must have happened in the last $\tau_{BS}$ years, where $\tau_{BS}$ is the lifetime of the merger product, a formation scenario is likely only if the derived encounter time-scale is shorter than the lifetime of the merger product(s)." + Conversely. if the derived: encounter ime-scale ds. longer than the Lifetime of the merger wocuet(s). then that dynamical formation scenario is unlikely to have occurred in the last regs vears.," Conversely, if the derived encounter time-scale is longer than the lifetime of the merger product(s), then that dynamical formation scenario is unlikely to have occurred in the last $\tau_{BS}$ years." + In general. he shorter the derived encounter time-scale. the more likely it is that one or more such encounters actually took place within the lifetime of the merger product(s).," In general, the shorter the derived encounter time-scale, the more likely it is that one or more such encounters actually took place within the lifetime of the merger product(s)." + Finally. if the derived encounter time-scale is longer than res for every possible dynamical formation scenario. then a dynamical origin is altogether unlikely for an observed: multiple star system containing one or more Bss.," Finally, if the derived encounter time-scale is longer than $\tau_{BS}$ for every possible dynamical formation scenario, then a dynamical origin is altogether unlikely for an observed multiple star system containing one or more BSs." + Either that. or the encounter time-scales must have been shorter in the recent past Cor. equivalently. the central cluster density must have been higher).," Either that, or the encounter time-scales must have been shorter in the recent past (or, equivalently, the central cluster density must have been higher)." + Consider an encounter in which at least one of the two bodies involved is a binary or triple star., Consider an encounter in which at least one of the two bodies involved is a binary or triple star. + Phough a complex exchange of energies occurs. energy must. ultimately be conserved in any dynamical interaction.," Though a complex exchange of energies occurs, energy must ultimately be conserved in any dynamical interaction." + The total energy that goes into the encounter must therefore be equal to the, The total energy that goes into the encounter must therefore be equal to the +"between 5«LO""0 and 5«LOM AL. in the random sample.",between $5\times10^{9}$ and $5\times10^{10}$ $M_{\odot}$ in the random sample. + The two data sets are consistent for AMx galaxies., The two data sets are consistent for $M*$ galaxies. + These results are also not inconsistent with quasar absorption line statistics., These results are also not inconsistent with quasar absorption line statistics. +" According to Rao ancl Briges (1993) we should expect z10 cdamped Ly, lines in 1000 sigh1 lines to quasars at z=0.65 εν=0.5).", According to Rao and Briggs (1993) we should expect $\approx$ 10 damped $Ly_{\alpha}$ lines in 1000 sight lines to quasars at z=0.65 $q_{o}=0.5$ ). + Lowe treat our 2506) sight lines as pencil beams (to give a lower limit) to e12006) km s1 then we would expect 14 damped Ly. svstems in. our random sight lines., If we treat our 2500 sight lines as pencil beams (to give a lower limit) to $\approx12000$ $km$ $s^{-1}$ then we would expect 14 damped $Ly_{\alpha}$ systems in our random sight lines. +" As the survey column density lini is =102? atoms em7 an order of magnitudo less than tha required for a camped Ly. system we would. also expec to find approximately 14Ob!""z650 Lyman limi systems (Rao&Briggs1993).", As the survey column density limit is $\approx10^{19}$ $atoms$ $cm^{-2}$ an order of magnitude less than that required for a damped $Ly_{\alpha}$ system we would also expect to find approximately $14\times(10)^{1.67} \approx 650$ Lyman limit systems \cite{rao93}. +. Using the numbers agains redshift’ relation of Streneler-Larrea et al (1995). which includes Lyman limit svstem evolution we come to a similar number (zc300).," Using the numbers against redshift relation of Strengler-Larrea et al (1995), which includes Lyman limit system evolution we come to a similar number $\approx300$ )." + In fact we have found less than we migh have expected. from quasar absorption line statistics., In fact we have found less than we might have expected from quasar absorption line statistics. + This highlights a discrepancy between 2lem ancl qso absorber observations., This highlights a discrepancy between 21cm and qso absorber observations. + Either the column density dependence of the frequeney of occurence of quasar absorption lines is strongly evolving or most of the lines fall below our survey limits., Either the column density dependence of the frequency of occurence of quasar absorption lines is strongly evolving or most of the lines fall below our survey limits. + Typically Lyman limit) absorption lines have measured velocity widths of 10-30. fan os1. but of course the [ine- only passes through a small part of the object.," Typically Lyman limit absorption lines have measured velocity widths of 10-30 $km$ $s^{-1}$, but of course the line-of-sight only passes through a small part of the object." + Lf the Lyman limit svstems are pressure supported then 10-30 kis+ μιαν well be the typical velocity dispersion of the gas ancl we would only detect. those with the largest line widths., If the Lyman limit systems are pressure supported then 10-30 $km$ $s^{-1}$ may well be the typical velocity dispersion of the gas and we would only detect those with the largest line widths. + Hf they are rotationally supported then perhaps we are only detecting those that are sullicicnthy face-on to have high enough central intensities to be detected., If they are rotationally supported then perhaps we are only detecting those that are sufficiently face-on to have high enough central intensities to be detected. + In either case these observations are not inconsistent. with absorption line stuclies of quasars., In either case these observations are not inconsistent with absorption line studies of quasars. + 39 of the S2 detections in the random sample have line widths of 50 Ais+ or loss., 39 of the 82 detections in the random sample have line widths of 50 $km$ $s^{-1}$ or less. + In the same wav as we tried to find corresponding optical and LL detections for the LSB sample we have also tried to identify optical counterparts of the random LU detections., In the same way as we tried to find corresponding optical and HI detections for the LSB sample we have also tried to identify optical counterparts of the random HI detections. + As described before this is very cillicult for distant sources. but for nearby objects we might hope that they are both larger and brighter.," As described before this is very difficult for distant sources, but for nearby objects we might hope that they are both larger and brighter." + Phere is a clear distinction between the optical identification of small (less than 50 Am 5n 7) ancl large velocity. width. objects., There is a clear distinction between the optical identification of small (less than 50 $km$ $s^{-1}$ ) and large velocity width objects. +. Nearby. large velocity. width objects are invariably associated with a bright galaxy. the M* galaxies that we might have expected to detect. (see above). small velocity widths with apparently. blank fields on the DSS.," Nearby large velocity width objects are invariably associated with a bright galaxy, the M* galaxies that we might have expected to detect (see above), small velocity widths with apparently blank fields on the DSS." + Our initial intention was to try and find massive LIL galaxies. like Malin. 1. by looking at the LL properties of a sample of LSB galaxies.," Our initial intention was to try and find massive HI galaxies, like Malin 1, by looking at the HI properties of a sample of LSB galaxies." + No objects as extreme as Malin l. with regard to total HE mass. have been found.," No objects as extreme as Malin 1, with regard to total HI mass, have been found." + We have detected a population of extremely σας rich galaxies., We have detected a population of extremely gas rich galaxies. + These galaxies all have masses within the range of previous well studied galaxies., These galaxies all have masses within the range of previous well studied galaxies. + One striking feature is the very hieh IL mass conipared to stellar mass., One striking feature is the very high HI mass compared to stellar mass. + These galaxies are cither, These galaxies are either +condition ης)=ps after having suitably set the (3.0.5.0d.).,"condition $\rho(r_s) = \rho_s$ after having suitably set the $(\beta, a, b, c, d, \gamma)$." + Unfortunately. the result we get by letting completely unspecified the above parameters. turns out to be extremely complicated involving the exponential of a combination of hypergeometric ancl trigonometric functions.," Unfortunately, the result we get by letting completely unspecified the above parameters turns out to be extremely complicated involving the exponential of a combination of hypergeometric and trigonometric functions." + As a consequence. it is not surprising that also the simplest dynamical quantities (such as the mass profile) are analytically impossible to derive so that I20.(2)) is useless for astrophysical applications.," As a consequence, it is not surprising that also the simplest dynamical quantities (such as the mass profile) are analytically impossible to derive so that \ref{eq: genslope}) ) is useless for astrophysical applications." + We have thus to look for general. but simpler expressions for the logarithmic slope a(r)," We have thus to look for general, but simpler expressions for the logarithmic slope $\alpha(r)$." + Jo this aim. let us observe that most. of the euspy models frequently: used. in. literature may. be. deduced: by integrating Eq(2)) with 6=d0 so that. heron. we will restrict. our. attention to models having the following expression for the logarithmic:: Let us first consider the case eσὲ0.," To this aim, let us observe that most of the cuspy models frequently used in literature may be deduced by integrating \ref{eq: genslope}) ) with $b = d = 0$ so that, heron, we will restrict our attention to models having the following expression for the logarithmic: Let us first consider the case $c \ne 0$." + Without loss of eencrality. we may set e=1 thus:: lf cez1. we may rescale all the results obtained starting from I2q.(4)) bv:: For >=0. Eq.(4)) reducesto: that may be considered as a generalization of a lot of double power law models (see 11 in Appendix A).," Without loss of generality, we may set $c = 1$ thus: If $c \ne 1$, we may rescale all the results obtained starting from \ref{eq: semigenslope}) ) by: For $\gamma = 0$, \ref{eq: semigenslope}) ) reduces: that may be considered as a generalization of a lot of double power law models (see 1 in Appendix A)." + On the other hand. by setting e—=0 and 5#0. weget: For 63.5)=(2.0.17). this reduces to the model recently proposed by Navarro et. al. (," On the other hand, by setting $a = c = 0$ and $\gamma \ne 0$, we: For $(\beta, \gamma) = (2, 0.17)$, this reduces to the model recently proposed by Navarro et al. (" +2004. hereafter. NO4) on the basis of a set ofhieh resolution numerical simulations of dark matter haloes.,"2004, hereafter N04) on the basis of a set ofhigh resolution numerical simulations of dark matter haloes." + Finally. for e=0 and 5z0. we may set a=1 and obtain a fourth class of modelswith: that may be generalized. to the case @z1 by the Following :: Sununarizine. we have defined four set of moclels characterized by logarithmic slopes given by. [5es.(4)). (5)). (6)) and (7)) respectively.," Finally, for $c = 0$ and $\gamma \ne 0$, we may set $a = 1$ and obtain a fourth class of models: that may be generalized to the case $a \ne 1$ by the following : Summarizing, we have defined four set of models characterized by logarithmic slopes given by \ref{eq: semigenslope}) ), \ref{eq: slopeflos}) ), \ref{eq: preslopepolls}) ) and \ref{eq: linearslope}) ) respectively." + We have checked that. while it is possible to ect an analytical expression (at least. in terms of special functions) for the density profile in all four cases. the mass profile is analytical only for mocdels with a(r) given by LEq.(5)) and Eq.(6)).," We have checked that, while it is possible to get an analytical expression (at least, in terms of special functions) for the density profile in all four cases, the mass profile is analytical only for models with $\alpha(r)$ given by \ref{eq: slopeflos}) ) and \ref{eq: preslopepolls}) )." + Our aim here is to study galaxy models that are both general ancl analytically amenable so that they may. be easily. compared. to observational data. (such as those on the rotation curve)., Our aim here is to study galaxy models that are both general and analytically amenable so that they may be easily compared to observational data (such as those on the rotation curve). + That is why only. Eqs.(5)) and Eq.(9)) are worth to be considered in detail., That is why only \ref{eq: slopeflos}) ) and \ref{eq: slopepolls}) ) are worth to be considered in detail. + Moreover. itis easy to show that integrating I20.(5)) gives rise to a class of models that is only a subset of the more general. family of the Zhao models.," Moreover, it is easy to show that integrating \ref{eq: slopeflos}) ) gives rise to a class of models that is only a subset of the more general family of the Zhao models." + This is partially true also for models with a(r) given by Eq.(6)) that may indeed be obtained as a limiting case., This is partially true also for models with $\alpha(r)$ given by \ref{eq: preslopepolls}) ) that may indeed be obtained as a limiting case. + However. the dynamical properties of these particular models have not been investigated. in detail by Zhao.," However, the dynamical properties of these particular models have not been investigated in detail by Zhao." + Moreover. the result of Navarro et al.," Moreover, the result of Navarro et al." + (2004). quoted above is a strong motivation to dedicate much attention to these mocdels which we will refer to in the following as PoLLS Slope) models., \shortcite{Nav04} quoted above is a strong motivation to dedicate much attention to these models which we will refer to in the following as ) models. +" The logarithmic slope of the racial density profile for PoLLS models is given by Eq.(9)) and is characterized by four parameters. namely the scaling radius ry. the characteristic density p, and the two slope parameters (7.5)."," The logarithmic slope of the radial density profile for PoLLS models is given by \ref{eq: slopepolls}) ) and is characterized by four parameters, namely the scaling radius $r_s$, the characteristic density $\rho_s$ and the two slope parameters $(\beta, \gamma)$." + Actually. it is possible to reduce the number of parameters by redefining the scale. radius.," Actually, it is possible to reduce the number of parameters by redefining the scale radius." + To this aim. let us evaluate r£». the radius at which the logarithmic slope equals the value of the isothermal sphere.," To this aim, let us evaluate $r_{-2}$, the radius at which the logarithmic slope equals the value of the isothermal sphere." + By solving a(r2)=2. we easily Replacing Ες with r2. Eq.(9)) may be writtenas: so that the parameter 3 may. indeed. be eliminated.," By solving $\alpha(r_{-2}) = -2$, we easily: Replacing $r_s$ with $r_{-2}$, \ref{eq: slopepolls}) ) may be written: so that the parameter $\beta$ may indeed be eliminated." + It is interesting to look at the asymptotic behaviours of a(r): The logarithmic slope does not diverge in the centre so that the model is not singular which is a nice feature. while o is monotonically decreasing thus suggesting an Like decrease of the mass density.," It is interesting to look at the asymptotic behaviours of $\alpha(r)$: The logarithmic slope does not diverge in the centre so that the model is not singular which is a nice feature, while $\alpha$ is monotonically decreasing thus suggesting an like decrease of the mass density." + Actually. the density profile turns out tobe: so that p remains finite for r) which is what usually. happens in the case of cored nioclels as. c.g.. the non singular isothermal sphere (Binney&‘Tremaine1987:HinshawKrauss 1987).," Actually, the density profile turns out to: so that $\rho$ remains finite for $r \rightarrow 0$, which is what usually happens in the case of cored models as, e.g., the non singular isothermal sphere \cite{BT87,HK87}." +. “Phe exponential decrease of p is coherent with the asvmptotic limit of a for r x., The exponential decrease of $\rho$ is coherent with the asymptotic limit of $\alpha$ for $r \rightarrow \infty$ . + As a general remark. notethat PoLLS mocels. loosely speaking. may he considered. as à one parameter family with 5 as ordering parameter and (72.2) scaling quantities.," As a general remark, notethat PoLLS models, loosely speaking, may be considered as a one parameter family with $\gamma$ as ordering parameter and $(r_{-2}, \rho{-2})$ scaling quantities." + A strongconstraint on comes from the evaluation of the mass ::, A strongconstraint on $\gamma$ comes from the evaluation of the mass : +eive information about the electron density.ni. aud the conrponeut of the magnetic field parallel to the line of sight. By. in the ISM ou scales down to less than ~ 0.5 pe (< Vat an assuaued distance of ~ 500 pe}.,"give information about the electron density,$_{\rm e}$, and the component of the magnetic field parallel to the line of sight, $B_{\|}$, in the ISM on scales down to less than $\sim$ 0.5 pc $<$ $^{\prime}$ at an assumed distance of $\sim$ 500 pc)." + The diffuse nature of the polarized radio background allows (aliuost) colplete spatial mapping of RMs over large areas. provided one has observations at several frequencies.," The diffuse nature of the polarized radio background allows (almost) complete spatial mapping of RMs over large areas, provided one has observations at several frequencies." + This eives a large advantage over RAL determinations through individual objects. like pulsars or oextra-galactie radio SOlCCS.," This gives a large advantage over RM determinations through individual objects, like pulsars or extra-galactic radio sources." + Iu Fig., In Fig. + 1 we show a eray-scale represcutation of the polarized iutensitv in a 5 MIIDIZ wide frequeney baud centered at 319 MITz., \ref{f-pol349} we show a gray-scale representation of the polarized intensity in a 5 MHz wide frequency band centered at 349 MHz. +" The map shows a region of 6.17«97 centered at à=G10"".d53""((161°.)167) at an angular resolution of about [/."," The map shows a region of $6.4^{\circ}\times9^{\circ}$ centered at $\alpha = 6^h10^m, +\delta = 53^{\circ} (\ell = 161^{\circ}, b = 16^{\circ})$ at an angular resolution of about $^{\prime}$." + It is one of 8 frequency bands observed sinmltaueouslv., It is one of 8 frequency bands observed simultaneously. + Three of those have strong interference. but we obtained good data at 311. 319. 355. 360 and 375 AMI.," Three of those have strong interference, but we obtained good data at 341, 349, 355, 360 and 375 MHz." + All 5 naps were made combining mosaics of <5 pointing centres., All 5 maps were made combining mosaics of $\times$ 5 pointing centres. + This vields constant seusitivitv over a large area (see RReuselink et 11997)., This yields constant sensitivity over a large area (see Rengelink et 1997). + The observations were mace with the WSRT in Jaunary and February 1996. larecly at night. aud ionospheric Faraday rotation was therefore well-beliaved.," The observations were made with the WSRT in January and February 1996, largely at night, and ionospheric Faraday rotation was therefore well-behaved." + No corrections were applied., No corrections were applied. + The region iu Fig., The region in Fig. +" Lis rather special because Ti,54 eoes up to LO Ix. and because it contaius laree. aliost lnear structures in 77. Ou attention was drawn to lis field) by the panoramic view of galactic polarization xoduced. in the WENSS sirvey (de Bruyn Wateert 2000)."," \ref{f-pol349} is rather special because $T_{\rm +b,pol}$ goes up to 10 K, and because it contains large, almost linear structures in $P$ Our attention was drawn to this field by the panoramic view of galactic polarization produced in the WENSS survey (de Bruyn Katgert 2000)." +" ILowever. this field is not unique. and there are otherregions with similarly high ρω,"," However, this field is not unique, and there are otherregions with similarly high $T_{\rm b,pol}$." +" Over a very large yaction of the nap the P-signal is quite significant. with a roise στι,2: 0.5 With S/N-ratios of generally more than 3 and geome up to 30. polarization angles are well-defined."," Over a very large fraction of the map the $P$ -signal is quite significant, with a noise $\sigma_{\rm T_b} \approx$ 0.5 With S/N-ratios of generally more than 3 and going up to 30, polarization angles are well-defined." + Note that in this region. the upper lait to structure in Stokes F (total intensity) ou sinall scales (< 30’) is about LAs. or less than of the total 7.," Note that in this region, the upper limit to structure in Stokes $I$ (total intensity) on small scales $\la$ $^{\prime}$ ) is about 1 K, or less than of the total $I$." + There appear to be at least wo distinct commpoucuts mn the polarized intensity distribution., There appear to be at least two distinct components in the polarized intensity distribution. + The first one is a fairly sxiooth. ‘cloudy component. pervading the eutire map. with intensity variations on typical scales of (several) tens of arcuuinutes.," The first one is a fairly smooth, `cloudy' component, pervading the entire map, with intensity variations on typical scales of (several) tens of arcminutes." + Iu addition. there are conspicuous. very πο ης often quite long and wigglyee structures. which we will refer to as canals’. in which the polarized iuteusity is considerably lower than iu the inmediate surroundings.," In addition, there are conspicuous, very narrow and often quite long and wiggly structures, which we will refer to as `canals', in which the polarized intensity is considerably lower than in the immediate surroundings." + Iu this Letter we focus on the nature and implications of the narrow ‘canals’: we will discuss the ‘cloudy component in more detail in another paper (IHaverkoru et 22000)., In this Letter we focus on the nature and implications of the narrow `canals'; we will discuss the `cloudy' component in more detail in another paper (Haverkorn et 2000). + The strong and abrupt decrease of polarized inteusitv in the ‘canals’ suggests that depolarization is responsible., The strong and abrupt decrease of polarized intensity in the `canals' suggests that depolarization is responsible. + There are several uechauisius that can produce depolarization. but the ouly plausible type in this case is beam depolarization.," There are several mechanisms that can produce depolarization, but the only plausible type in this case is beam depolarization." + This occurs when the polarization angle varics sienificautly within ai beam., This occurs when the polarization angle varies significantly within a beam. +" Complete depolarization requires that for each line of sight there isa ""conpanion line of sight within the same beam that has the same polarized intensity but for which the polarization angle differs bv 907.", Complete depolarization requires that for each line of sight there is a `companion' line of sight within the same beam that has the same polarized intensity but for which the polarization angle differs by $^{\circ}$. +" Below we will show that our obscrvations indicate that the polarization angle indeed changes by large amounts across low polarized intensity ""canals. alc close to 005 across the ‘canals’ of lowest P."," Below we will show that our observations indicate that the polarization angle indeed changes by large amounts across low polarized intensity `canals', and close to $^{\circ}$ across the `canals' of lowest $P$." + Depolarization can also νο caused by differential Faraday rotation., Depolarization can also be caused by `differential Faraday rotation'. + This happens when along a liue of sight enüttue aud (Faraday) rotating plasimas cooxist BBurn 1966: Sokoloff ct 11998)., This happens when along a line of sight emitting and (Faraday) rotating plasmas coexist Burn 1966; Sokoloff et 1998). + However. the absence of correlated structure iu Stokes £ aud the high deeree of polarization suggest that this is not a dominating effect.," However, the absence of correlated structure in Stokes $I$ and the high degree of polarization suggest that this is not a dominating effect." + Significant bandwidth depolarization. which occurs when the volarization angle is rotated bv ercatly different inouuts iu different parts of a frequency band could ouly plax a rolle (given our 5 MITz bandwidth) if the RM were ( order SO rad 7. which is not the case in this region near the galactic auti-centre (sce below).," Significant bandwidth depolarization, which occurs when the polarization angle is rotated by greatly different amounts in different parts of a frequency band could only play a rôlle (given our 5 MHz bandwidth) if the RM were of order 80 rad $^{-2}$, which is not the case in this region near the galactic anti-centre (see below)." + Tn Fig., In Fig. + 2 we show the polarization vectors around a few of the deepest ‘canals’. superimposed on erav-scale plots of P. in two frequency bands.," \ref{f-phi349} we show the polarization vectors around a few of the deepest `canals', superimposed on gray-scale plots of $P$ in two frequency bands." + The area shown is indicated in Fie. l.., The area shown is indicated in Fig. \ref{f-pol349}. . +" The polarization vectors on either side of the ""canals are quite close to perpeudicular. demonstrating"," The polarization vectors on either side of the `canals' are quite close to perpendicular, demonstrating" +via the strong ealaxy-ealaxy interactions or the tidal Orces proposed iu eulier studies οολλ,"via the strong galaxy-galaxy interactions or the tidal forces proposed in earlier studies \citep{liu:95,belloni:95,zabludoff:96,caldwell:99}." +" The cluster environment provides a plethora of possible disruptive uechanisnis. οσο, iruannpresure stripping (?). gas conrpressiou (7).. perturbation bv the cluster tidal field C1). and galaxy. harassment (2)..."," The cluster environment provides a plethora of possible disruptive mechanisms, e.g. ram-pressure stripping \citep{gunn:72}, gas compression \citep{dressler:83}, perturbation by the cluster tidal field \citep{byrd:90}, , and galaxy harassment \citep{moore:96}." + Also. the high merecr yaction in MS1051 indicates galaxy-galaxy iicreimg is xossible between members with low relative velocities (?)..," Also, the high merger fraction in MS1054 indicates galaxy-galaxy merging is possible between members with low relative velocities \citep{vandokkum:99}." +" As these cluster E|A are predominantly disk-dominated «ποια», the more disruptive iuteractious would create uorphological signatures (c.g.77) that are visible diving he E|A lifetime (~1.5Cyr:???).."," As these cluster E+A's are predominantly disk-dominated systems, the more disruptive interactions would create morphological signatures \citep[e.g.][]{barnes:92,moore:98} that are visible during the E+A lifetime \citep[$\sim1.5$ +Gyr;][]{couch:87,barger:96,leonardi:96}." + By cxaminine the mnber of E|A’s that are cousidered mergers audor hat have high galaxy residuals. we attempt to isolate which interactions. if auv. are associated with the E|A hase.," By examining the number of E+A's that are considered mergers and/or that have high galaxy residuals, we attempt to isolate which interactions, if any, are associated with the E+A phase." + To ideutifv mergers. we use classifications from ?.. ?.. and ?..," To identify mergers, we use classifications from \citet{vandokkum:99}, \citet{fabricant:00}, and \citet{fabricant:03}." +" We consider high residual galaxies as those having a lüeh deeree of asvuuuetry CA,>0.5:7) and/or total residual (Rr290.1:?)..", We consider high residual galaxies as those having a high degree of asymmetry \citep[$R_A\geq0.5$;][]{schade:95} and/or total residual \citep[$R_T\geq0.1$;][]{tran:01}. + Despite MS105Us high merecr fraction (~1756:?).. only two of the merecrs are cousidered E|Avs: no other E|Αν iu our sanuple are associated with mergers.," Despite MS1054's high merger fraction \citep[$\sim17$\%;][]{vandokkum:99}, only two of the mergers are considered E+A's; no other E+A's in our sample are associated with mergers." + 2 aud D99 also observe a low incidence of niergers associated with cluster ΤίAs., \citet{wirth:94} and D99 also observe a low incidence of mergers associated with cluster E+A's. + We find only about half of the cluster E|Ας iive high galaxy residuals (Fig. 773)., We find only about half of the cluster E+A's have high galaxy residuals (Fig. \ref{RA_bt}) ). + For comparison. the raction of Ligh residual E|A’s is larger than that of carly-vpes (E-SO: «15% }) aud even carly-type spirals (SO/a-Sa: ~ 30%)) but less than that of cluster spirals (~80% }).," For comparison, the fraction of high residual E+A's is larger than that of early-types (E-S0; $<15$ ) and even early-type spirals (S0/a-Sa; $\sim30$ ) but less than that of cluster spirals $\sim80$ )." + The iuuber of cluster E|As with prominent disks combined with only half the sample having high galaxy residuals sugeests mergers are not the primary trigger of the E|A phase in cluster galaxies., The number of cluster E+A's with prominent disks combined with only half the sample having high galaxy residuals suggests mergers are not the primary trigger of the E+A phase in cluster galaxies. + Even though galaxies cau be brightened siguificautlv during the E|A phase (upto~1.5mag:?).. E|Avs in nearby clusters tend to be faint systems (Lm0.7).," Even though galaxies can be brightened significantly during the E+A phase \citep[up to $\sim1.5$ mag;][]{barger:96}, E+A's in nearby clusters tend to be faint systems \citep[$L\lesssim0.4L^{\ast}$." + ILowever. past studies of intermediate redshift clusters fine. EJAs with L>L (?.D99)..," However, past studies of intermediate redshift clusters find E+A's with $L> L^{\ast}$ \citep[D99]{wirth:94}." + Here we determine if the cluster E|AS in this saaple are as luminous as the brightest cluster members. and whether they also cover a wide Inuunosity range.," Here we determine if the cluster E+A's in this sample are as luminous as the brightest cluster members, and whether they also cover a wide luminosity range." + Tn Fig. ??..," In Fig. \ref{BVz_MBz}," + we show the color-magnitude (CAL) distribution of all cluster members and E|A candidates: all cluster members. including the E|ΑΔ candidates. have been corrected for simple passive evolution (822.1).," we show the color-magnitude (CM) distribution of all cluster members and E+A candidates; all cluster members, including the E+A candidates, have been corrected for simple passive evolution 2.1)." +" Iu all three clusters. we find bright E|A's (Mp.Ὁ19.11 Sloeh)): half of the Tl robust E|Às are brighter than Mp, (19.515loghat2=0.583:7)."," In all three clusters, we find bright E+A's $M_{Be}\lesssim-19.1$ ); half of the 14 robust E+A's are brighter than $M_{Be}^{\ast}$ \citep[$-19.5$\logh~at $z=0.83$;][]{hoekstra:00}." + Even more striking are the verv huuinous E|Απ at 2=0.83: these E|A’s are up to a magnitude brighter than their lower redshift counterparts and cover a larecr magnitude rauge., Even more striking are the very luminous E+A's at $z=0.83$: these E+A's are up to a magnitude brighter than their lower redshift counterparts and cover a larger magnitude range. + Note the cluster E|Αν teud to be bluer than tle red sequence., Note the cluster E+A's tend to be bluer than the red sequence. + The E|A huninosity range. particularly at 2=(RSS. only reinforces the conclusion that thev have a heterogeneous parent population.," The E+A luminosity range, particularly at $z=0.83$, only reinforces the conclusion that they have a heterogeneous parent population." + The fact that the brightest E|A’s in this sample are iu our most distaut cluster is additional evidence for down-sizing of the cluster E|A population., The fact that the brightest E+A's in this sample are in our most distant cluster is additional evidence for down-sizing of the cluster E+A population. + Simple models show that curing the post-starburst phase. galaxies can be brightened up to 1.5 magnitudes in the optical (77).," Simple models show that during the post-starburst phase, galaxies can be brightened up to 1.5 magnitudes in the optical \citep{newberry:90,barger:96}." +" For comparison. we place here observational constraints on AASp, using the internal velocity dispersions (0) acquired for 120 1ienibers aud the Fundamental Plane (??.seeAppendix).."," For comparison, we place here observational constraints on $\Delta M_{Be}$ using the internal velocity dispersions $\sigma$ ) acquired for 120 members and the Fundamental Plane \citep[see Appendix]{djorgovski:87,faber:87}." + As demonstrated in eg. ?7.. residuals from the FP cau be expressed as residuals iu the AME ratio.," As demonstrated in e.g. \citet{faber:87}, residuals from the FP can be expressed as residuals in the $M/L$ ratio." + We find the loe(Al/£) residuals of the nine cluster EΑν with measured o range from 0.5 to ~0.3 (Fig. ??7))., We find the $\log(M/L)$ residuals of the nine cluster E+A's with measured $\sigma$ range from $\sim-0.5$ to $\sim0.3$ (Fig. \ref{dlgML_dBV}) ). +" Asstumine E|A’s fade until Alog(M/L)=0. we estimate cluster E|A’s are xiehteued by as much as AASp,~1.25 mag. with a uedian of 0.25 mae."," Assuming E+A's fade until $\Delta\log(M/L)=0$ , we estimate cluster E+A's are brightened by as much as $\Delta M_{Be}\sim1.25$ mag, with a median of $0.25$ mag." + Asstuning the E|A’s at 2=0.83 redden aud. fade by 0.25 imag by +=0.33. the oulv. galaxies iu CL12358 in lis luminosity and color rauge are E-SO’s aud S0/2-Sa's (Fig. ?7)).," Assuming the E+A's at $z=0.83$ redden and fade by $\sim0.25$ mag by $z=0.33$, the only galaxies in CL1358 in this luminosity and color range are E-S0's and S0/a-Sa's (Fig. \ref{BVz_MBz}) )." + This suggests that some of the brightest carly-vpe galaxies in nearby clusters had an E|A pliase in their st., This suggests that some of the brightest early-type galaxies in nearby clusters had an E+A phase in their past. + Having demonstrated that E|Às at ligher redshift cau )o as Iuninous as the brightest cluster 1ienibers rofecud)). we now deteriune if these brighter E|A’s are alsogncssice galaxies. or whether they are simply ow |luinosity/imass embers that are temporarily xiehteued.," Having demonstrated that E+A's at higher redshift can be as luminous as the brightest cluster members \\ref{cmd}) ), we now determine if these brighter E+A's are also galaxies, or whether they are simply low luminosity/mass members that are temporarily brightened." + By determining the E|A ass distribution. we can characterize what the EA progenitors are and also constrain what their descendants at lower redshift cau 0.," By determining the E+A mass distribution, we can characterize what the E+A progenitors are and also constrain what their descendants at lower redshift can be." + To address this issue. diagnostics that are not likely o depend strongly ou redshift are needed. /.c. internal velocity dispersions aud halfleht radii.," To address this issue, diagnostics that are not likely to depend strongly on redshift are needed, $i.e.$ internal velocity dispersions and half-light radii." + While haltlieht radii ( sizes) are imeasured fairly robustly from the WEPC2 imaging (?).. determining internal velocity dispersions (0) at these redshifts is challenging.," While half-light radii $\sim$ sizes) are measured fairly robustly from the WFPC2 imaging \citep{tran:03a}, determining internal velocity dispersions $\sigma$ ) at these redshifts is challenging." + ILowever. we have obtained direct σ measurements for 120 cluster nienibers (277.IK00b)..," However, we have obtained direct $\sigma$ measurements for 120 cluster members \citep[K00b]{kelson:97,vandokkum:98b,kelson:01}." + With the colors. effectiveradii?.. bhuninosifies. aud ineasured dispersions. we estimate velocity dispersions for the rest of the cluster sample using the Fundamental Plane.," With the colors, effective, luminosities, and measured dispersions, we estimate velocity dispersions for the rest of the cluster sample using the Fundamental Plane." + Iu this method. we correct AL/L ratios of later-tvpo nenmibers aud essentially evolve them outo the color-magnitude relation efiued by the earbv-tyvpes: see the Appendix for a detailed xplanation of this method.," In this method, we correct $M/L$ ratios of later-type members and essentially evolve them onto the color-magnitude relation defined by the early-types; see the Appendix for a detailed explanation of this method." + Figure ??7 shows the distribution of iuterual velocity dispersious (1ueasured ancl estimated 0) for cluster members brighter than our magnitude cut., Figure \ref{nsigma_hist} shows the distribution of internal velocity dispersions (measured and estimated $\sigma$ ) for cluster members brighter than our magnitude cut. + The rauge iu velocity dispersion for E|A galaxies increases at higher redshift: E|A’s at 2=0.33 have sinaller velocity dispersious (0.=150 13) than at>=O.58 (σEz 1)) aud :=(483(σ=250 1j," The range in velocity dispersion for E+A galaxies increases at higher redshift: E+A's at $z=0.33$ have smaller velocity dispersions $\sigma\lesssim 150$ ) than at$z=0.58$ $\sigma\lesssim 200$ ) and $z=0.83$$\sigma\lesssim +250$ )." +", The difference between +=0.33 aud 2=0.83 is most striking.", The difference between $z=0.33$ and $z=0.83$ is most striking. + Cousidering the robustuess of the spectroscopic data aud hieh quality of the WEPC2 imaging. auv E|A’s with a>200k ," Considering the robustness of the spectroscopic data and high quality of the WFPC2 imaging, any E+A's with $\sigma>200$ " +center or sky values.,center or sky values. + We refi roughlv with slieht changes in centroid or background value. but usually the differences in the fit parameters are negligible.," We refit roughly with slight changes in centroid or background value, but usually the differences in the fit parameters are negligible." +" Iu Figure 5r, we show the V-band nuages of the 20 clusters with the highest Z2 values.", In Figure \ref{fig:High ChiSq} we show the $V$ -band images of the 20 clusters with the highest $\chi^2_{\nu}$ values. + This Figure demonstrates that poorly fitting clusters are not necessarily extremely poor or mareiual clusters., This Figure demonstrates that poorly fitting clusters are not necessarily extremely poor or marginal clusters. + Ou occasion they have a ucielboring cluster that affects the fit. but iu most cases the appear normal.," On occasion they have a neighboring cluster that affects the fit, but in most cases the appear normal." + This suggests that the ligh AZ. reflects a more basic problem with the fitting profile rather than with the data themselves., This suggests that the high $\chi^2_{\nu}$ reflects a more basic problem with the fitting profile rather than with the data themselves. + However. it is also true that iu such a large sample. oue naturally expects some outliers. particularly because our statistical errors do not include for the possibility backerouud fluctuations.," However, it is also true that in such a large sample, one naturally expects some outliers, particularly because our statistical errors do not include for the possibility background fluctuations." + We test our EFF-anodol ft parzuueters against those derived using superior data preseuted bw Mackey& (2003b)., We test our EFF-model fit parameters against those derived using superior data presented by \cite{mackey03b}. +". They do not present roy for their clusters iud we do uot trust our estimates of the tidal radi. so the one radius we can compare between the two studies is the core radius. r,."," They do not present $r_{90}$ for their clusters and we do not trust our estimates of the tidal radii, so the one radius we can compare between the two studies is the core radius, $r_c$." + There are 16 clusters iu cohbunon with the necessary data between the two sticies and the comparison is preseuted in Figure 6.., There are 16 clusters in common with the necessary data between the two studies and the comparison is presented in Figure \ref{fig:Mackey Core Radius}. + The agreement is ecucrally οσους. although there may be au quication for a slight svstematic bias in the seuse that we would be overestimating r..," The agreement is generally good, although there may be an indication for a slight systematic bias in the sense that we would be overestimating $r_c$." + Such a bias would not he surprising given the superior resolution of theHST daa. although if we cousider oulv those clusters for which our fits cannot be rejected with 2 confidence (those wi low axis error bars) we find weaker evidence for any systematic difference between the two studies.," Such a bias would not be surprising given the superior resolution of the data, although if we consider only those clusters for which our fits cannot be rejected with $>$ confidence (those with x axis error bars) we find weaker evidence for any systematic difference between the two studies." + Both Ning aud EFF profiles fit most of the clusters well., Both King and EFF profiles fit most of the clusters well. + However. as Wall&Zaritsky(2006) found for the," However, as \cite{hz} found for the" +colours versus metallicity.,colours versus metallicity. + We use the Galactic GCs with 13«0.5 mag. following Barmbyetal.20003: where (.Xl) represents any colour. and (LVHam represents the relevant intrinsic. colour obtained based on the reddening values listed in HO3.," We use the Galactic GCs with $E(B-V)<0.5$ mag, following \citet{bh00}: where $(X-Y)$ represents any colour, and $(X-Y)_0$ represents the relevant intrinsic colour obtained based on the reddening values listed in H03." + The reddening ratio can be determined from the Galactic extinction law of Cardellietal. (1989).., The reddening ratio can be determined from the Galactic extinction law of \citet{car89}. . + The fit results with correlation coefficients ο0.5 are listed in Table 3.. We use bi-sector linear fits. as described by Akritas&Bershady(1996).. because we are not only interested in the case where metallicity is used to predict colour. but also in the reverse ease where colour is used to predict metallicity (seede-tailsinBarmbyetal. 2000).," The fit results with correlation coefficients $r>0.8$ are listed in Table \ref{t3.tab}.. We use bi-sector linear fits, as described by \citet{Akritas96}, because we are not only interested in the case where metallicity is used to predict colour, but also in the reverse case where colour is used to predict metallicity \citep[see details in][]{bh00}." +. Next. we construct relationships between (9 parameters and intrinsic colours. to estimate the reddening for clusters without spectroscopic metallicities.," Next, we construct relationships between $Q$ parameters and intrinsic colours, to estimate the reddening for clusters without spectroscopic metallicities." + The 6) parameters are detined as where .X.Y and Z refer to photometric magnitudes in any filter.," The $Q$ parameters are defined as where $X, Y $ and $Z$ refer to photometric magnitudes in any filter." + The relation between an intrinsic colour and the 6) parameter is and The fit results with correlation coefficients r.—0.5 are listed in Table 4.., The relation between an intrinsic colour and the $Q$ parameter is and The fit results with correlation coefficients $r>0.8$ are listed in Table \ref{t4.tab}. + Fig., Fig. + | shows the relationships of a few representative fits between ()-parameter and colour for Galactic GCs. randomly selected from the set of relations included in Table 3.," 1 shows the relationships of a few representative fits between $Q$ -parameter and colour for Galactic GCs, randomly selected from the set of relations included in Table 3." + In this section. we will test the methods adopted to derive the reddening values. using the heavily reddened Galactic GCs with f(bV)>0.5 mag from HO3 (which were not used to construct the calibrations discussed above).," In this section, we will test the methods adopted to derive the reddening values, using the heavily reddened Galactic GCs with $E(B-V)>0.5$ mag from H03 (which were not used to construct the calibrations discussed above)." + Based on Eqs. (, Based on Eqs. ( +1}46) and the correlation parameters from Tables 3. and 4.. we can determine the reddening values for these highly reddened Galactic GCs.,"1)–(6) and the correlation parameters from Tables \ref{t3.tab} and \ref{t4.tab}, we can determine the reddening values for these highly reddened Galactic GCs." + For each of the two methods we averaged all values of /(15 to produce one final value of (D1) per method., For each of the two methods we averaged all values of $E(B-V)$ to produce one final value of $E(B-V)$ per method. + The standard deviation of the average value of οV) is taken as its error for each method., The standard deviation of the average value of $E(B-V)$ is taken as its error for each method. + The result of the comparison is shown in Fig. 2..," The result of the comparison is shown in Fig. \ref{fig2}," + from which we can see that the results are encouraging., from which we can see that the results are encouraging. + The average offset between (D.V) from the Q-parameter method and the HO3 value is 0.01+ mag: for the colour-metallicity method. the average offset is 0.00+0.01 mag.," The average offset between $E(B-V)$ from the $Q$ -parameter method and the H03 value is $0.01\pm0.01$ mag; for the colour-metallicity method, the average offset is $0.00\pm0.01$ mag." + It is clear that the two data sets agree very well., It is clear that the two data sets agree very well. + Barmbyetal...(2000). showed that the M31 and the Milky Way reddening laws are the same within the observational errors., \citet{bh00} showed that the M31 and the Milky Way reddening laws are the same within the observational errors. + Therefore. in this section. we will determine the reddening values for the M31 clusters and cluster candidates based on the calibrated colour-metallicity (C-M) and (Q-parameter relations for the Milky Way from Tables 3. and 4..," Therefore, in this section, we will determine the reddening values for the M31 clusters and cluster candidates based on the calibrated colour–metallicity (C-M) and $Q$ -parameter relations for the Milky Way from Tables \ref{t3.tab} + and \ref{t4.tab}." + The metallicities are from the SMCat and the optical and infrared photometric data are from Galletial. (2004)... as discussed in Sections 2.2 and 2.3.," The metallicities are from the SMCat and the optical and infrared photometric data are from \citet{gall04}, as discussed in Sections 2.2 and 2.3." + For each object. we average all reddening values obtained using the various C-M and C(Q-colour relations. to get one value for the reddening.," For each object, we average all reddening values obtained using the various C-M and $Q$ -colour relations, to get one value for the reddening." + The uncertainty in the reddening value thus derived is caleulated as the standard deviation of the resulting reddening values., The uncertainty in the reddening value thus derived is calculated as the standard deviation of the resulting reddening values. + We determined the reddening values for all M31 GCs and GC candidates with sufficient data. à total of 658 objects.," We determined the reddening values for all M31 GCs and GC candidates with sufficient data, a total of 658 objects." + However. some reddening values are not reliable.such as those based on only one C-M or Q-colour relation. and those with large reddening errors.," However, some reddening values are not reliable,such as those based on only one C-M or $Q$ -colour relation, and those with large reddening errors." +" In order to maintain consistency with Barmby 9000)...we adopted the rules followed by these authors who rejected reddening values ge,6v,/οV)>05 "," In order to maintain consistency with \citet{bh00}, ,we adopted the rules followed by these authors who rejected reddening values $\sigma_{E(B-V)}~/~ \overline{E(B-V)}>0.5$ " +Another independent distance can be determined [rom the position of the red clump.,Another independent distance can be determined from the position of the red clump. + Figure ὃ shows the /-bancl bIuminositv function in the reeion of the red clump., Figure \ref{figRC} shows the $I$ -band luminosity function in the region of the red clump. +" Our best fit to the luminosity finetion was obtained with a Gaussian centered at 7=24.91+0.01 with a width of o,=0.30x0.02.", Our best fit to the luminosity function was obtained with a Gaussian centered at $I = 24.91 \pm 0.01$ with a width of $\sigma_I = 0.30 \pm 0.02$. + Using the semi-empirical red clump calibration described bv Dolphinetal.(2001a).. we caleulate an absolute magnitude of M;=—0.67£0.15 Lor Sexians A: this produces a true distance modulus of jiu=25.5114d£0.15.," Using the semi-empirical red clump calibration described by \citet{dol01a}, we calculate an absolute magnitude of $M_I = -0.67 \pm 0.15$ for Sextans A; this produces a true distance modulus of $\mu_0 = 25.51 \pm 0.15$." + Combining our three distance determinations. we calculate the true distance modulus to Sextans A to be ji=25.6140.07. corresponding to a distance of d=1.3240.04 \Ipe.," Combining our three distance determinations, we calculate the true distance modulus to Sextans A to be $\mu_0 = 25.61 \pm 0.07$, corresponding to a distance of $d = 1.32 \pm 0.04$ Mpc." + We note that this distance is significantly closer (han the value of 1.44 Alpe assumed in Paper I (adopted [roii Dolin-Palimer et al., We note that this distance is significantly closer than the value of 1.44 Mpc assumed in Paper I (adopted from Dohm-Palmer et al. + 1997)., 1997). + We also note that. while we do not explicitly include calibration uncertainties. these are ~0.02 magnitudes and thus do not add to our reported uncertainties.," We also note that, while we do not explicitly include calibration uncertainties, these are $\sim 0.02$ magnitudes and thus do not add to our reported uncertainties." +" Our distance is consistent with (the Piotto.Capaccioli.&Pellegrini(1994) Cepheid distance of (ju,=25.712 0.20). but is inconsistent at the la level with the Sakai.Madore. Cepheicl distance (ja)=25.85+ 0.15)."," Our distance is consistent with the \citet{pio94} Cepheid distance of $\mu_0 = 25.71 \pm 0.20$ ), but is inconsistent at the $1 \sigma$ level with the \citet{sak96} Cepheid distance $\mu_0 = 25.85 \pm 0.15$ )." + We note. however. that the Sakai.Freedman(1996) Cepheid distance is based on sinele-epoch photometry ancl {hus is more uncertain than is indicated by their error bars.," We note, however, that the \citet{sak96} Cepheid distance is based on single-epoch photometry and thus is more uncertain than is indicated by their error bars." + In addition. Sakai.\laclore.(1996) present an RGB tip distance modulus of ji=25.74+0.13. which is consistent. with our distance at the lo level.," In addition, \citet{sak96} present an RGB tip distance modulus of $\mu_0 = 25.74 \pm 0.13$, which is consistent with our distance at the $1 \sigma$ level." + Distance measurement using Cepheids tvpicallv rely on longer-period Cepheids with GP>10 davs)., Distance measurement using Cepheids typically rely on longer-period Cepheids with $P > 10$ days). + As we have observed in Sextans A and previously in Leo A. large munbers of short-period Cepheids are present in low-metallicily stu-Iorming galaxies. due to the passage of the BlleB sequence through the instabilitw strip at fainter magnitudes 2002).," As we have observed in Sextans A and previously in Leo A, large numbers of short-period Cepheids are present in low-metallicity star-forming galaxies, due to the passage of the BHeB sequence through the instability strip at fainter magnitudes \citep{dol02}." +. This allows for the determination of the distance using 82 Cepheids. which is potentially much more accurate than that using the 5 longer-period Cepheids of (1982).," This allows for the determination of the distance using 82 Cepheids, which is potentially much more accurate than that using the 5 longer-period Cepheids of \citet{san82}." +. ILowever. one must first examine (he question of whether or not these objects serve as reliable standard candles.," However, one must first examine the question of whether or not these objects serve as reliable standard candles." + To address (his question. we present distance moduli to five nearby galaxies in Table 3. as determined by a varietv of distance indicators.," To address this question, we present distance moduli to five nearby galaxies in Table \ref{tabcompare} as determined by a variety of distance indicators." + Because of its relative insensitivitv (o age and metallicitv. we will adopt the RGB tip distance as (he comparison standard.," Because of its relative insensitivity to age and metallicity, we will adopt the RGB tip distance as the comparison standard." + Comparing the short-period Cepheid distances with the RGB tip distances. we see no significant svstematic," Comparing the short-period Cepheid distances with the RGB tip distances, we see no significant systematic" +Clusters of galaxies are the largest eravitationally collapsed objects in the universe and their internal dynamics ancl morphologies provide useful cosmological information.,Clusters of galaxies are the largest gravitationally collapsed objects in the universe and their internal dynamics and morphologies provide useful cosmological information. + In recent vears many studies of cluster shapes and orientations have showed that they are strongly elongated. maybe more so than elliptical galaxies. and they tend to point towards their neighbours (Carter Aletcalfe 1980: Bingelli: 1982: Di Fazio Flin 1988: Plionis. Barrow brenk 1991: De 'Theije. IXatgert van Ixampen 1995).," In recent years many studies of cluster shapes and orientations have showed that they are strongly elongated, maybe more so than elliptical galaxies, and they tend to point towards their neighbours (Carter Metcalfe 1980; Bingelli 1982; Di Fazio Flin 1988; Plionis, Barrow Frenk 1991; De Theije, Katgert van Kampen 1995)." + Plionis. Barrow anc Frenk (1991) (hereafter. PDBE) have computed. ellipticities and major axis orientations for the largest up to date sample of about 400 Abell clusters ancl found that their apparen shapes are consistent with those expected from a population of prolate spheroids.," Plionis, Barrow and Frenk (1991) (hereafter PBF) have computed ellipticities and major axis orientations for the largest up to date sample of about 400 Abell clusters and found that their apparent shapes are consistent with those expected from a population of prolate spheroids." + Support to the prolate spheroida case was presented recently by Cooray (1999) analysing a sample of 25 Einstein X-ray elusters of Mohr ct al. (, Support to the prolate spheroidal case was presented recently by Cooray (1999) analysing a sample of 25 Einstein X-ray clusters of Mohr et al. ( +1995).,1995). + Struble and Ftaclas (1994) analysed a compilation of 344 Abell cluster cllipticities and. found. that rich clusters are intrinsically more spherical than poorer clusters., Struble and Ftaclas (1994) analysed a compilation of 344 Abell cluster ellipticities and found that rich clusters are intrinsically more spherical than poorer clusters. + In the same framework MeMilaa et., In the same framework McMilan et. + al (1989). studied: the ellipticitios and orientations of 49 Abell clusters using Einstein. X-ray data to trace the hot eas. ancl also found that the eluster potential is quite Hat although less so than that found in optical studies.," al (1989) studied the ellipticities and orientations of 49 Abell clusters using Einstein X-ray data to trace the hot gas, and also found that the cluster potential is quite flat although less so than that found in optical studies." + Buote Canizares (1996) analyzed LOSAT PSPC images for 4 Abell clusters (including Coma) and. assuming hydrostatic equilibrium.they. found. cllipticities of order ον20.40.0.55 (see also Canizares Buote 1997).," Buote Canizares (1996) analyzed ROSAT PSPC images for 4 Abell clusters (including Coma) and, assuming hydrostatic equilibrium,they found ellipticities of order $\epsilon_{mass}\simeq 0.40-0.55$ (see also Canizares Buote 1997)." +" ""Theoretical expectations regarding cluster shape arc morphology have been investigated. via N-body simulations. which show that the intrinsic shapes of simulated: clusters are rather triaxial with an almost uniform cistribution of shapes between prolate ancl oblate spheroids (cf"," Theoretical expectations regarding cluster shape and morphology have been investigated via N-body simulations, which show that the intrinsic shapes of simulated clusters are rather triaxial with an almost uniform distribution of shapes between prolate and oblate spheroids (cf." + Frenk e al., Frenk et al. + 1988: Efstathiou et al., 1988; Efstathiou et al. + 1988)., 1988). + Detailed analvsis of cluster morphological parameters and substructure. utilising the concept of power ratios (ef," Detailed analysis of cluster morphological parameters and substructure, utilising the concept of power ratios (cf." +" Boute ""Tsai 1994). can be used to constrain dillerent cosmological models (c£."," Boute Tsai 1994), can be used to constrain different cosmological models (cf." + Thomas et al 1998: Valdarnini. Ghizzardi Bonometto 1999).," Thomas et al 1998; Valdarnini, Ghizzardi Bonometto 1999)." + lt ds obvious wt information about the intrinsic shape of a cluster is lost when projected. on the plane of the sky., It is obvious that information about the intrinsic shape of a cluster is lost when projected on the plane of the sky. + Many. clillerent studies have attempted: to recover the distribution of intrinsic cluster shapes from, Many different studies have attempted to recover the distribution of intrinsic cluster shapes from + The dynamical nature of the solar-surface layers. manifested for instance in granules and sunspots. has been known for a long time.," The dynamical nature of the solar-surface layers, manifested for instance in granules and sunspots, has been known for a long time." + With every improvement of ground-based or spaceborne instruments the complexity of the observed processes increased., With every improvement of ground-based or spaceborne instruments the complexity of the observed processes increased. + Red supergiant (RSG) stars are among the largest stars in. the universe anc the brightest in. the optical and near infrared., Red supergiant (RSG) stars are among the largest stars in the universe and the brightest in the optical and near infrared. + They are massive stars with masses between roughly 10 and 25 M. with effective temperatures ranging from 34450 to KK. lummosities of 0000 to 3000000L... and radii up to 5500R (2)..," They are massive stars with masses between roughly 10 and 25 $M_{\odot}$ with effective temperatures ranging from 450 to K, luminosities of 000 to $L_\odot$, and radii up to $R_\odot$ \citep{2005ApJ...628..973L}." + These stars exhibit variations in integrated brightness. surface features. and the depths. shapes. and Doppler shifts of spectral lines: as a consequence. stellar parameters and abundances are difficult to determine.," These stars exhibit variations in integrated brightness, surface features, and the depths, shapes, and Doppler shifts of spectral lines; as a consequence, stellar parameters and abundances are difficult to determine." +" Progress has been done using ID hydrostatic models revising the 7,4-scale and reddening both at solar and Magellanic Clouds metallicities (2222?) but problems still remain. e.g. the blue-UV excess that may be due to scattering by circumstellar dust or to an insufficiency in the models. and the visual-infrared effective temperature mismatch (?).."," Progress has been done using 1D hydrostatic models revising the $T_{\rm eff}$ -scale and reddening both at solar and Magellanic Clouds metallicities \citep{2005ApJ...628..973L,2006ApJ...645.1102L,2007ApJ...660..301M,2007ApJ...667..202L,2010NewAR..54....1L} but problems still remain, e.g. the blue-UV excess that may be due to scattering by circumstellar dust or to an insufficiency in the models, and the visual-infrared effective temperature mismatch \citep{2006ApJ...645.1102L}." + Finally. RSGs eject massive amounts of mass back to the interstellar medium with an unidentified process that may be related to acoustic Waves and radiation pressure on molecules (?).. or to the dissipation of Alfvénn waves from magnetic field. recently discovered on RSGs (??).. as early suggested by ??2.. ," Finally, RSGs eject massive amounts of mass back to the interstellar medium with an unidentified process that may be related to acoustic waves and radiation pressure on molecules \citep{2007A&A...469..671J}, or to the dissipation of Alfvénn waves from magnetic field, recently discovered on RSGs \citep{2010A&A...516L...2A,2010MNRAS.408.2290G}, as early suggested by \cite{1984ApJ...284..238H, 1989A&A...209..198P, 1997A&A...325..709C}." +The dynamical convective pattern of RSGs 1s then crucial for the understanding of the physics of these stars that contribute extensively to the chemical enrichment of the Galaxy., The dynamical convective pattern of RSGs is then crucial for the understanding of the physics of these stars that contribute extensively to the chemical enrichment of the Galaxy. + There is a number of multiwavelength imaging examples of RSGs (e.g. « Ori) because of their high luminosity and large angular diameter., There is a number of multiwavelength imaging examples of RSGs (e.g. $\alpha$ Ori) because of their high luminosity and large angular diameter. + Concerning a Ori. ?????? detected the presence of time-variable inhomogeneities on his surface with WHT and COAST; ? reported a reconstructed image in the H band with two large spots: ?? attributed motions detected by VLTI/AMBER observations to convection: ? resolved « Ort using diffraction-limited adaptive optics in the near-infrared and found an asymmetric envelope around the star with a bright plume extending in the southwestern region.," Concerning $\alpha$ Ori, \cite{1990MNRAS.245P...7B, 1992MNRAS.257..369W, 1997MNRAS.285..529T, + 1997MNRAS.291..819W, 2000MNRAS.315..635Y, 2004young} detected the presence of time-variable inhomogeneities on his surface with WHT and COAST; \cite{2009A&A...508..923H} reported a reconstructed image in the H band with two large spots; \cite{2009A&A...503..183O,2011A&A...529A.163O} attributed motions detected by VLTI/AMBER observations to convection; \cite{2009A&A...504..115K} resolved $\alpha$ Ori using diffraction-limited adaptive optics in the near-infrared and found an asymmetric envelope around the star with a bright plume extending in the southwestern region." + ? the presence of bright spots on the surface of the supergiants a Her and a SCO using WHT and ? on VX Sgr using VLTI/AMBER., \cite{1997MNRAS.285..529T} the presence of bright spots on the surface of the supergiants $\alpha$ Her and $\alpha$ SCO using WHT and \cite{2010A&A...511A..51C} on VX Sgr using VLTI/AMBER. + The effects of convection and non-radial waves can be represented by numerical multi-dimenstonal time-dependent radiation hydrodynamics (RHD) simulations with realistic input physics., The effects of convection and non-radial waves can be represented by numerical multi-dimensional time-dependent radiation hydrodynamics (RHD) simulations with realistic input physics. + Three-dimensional radiative hydrodynamics simulations are no longer restricted to the Sun (forare-viewontheSunmodelssee?) but cover a substantial portion of the Hertzsprung-Russell diagram (2)..., Three-dimensional radiative hydrodynamics simulations are no longer restricted to the Sun \citep[for a review on the Sun models see][]{2009LRSP....6....2N} but cover a substantial portion of the Hertzsprung-Russell diagram \citep{2009MmSAI..80..711L}. + Moreover. they have been already extensively employed to study the effects of photospheric inhomogeneities and velocity fields on the formation of spectral lines and on interferometric observables in a number of cases. including the Sun. dwarfs and subgiants (e.g.222929)22222?).. red giants (e.g.2229)????).. asymptotic giant branch stars (2).. and red supergiant stars (???).. ," Moreover, they have been already extensively employed to study the effects of photospheric inhomogeneities and velocity fields on the formation of spectral lines and on interferometric observables in a number of cases, including the Sun, dwarfs and subgiants \citep[e.g. ][]{1999A&A...346L..17A, 2001A&A...372..601A, + 2009ARA&A..47..481A,2010SoPh..tmp...66C,2010A&A...513A..72B,2010A&A...522A..26S}, red giants \citep[e.g.][]{2010A&A...524A..93C,2007A&A...469..687C, + 2009MmSAI..80..719C,2009A&A...508.1429W}, asymptotic giant branch stars \citep{2010A&A...511A..51C}, and red supergiant stars \citep{2009A&A...506.1351C, 2010A&A...515A..12C,2011A&A...528A.120C}." +In particular. the presence and the characterization of the size of convective cells on a Ori has been showed by ? by comparing a large set of interferometric observations ranging from the optical to the infrared wavelengths.," In particular, the presence and the characterization of the size of convective cells on $\alpha$ Ori has been showed by \cite{2010A&A...515A..12C} by comparing a large set of interferometric observations ranging from the optical to the infrared wavelengths." + This paper is the fourth in a series aimed to present the numerical simulations of red supergiant stars with CO? BOLD and to introduce the new generation of RSG simulations with a more sophisticated opacity treatment., This paper is the fourth in a series aimed to present the numerical simulations of red supergiant stars with $^5$ BOLD and to introduce the new generation of RSG simulations with a more sophisticated opacity treatment. + Such simulations are of great importance for an accurate quantitative analysis of observed data., Such simulations are of great importance for an accurate quantitative analysis of observed data. + The code solves the coupled equations of compressible hydrodynamics and non-local radiation transport, The code solves the coupled equations of compressible hydrodynamics and non-local radiation transport +SiO outflows.,SiO outflows. + In particular the southeast elongated feature in HCO — coincides well with the jet-like SE SiO outflow., In particular the southeast elongated feature in $^{13}$ $^+$ coincides well with the jet-like SE SiO outflow. + For 123151. the major and minor peaks in the integrated ILCO enission correlates well with the SiO clumps.," For I23151, the major and minor peaks in the integrated $^{13}$ $^+$ emission correlates well with the SiO clumps." + The quasi-parabolic shaped SiO outflow. also has counterparts in 00ο |. especially in the -54.0 ! channel and integrated emission.," The quasi-parabolic shaped SiO outflow also has counterparts in $^{13}$ $^+$, especially in the -54.0 $^{-1}$ channel and integrated emission." + The correlation between the integrated. IMCO — emission and SiO emission [or the two sources suggests that the IL gas may be influenced by the outflows., The correlation between the integrated $^{13}$ $^+$ emission and SiO emission for the two sources suggests that the $^{13}$ $^+$ gas may be influenced by the outflows. + Adopting an abundance of 1x10.? (vanDishoeckοἱal.1993) anda C to MC ratio of 67 1990).. we can estimate the gas masses of the 0ο — condensations with the similar method used in the estimation of the gas masses in the SiO outflows.," Adopting an ${^+}$ abundance of $1\times10^{-9}$ \citep{Dishoeck93} and a C to $^{13}$ C ratio of 67 \citep{Langer90}, we can estimate the gas masses of the $^{13}$ $^+$ condensations with the similar method used in the estimation of the gas masses in the SiO outflows." + The results (Algens.) are listed in Table 1.., The results $M_{dense}$ ) are listed in Table \ref{table1}. + Note that the masses derived from the 0Ο — emission are much larger than the core masses derived from the mm continuum., Note that the masses derived from the $^{13}$ $^+$ emission are much larger than the core masses derived from the mm continuum. + The integrated 10Ο — emission is much more extended (han the interferometric mm conünuum for both sources., The integrated $^{13}$ $^+$ emission is much more extended than the interferometric mm continuum for both sources. + Dased on the single-dish 1.2 mm continumin observations. Beutheretal.(2002b) derive the masses ο210041. and 2280007. respectively for (he near and far distances for 118264 and 7620... [or I23151. which are consistent with the the masses of the ICO — condensations here.," Based on the single-dish 1.2 mm continumm observations, \citet{Beuther02b} derive the masses ${\sim}2100M_{\odot}$ and ${\sim}28000M_{\odot}$ respectively for the near and far distances for I18264 and ${\sim}620M_{\odot}$ for I23151, which are consistent with the the masses of the $^{13}$ $^+$ condensations here." + Thus (he interferometric mim dust continuum probably (races the densest cores. filtering out most emission and hence vielding less masses. whereas the ICO traces lower density gas and may even be slightly optically thick.," Thus the interferometric mm dust continuum probably traces the densest cores, filtering out most emission and hence yielding less masses, whereas the $^{13}$ $^+$ traces lower density gas and may even be slightly optically thick." + In addition. the ILCO — emission is obviously affected by the outflows and and ΠΟ can be enhanced by shocks.," In addition, the $^{13}$ $^+$ emission is obviously affected by the outflows and $^+$ and $^{13}$ $^+$ can be enhanced by shocks." + Toward the bipolar molecular outflow of L1157. Bachiller&Gutiérrez(1997) detect the abundance of to be enhanced by a [actor of 26—30.," Toward the bipolar molecular outflow of L1157, \citet{Bachiller97} detect the abundance of $^+$ to be enhanced by a factor of $26 - 30$." + Jorgensenοἱal.(2004) reveal an — abundance of 2.9x10? in the NGC 1333 outflow region., \citet{Jorgensen04} reveal an $^+$ abundance of $2.9{\times}10^{-9}$ in the NGC 1333 outflow region. + Girartοἱal.(2005) derive an averaged abundance of 3.2x10.? over the core located ahead of ΠΠ., \citet{Girart05} derive an averaged $^+$ abundance of $3.2{\times}10^{-9}$ over the core located ahead of HH2. + Thus the abundance of can be enhanced by a [actor of ~3—30.," Thus the abundance of $^+$ can be enhanced by a factor of ${\sim}\,3-30$." + Assuming the UMCO to ratio to be constant. the abundance of ICO may be underestimated. and consequently the mass is overestimated by a [factor of ~3—30.," Assuming the $^{13}$ $^+$ to $^+$ ratio to be constant, the abundance of $^{13}$ $^+$ may be underestimated, and consequently the mass is overestimated by a factor of ${\sim}\,3-30$." + Sridharanetal.(2002) detected the NIL4CJ.Ix)2(1.1). (2.2) inversion lines toward 118264 with the Effelsberg 100m telescope.," \citet{Sridharan02} detected the $_3$ (J,K)=(1,1), (2,2) inversion lines toward I18264 with the Effelsberg 100m telescope." +" The NIL, emission toward 123151 was also detected with the Effelshere telescope. but is about an order of magnitude weaker than for 115264 (Deuther. priv com.)."," The $_3$ emission toward I23151 was also detected with the Effelsberg telescope, but is about an order of magnitude weaker than for I18264 (Beuther, priv com.)." + With the VLA we observed the NIL;(1.1) ancl (2.2) lines toward the {wo regions and detected the NIL;CI.1) and (2.2) emission only in [18264.," With the VLA we observed the $_3$ (1,1) and (2,2) lines toward the two regions and detected the $_3$ (1,1) and (2,2) emission only in I18264." +" We derive the optical depth. 7(1.1.:5) lor the main component of the NII4(I.1) line and. the rotational temperature 7,,(2.2:1.1) (Ilo&Townes1983). at three positions as denoted in Fig."," We derive the optical depth $\tau(1,1,m)$ for the main component of the $_3$ (1,1) line and the rotational temperature $T_{rot}$ (2,2:1,1) \citep{Ho83} at three positions as denoted in Fig." + Saa., \ref{nh3}a a. +"INTEGRAL//IBIS has also detected and classified a large number of persistent sources such as AGN, which obtain their peak significance after mosaicking many individual ScWs.","/IBIS has also detected and classified a large number of persistent sources such as AGN, which obtain their peak significance after mosaicking many individual ScWs." +" In this case it is not always easy to establish how many pointings were used where the source candidate was in the FCFOV or the PCFOV, and so it is not trivial to establish which PSLA to use."," In this case it is not always easy to establish how many pointings were used where the source candidate was in the FCFOV or the PCFOV, and so it is not trivial to establish which PSLA to use." + In these cases we suggest a conservative approach and use the PCFOV PSLA estimate., In these cases we suggest a conservative approach and use the PCFOV PSLA estimate. +" We have also carried out the same analysis for data reduced with and older version of the analysis software, OSA 5.0, and find after fitting the 9096 PSLA, that an improvement on the estimated error circle size had already been achieved with OSA 5.0 compared to the ? result based on OSA 3.0; however with the latest version of the software release, OSA 7.0, the improvement is even more evident."," We have also carried out the same analysis for data reduced with and older version of the analysis software, OSA 5.0, and find after fitting the $90\%$ PSLA, that an improvement on the estimated error circle size had already been achieved with OSA 5.0 compared to the \cite{gros} result based on OSA 3.0; however with the latest version of the software release, OSA 7.0, the improvement is even more evident." +" This result also indicates that a re-analysis of archival data with the latest software will often yield far better source positions, and may allow observers to distinguish between multiple candidate counterparts far better than previously."," This result also indicates that a re-analysis of archival data with the latest software will often yield far better source positions, and may allow observers to distinguish between multiple candidate counterparts far better than previously." + This work has shown that the IBIS/ISGRI PSLA (ie the size of the error circle) has dramatically improved since the last study of ? ?)), This work has shown that the IBIS/ISGRI PSLA (ie the size of the error circle) has dramatically improved since the last study of \cite{gros} \citealt{cat4}) + This work has shown that the IBIS/ISGRI PSLA (ie the size of the error circle) has dramatically improved since the last study of ? ?))., This work has shown that the IBIS/ISGRI PSLA (ie the size of the error circle) has dramatically improved since the last study of \cite{gros} \citealt{cat4}) +One use of dEBs is to probe chemical peculiarities. such as the Am phenomenon in stars (Titus&Morgan1940:Conti1970). by measuring their physical properties to high accuracy.,"One use of dEBs is to probe chemical peculiarities, such as the Am phenomenon in stars \citep{TitusMorgan40apj,Conti70pasp} by measuring their physical properties to high accuracy." + Am stars are Asstars which show photospherie abundance anomalies thought to be caused by radiative diffusion and gravitational settling (Michaud1970:Turcotteetal.2000:Talon 2006)..," Am stars are stars which show photospheric abundance anomalies thought to be caused by radiative diffusion and gravitational settling \citep{,Michaud70apj,Turcotte+00aa,Talon++06apj}." + These effects are able to operate in the radiative atmospheres possessed by sstars with rotational velocities slower than roughly citepAbtLevySSapjs.Budaj96aa.Budaj97au..," These effects are able to operate in the radiative atmospheres possessed by stars with rotational velocities slower than roughly \\citep{AbtLevy85apjs,Budaj96aa,Budaj97aa}." + Am stars are preferentially found in short-period binaries where tidal effects have been able to slow their rotation (Abt1961.1965:&Prieur 2007)..," Am stars are preferentially found in short-period binaries where tidal effects have been able to slow their rotation \citep{Abt61apjs,Abt65apjs,CarquillatPrieur07mn}." + This in turn means that Am stars are strongly represented among the well-studieddEBs!.. such as AAur (Southworthetal. 2007).. LLac (Torresetal.1999).. HHer 1984). CCas (Lacyetal.2004... CCam (Lacyetal.20023. and RRLLyn (Tomkin&Fekel2006)...," This in turn means that Am stars are strongly represented among the well-studied, such as $\beta$ Aur \citep{Me++07aa}, , Lac \citep{Torres+99aj}, Her \citep{Popper84aj2}, Cas \citep{Lacy++04aj}, Cam \citep{Lacy+02aj} and Lyn \citep{TomkinFekel06aj}." + The prevailing viewpoint from these studies is that the Am phenomenon is a surface disease — the properties of Am stars can in general be matched by theoretical predictions just as well as those of normal sstars — although a high bulk metal abundance by mass) was found for the component stars of AAurigae by Southworthetal. (20056)., The prevailing viewpoint from these studies is that the Am phenomenon is a surface disease – the properties of Am stars can in general be matched by theoretical predictions just as well as those of normal stars – although a high bulk metal abundance by mass) was found for the component stars of Aurigae by \citet{Me+05mn}. + CCeti is a dEB containing Am stars which has been studied on many occasions but whose physical properties were not firmly established., Ceti is a dEB containing Am stars which has been studied on many occasions but whose physical properties were not firmly established. + Inthis work we present new spectroscopy and extensive photometric measurements from the SuperWASP survey, Inthis work we present new spectroscopy and extensive photometric measurements from the SuperWASP survey +the middle panel essentially quantifies the anisotropy in integrated fluid displacements.,the middle panel essentially quantifies the anisotropy in integrated fluid displacements. + It is interesting to uote that the magnetic feld for weak stivring is close to isotropic iu the conductive case. while it remains prefercutially taugeutial iu the absence of conduction.," It is interesting to note that the magnetic field for weak stirring is close to isotropic in the conductive case, while it remains preferentially tangential in the absence of conduction." + We argue that this effect can be qualitatively uuderstood in ternis of the magnitude of the buovant restorime force., We argue that this effect can be qualitatively understood in terms of the magnitude of the buoyant restoring force. + The magnitude of the restoring force in the magnetized medi with anisotropic couduction depends on VT whereas for the pure MIID the restoring force depends ou VS. where S is the eas entropy.," The magnitude of the restoring force in the magnetized medium with anisotropic conduction depends on $\nabla T$ whereas for the pure MHD the restoring force depends on $\nabla S$ , where $S$ is the gas entropy." + The entropy eracdicut Insceper than the temperature eracdient. so the buovaut restoring force in the conductive case is weaker then in the pure ΑΠΟ case.," The entropy gradient is steeper than the temperature gradient, so the buoyant restoring force in the conductive case is weaker then in the pure MHD case." + This mieaus that it is easier to perturh and isotropize such a fluid., This means that it is easier to perturb and isotropize such a fluid. + This may explain why the distribution of maguetic field in a turbuleut magnetized aud couducting ICALis more isotropic than in the absence of conduction., This may explain why the distribution of magnetic field in a turbulent magnetized and conducting ICM is more isotropic than in the absence of conduction. + We also note that the tanecutial bias has been seen iu non-MIID adiabatic cosinological simulations that did not involve thermal couduction (Rasia et al., We also note that the tangential bias has been seen in non-MHD adiabatic cosmological simulations that did not involve thermal conduction (Rasia et al. + 2001)., 2004). + In these simulations the characteristic velocity dispersion iu the ICAL was also lughly subsonic and the volume-averaged velocity field anisotropy (coincidentally defined the same wav as here) was 253<0., In these simulations the characteristic velocity dispersion in the ICM was also highly subsonic and the volume-averaged velocity field anisotropy (coincidentally defined the same way as here) was $-2\la\beta\la 0$. + This result is consisteut with the idea of trapping of internal gravity The results for the stroug stirring case are presented as solid blue (turbulence without thermal conduction) and solid ercen (turbulence with thermal couduction)., This result is consistent with the idea of trapping of internal gravity The results for the strong stirring case are presented as solid blue (turbulence without thermal conduction) and solid green (turbulence with thermal conduction). + Iu these cases. the gas velocity dispersion is of the order of σ~150 kis (see next paragraph for the discussion of the velocity dispersion).," In these cases, the gas velocity dispersion is of the order of $\sigma\sim 150$ km/s (see next paragraph for the discussion of the velocity dispersion)." + Such motions. while being clearly subsonic. are nevertheless sufficiently vigorous to isotropize the velocity ficld with and without anisotropic conduction.," Such motions, while being clearly subsonic, are nevertheless sufficiently vigorous to isotropize the velocity field with and without anisotropic conduction." + They are also sufficicuth powerful overwhelin the buovanut restoring force aud make the magnetic field distribution isotropic in both cases., They are also sufficiently powerful to overwhelm the buoyant restoring force and make the magnetic field distribution isotropic in both cases. + The Spitzer fraction is effectivelv 1/3 in this case (note that in the purely hwdrodywuanüc case. the effective conduction is computed at the post-processing Tn Figure Lowe show the evolution of the volwme-averaged velocity dispersions (left paucl) aud the profiles of velocity dispersious in the final state (right panel).," The Spitzer fraction is effectively 1/3 in this case (note that in the purely hydrodynamic case, the effective conduction is computed at the post-processing In Figure 4 we show the evolution of the volume-averaged velocity dispersions (left panel) and the profiles of velocity dispersions in the final state (right panel)." +" As expected. the unperturbed TIBI case leads to very sinall velocity dispersious whereas the volumce-averaged velocity dispersion saturates at ~50 kms and ~150 laus in the weak aud strong stirring cases. respectively,"," As expected, the unperturbed HBI case leads to very small velocity dispersions whereas the volume-averaged velocity dispersion saturates at $\sim 50$ km/s and $\sim 150$ km/s in the weak and strong stirring cases, respectively." + The velocity dispersion profiles also show that the tvpical velocities are always siguificautlv subsonic throughout the ICAL, The velocity dispersion profiles also show that the typical velocities are always significantly subsonic throughout the ICM. + Black aud. ercen lines are for the couductive case and purple aud blue for the non-couductive Iu Figure 5 we present characteristic frequencies iu the cluster: orbital (black). DBruut-Viuisallà (blue) zpy for hydrodynamic case. (ereeu) for MITID case. stirring frequency in the non-conductivewpe case (vellow). stirring frequency in the MIID case (red).," Black and green lines are for the conductive case and purple and blue for the non-conductive In Figure 5 we present characteristic frequencies in the cluster: orbital (black), Brunt-Väiisällä (blue) $\omega_{\rm BV}$ for hydrodynamic case, $\omega_{\rm BV}^{\rm MHD}$ (green) for MHD case, stirring frequency in the non-conductive case (yellow), stirring frequency in the MHD case (red)." + The stirring frequency is defined as ~0/À. where A=20 kpe is some reference leugtLot the order of the cobhereuce scale of the turbulent velocity field.," The stirring frequency is defined as $\sim\sigma/\lambda$, where $\lambda = 20$ kpc is some reference length of the order of the coherence scale of the turbulent velocity field." + Let panel is for the weak turbulence aud the right panel for the strong urbuleuce case., Left panel is for the weak turbulence and the right panel for the strong turbulence case. + This figure is helpful iu explaining the trends secu in the topology of the feld aux the Spitzer fraction (sce Fieure 3)., This figure is helpful in explaining the trends seen in the topology of the field and the Spitzer fraction (see Figure 3). +" Specifically, it can be secu hat for the weak stirring and nou-couductive Case. the frequency exceeds the stirring frequency."," Specifically, it can be seen that for the weak stirring and non-conductive case, the frequency exceeds the stirring frequency." + This miplies trapping of internal eravity waves aud taiceutial blas in the velocity and maguetic fields., This implies trapping of internal gravity waves and tangential bias in the velocity and magnetic fields. + This is cousisteut with the magnetic field topoogv in this case (purple curve. middle panel iu Figure 3) that shows prefercutially tanseutia nmuagnetic fields.," This is consistent with the magnetic field topology in this case (purple curve, middle panel in Figure 3) that shows preferentially tangential magnetic fields." +" Iu he weak stinius couductive case. tie stirriue requeney is either comparable to the ""uaenetie frequency? wht? or it exceeds this frequency."," In the weak stirring conductive case, the stirring frequency is either comparable to the “magnetic frequency” $\omega_{\rm BV}^{\rm MHD}$ or it exceeds this frequency." + This implies that it shouk be easier to ralonize the uagnetic fields., This implies that it should be easier to randomize the magnetic fields. + This is also cousisteut what is seen iu Figure 3 (black curve. nikdle pancl) that shows more isotropic inaegnetic fields iu this Case.," This is also consistent what is seen in Figure 3 (black curve, middle panel) that shows more isotropic magnetic fields in this case." + The results for he corresponding strong siris case are shown in the right panel of Figure 5., The results for the corresponding strong stirring case are shown in the right panel of Figure 5. + Iu 1th the conductive aud non-conductive cases. the stimiug frequencies exceed wpy aud pP which. consistent with our fiudiugs. leads to isotropic mmaguetic field disvibution.," In both the conductive and non-conductive cases, the stirring frequencies exceed $\omega_{\rm BV}$ and $\omega_{\rm BV}^{\rm MHD}$ which, consistent with our findings, leads to isotropic magnetic field distribution." + We now discuss the us with radiative cooling., We now discuss the runs with radiative cooling. + We performed a umber of sinulations that sunultaicouslv inchue anisotropic thermal conduction. radiative cooling and different levels of stiniug.," We performed a number of simulations that simultaneously include anisotropic thermal conduction, radiative cooling and different levels of stirring." + These uus were done for a range of eas deusities and temperatures., These runs were done for a range of gas densities and temperatures. + We now Xxeseut two cases for the iitial couditious described in Section 3 and then briefly comment ou the cooling ruus for different backerouud ICAL xofiles., We now present two cases for the initial conditions described in Section 3 and then briefly comment on the cooling runs for different background ICM profiles. +" Ax αἱJOVO, WE consider exact same numerical setup as for the previous aclabatic cases but now add radiative cooling."," As above, we consider exact same numerical setup as for the previous adiabatic cases but now add radiative cooling." + As vefore. the weak stirring case has an extremely simall turbulent gas velocity dispersion o50kmsL whic ‘his much smaller than the gas sound. speed.," As before, the weak stirring case has an extremely small turbulent gas velocity dispersion $\sigma \sim 50 \, {\rm km \, s^{-1}}$, which is much smaller than the gas sound speed." + Iu general. the oresence of radiative cooling should not dramatically chanec he conclusious related to the opology of the magneic field.," In general, the presence of radiative cooling should not dramatically change the conclusions related to the topology of the magnetic field." + The cooling catastrophe is delaved with res)vct to initial cooling time bv a factx of ~L3, The cooling catastrophe is delayed with respect to the initial cooling time by a factor of $\sim 4.3$. + Note t the euerev in turbulent motions is match less flal thermal euerey of the gas., Note that the energy in turbulent motions is much less than the thermal energy of the gas. + This ratio is: where MM is the Mach nmuuber defined here Vo=ofc. and we have used =2sIPp—van ," This ratio is: where $\mathcal{M}$ is the Mach number defined here as $\mathcal{M}=\sigma/c_{s}$, and we have used $c_{s}^{2}=\gamma P/\rho = \gamma \sigma_{\rm gas}^{2}/3$." +For example. for T- keV and σ=40 kms (cf.," For example, for $T=3$ keV and $\sigma =50$ km/s (cf." + Figure 1). we get gq~LivἹ)35," Figure 4), we get $q\sim 1.4\times 10^{-3}$." + Eol Figure 1. we see that the turbulent energy is injected on a timescale T105 vears. which is comparale to t16 central cooling time.," From Figure 4, we see that the turbulent energy is injected on a timescale $7\times 10^{8}$ years, which is comparable to the central cooling time." + Since ¢l. the turbulent energy injection rate is much. smaller then the cooling rate.," Since $q\ll 1$, the turbulent energy injection rate is much smaller then the cooling rate." + This estimate is independent of the presence of radiaive toolius., This estimate is independent of the presence of radiative cooling. + The results for the stroug stirring equivaleu of the above run (q1.5«102j show that the cooling; catastrophe can be averted., The results for the strong stirring equivalent of the above run $q \sim 1.3\times 10^{-2}$) show that the cooling catastrophe can be averted. + The temperature ]xofile flattens smoothly with time as a result of therma coudction and mixine (see Figure, The temperature profile flattens smoothly with time as a result of thermal conduction and mixing (see Figure +superposition of various components of the CND surrouncing SgrA* (e.e.. see Dwarakanath et al.,"superposition of various components of the CND surrounding SgrA* (e.g., see Dwarakanath et al." + 2001 for more details)., 2004 for more details). + The majority of continuum sources in this study lave absorption due to the 73-kpe arm (at a velocity of ~—51 aud at a distance of 2 kpc)., The majority of continuum sources in this study have absorption due to the “3-kpc arm” (at a velocity of $\sim$$-$ 54 and at a distance of $\sim$ 5 kpc). + Table 5 lists the preseuce of this absorption feature in each spectrum., Table 5 lists the presence of this absorption feature in each spectrum. + The presence of this feature suggests that tliese sources must lie beyond 5 kpc., The presence of this feature suggests that these sources must lie beyond 5 kpc. + Additionally. many of these sources are associated with forbidden-velocity molecular clouds that are believed to lie at the GC.," Additionally, many of these sources are associated with forbidden-velocity molecular clouds that are believed to lie at the GC." + The HI spectra. therefore. of the majority of tlie sources in Table 5 are consistent. with the sources being at a GC distauce of d-8 kpc.," The HI spectra, therefore, of the majority of the sources in Table 5 are consistent with the sources being at a GC distance of d=8 kpc." + Ouly three sources GO.31-0.20. and G359.28-0.26) do not show absorption by the 3-kpe arm.," Only three sources (G0.32-0.19, G0.31-0.20, and G359.28-0.26) do not show absorption by the 3-kpc arm." + The absence of this feature suggestsMOD that these sources may lie between the Sun aud the 3-kpe arm ancl we consider these to be foreground sources., The absence of this feature suggests that these sources may lie between the Sun and the 3-kpc arm and we consider these to be foreground sources. + Finally. the extragalactic source G359.87+0.18 has been studied by Lazio et al. (," Finally, the extragalactic source G359.87+0.18 has been studied by Lazio et al. (" +1999) aud our HI spectrum for this source is in agreement with these fiudiugs.,1999) and our HI spectrum for this source is in agreement with these findings. + A website has been created to disseminate the images. profiles and data to the astronomical community. (see uiowa.edu/-clang/gchi).," A website has been created to disseminate the images, profiles and data to the astronomical community (see $\sim$ clang/gchi)." +One thus finds three equations feqs. (13))-(20))],One thus finds three equations [eqs. \ref{equ_critical1}) \ref{equ_critical3}) )] + with four unknowns. namely: qi. we. o;ο. and the value of in.," with four unknowns, namely: $q_c$, $\omega_c$, $\omega'_c$ , and the value of $\dot{m}$." + Therefore. the ceriücal point cannot be uniquely. determined by a(q). f(q). g(q). aud s(q).," Therefore, the critical point cannot be uniquely determined by $a(q)$, $f(q)$, $g(q)$, and $s(q)$." + Thus. when gas pressure elfects are included. the nozzle hunction n(q) cannot by itself determine (he exact position of the critical point. contrary to the case where gas pressure effects are neglected (Paper I).," Thus, when gas pressure effects are included, the nozzle function $n(q)$ cannot by itself determine the exact position of the critical point, contrary to the case where gas pressure effects are neglected (Paper I)." + The position of the critical point is determined with an additional model constraint which is normally the sonic point position., The position of the critical point is determined with an additional model constraint which is normally the sonic point position. + That is. the equation of motion. upon integration from the critical point to lower velocities. must obtain the correct sonic point.," That is, the equation of motion, upon integration from the critical point to lower velocities, must obtain the correct sonic point." +" In relsec,ppendirfFanalyzeindetaillheeriticalpointeonditionsandderiveexplicilexpressions foro, we and rin as functions of the critical point ας (eqs. ΑΟ A17]."," In \\ref{sec_appendix} I analyze in detail the critical point conditions and derive explicit expressions for $\omega_c$, $\omega'_c$ and $\dot{m}$ as functions of the critical point $q_c$ (eqs. \ref{equ_critical18}- \ref{equ_critical20}] ])." + Additionally. in . Falsof indlhaltinorder forq. (o be a critical point (i.e... in order for wy. at. and 5» to be determinable). it must hold that For an isothermal wind (ds/dq= 0) these wo conditions for the existence of a critical point. reduce to Although the nozzle hinetion n cannot by itself determine a unique value for the critical point. it can constrain the location of the criGical point. and in some cases it can be showncalculations that a steady solution does not exist (e.g.. in an isothermal wind with a monotonically decreasing nozzle function).," Additionally, in \\ref{sec_appendix}, I also find that in order for $q_c$ to be a critical point (i.e., in order for $\omega_c$, $\omega'_c$, and $\dot{m}$ to be determinable), it must hold that For an isothermal wind $ds/dq=0$ ) these two conditions for the existence of a critical point, reduce to Although the nozzle function $n$ cannot by itself determine a unique value for the critical point, it can constrain the location of the critical point, and in some cases it can be shown that a steady solution does not exist (e.g., in an isothermal wind with a monotonically decreasing nozzle function)." + The existence of a critical point (ie.. the determination of values for dy. a. ancl 11) reqs. (AL5))-CALT)))," The existence of a critical point (i.e., the determination of values for $\omega_c$, $\omega'_c$, and $\dot{m}$ [eqs. \ref{equ_critical18}) \ref{equ_critical20}) )]" + such that the critical point conditions hold leqs. (18))-(20))]), such that the critical point conditions hold [eqs. \ref{equ_critical1}) \ref{equ_critical3}) )]) + does not imply that the equation of motion feq. (6))], does not imply that the equation of motion [eq. \ref{equ_motion}) )] + is locally or globally integrable., is locally or globally integrable. + That is. the existence of a point that satisfies the critical point conditions does not ensure (hat a local (in the vicinity of the point)steady solution exists or that a elobal (throughout the spatial range being considered) steady solution exists.," That is, the existence of a point that satisfies the critical point conditions does not ensure that a local (in the vicinity of the point)steady solution exists or that a global (throughout the spatial range being considered) steady solution exists." + In the work of CAIx75 [or line-driven stellar winds. the existence of a steady solution," In the work of CAK75 for line-driven stellar winds, the existence of a steady solution" +"where ray. T, and ry are the position vectors of center of mass. the planet. and the star respectively.","where $\bm{r}_{\rm cm}$ , $\bm{r}_{\rm p}$ and $\bm{r}_{\rm s}$ are the position vectors of center of mass, the planet, and the star respectively." +" Phe angular velocity of the star.planet binary system is We adopt units where à=AL|Ad,QO),1.", The angular velocity of the star–planet binary system is We adopt units where $a=M_{\rm s}+M_{\rm p}=\Omega_{\rm p}=1$. + Phe equations of motion for the particle with Cartesian coordinates Grey). whose origin is at the center of mass. are then and Following the standard: procedure to obtain the Lill equations. we transform these equations to à coordinate svstem centered. on the planet and. rescale the coordinates.," The equations of motion for the particle with Cartesian coordinates $(x,y)$, whose origin is at the center of mass, are then and Following the standard procedure to obtain the Hill equations, we transform these equations to a coordinate system centered on the planet and rescale the coordinates." + The scaling is chosen so that the new coordinates scale with the Lill radius. sce equation (1)).," The scaling is chosen so that the new coordinates scale with the Hill radius, see equation \ref{rh}) )." +" We make the change of variables to rescaled radius f? defined hy where f,an is the displacement of the planet from the center of mass.", We make the change of variables to rescaled radius $R$ defined by where $\bm{r}_{\rm p-cm}$ is the displacement of the planet from the center of mass. + The equation of motion (9)) is then where e is the potential in this new frame that we determine in Section 3.2.., The equation of motion \ref{eqmot}) ) is then where $\Phi$ is the potential in this new frame that we determine in Section \ref{potential}. + We let XY=loge|porc and Y—qpy.," We let $X = 1-\mu +\mu^\frac{1}{3}x$ and $Y +=\mu^\frac{1}{3}y$." + Since ois small. we consider here only the terms to lowest order in jr.," Since $\mu$ is small, we consider here only the terms to lowest order in $\mu$." + “Phe equations to order yo become and In Section 3.4 weconsider the higher order terms in ye that have been neglected here., The equations to order $\mu^\frac{1}{3}$ become and In Section \ref{cross} weconsider the higher order terms in $\mu$ that have been neglected here. + The terms in equations (16)) and (17)) that are functions of VY and Y. are expressed as the potential gradients and Integrating these. we find the potential in the Hill approximation to be In polar coordinates centered on the planet. so that VY=Rcos@ and Y=Rsind. the potential is given by The first term is a point mass potential of the planet.," The terms in equations \ref{xeq}) ) and \ref{yeq}) ) that are functions of $X$ and $Y$ are expressed as the potential gradients and Integrating these, we find the potential in the Hill approximation to be In polar coordinates centered on the planet, so that $X=R \cos \theta$ and $Y=R\sin \theta$, the potential is given by The first term is a point mass potential of the planet." + Ehe other two terms are due to the rotation ofthe frame and the eravitational cllects of the star., The other two terms are due to the rotation ofthe frame and the gravitational effects of the star. + In dimensional form. the potential is given hy which is valid for r—Oe Fay.," In dimensional form, the potential is given by which is valid for $r \sim O (\mu^{1/3} a)$ ." +is not well mapped in Ilipparcos data aud this prevented us frou acJusting even the temperature difference.,is not well mapped in Hipparcos data and this prevented us from adjusting even the temperature difference. + Using the calibrations from Straizyvs&I&uiliene(1981).. à Fs spectral type iuplies an eective temperature of 6150 Ix. while a €) type gives. T. = 5950 Ix. The spectrmm iu Fig.," Using the calibrations from \citet{straizys1}, an F8 spectral type implies an effective temperature of 6150 K, while a G0 type gives $T_{\rm eff}$ = 5950 K. The spectrum in Fig." +" 1 how""vor shows al apxeciable Paschen 11 line which intensity relative to the Call triplet supports a somewhat lugher 650 VIS temperature (cf.", 1 however shows an appreciable Paschen 14 line which intensity relative to the CaII triplet supports a somewhat higher 6500 K temperature (cf. + svuthetic spectral atlas of Abunari and Castelli 2000)., synthetic spectral atlas of Munari and Castelli 2000). + We thus tried four ciffereut inodel solutions: Ta Τμ = 6500 K. Tig) = μου = 0150 Kk. Tag) = 06150 I aud Tig = 5950 WN (d) Tiga = Tig = 5950 Kk. Alodel gave a better convergence aud thus Z;g 6500 was adopted for both stars.," We thus tried four different model solutions: ) $T_{\rm eff,1}$ = $T_{\rm eff,2}$ = 6500 K, ) $T_{\rm eff,1}$ = $T_{\rm eff,2}$ = 6150 K, ) $T_{\rm eff,1}$ = 6150 K and $T_{\rm eff,2}$ = 5950 K ) $T_{\rm eff,1}$ = $T_{\rm eff,2}$ = 5950 K. Model gave a better convergence and thus $T_{\rm +eff}$ = 6500 was adopted for both stars." + The relative itensity of Paschen 11 aud Call lines iu the spectrum of Fig., The relative intensity of Paschen 14 and CaII lines in the spectrum of Fig. + 1 strmelv support such a temperature when conrpared witji the svuthetic spectral atlas of Minimi aid. Castelli (200)., 1 strongly support such a temperature when compared with the synthetic spectral atlas of Munari and Castelli (2000). + The derived masses aud radi (A4 1.06 AL... Mo» = LOL AM... Ry = 125 R.. Ro = 1.21 RR.) are σοιsistent with those of ucarly equal stars sheiflv hotter alc jieavier than the Sun aud still within the aad sequence baud even i slightly away from the ZAMS locus.," The derived masses and radii $M_{1}$ = 1.06 $M_{\odot}$, $M_{2}$ = 1.04 $M_{\odot}$, $R_{1}$ = 1.23 $R_{\odot}$, $R_{2}$ = 1.21 $R_{\odot}$ ) are consistent with those of nearly equal stars slightly hotter and heavier than the Sun and still within the main sequence band even if slightly away from the ZAMS locus." + Caifin (2001) sueeestedOO that both components of the systen are more Dunimous than MS stars., Griffin (2001) suggested that both components of the system are more luminous than MS stars. + The derived lass ratio (q = + 0.009) is completely consistent witi that obtained by Coifüuü (2001) whose 4 1.017 trasος fo = 0.983 when stars are labeled according to our scheno., The derived mass ratio $q$ = $~\pm$ 0.009) is completely consistent with that obtained by Griffin (2001) whose $q$ = 1.017 transforms to $q$ = 0.983 when stars are labeled according to our scheme. +Very metal-poor halo stars show a great diversity in their element abundances and therefore a scatter in their element-to-iron ratios [El/Fe] of order | dex.,Very metal-poor halo stars show a great diversity in their element abundances and therefore a scatter in their element-to-iron ratios [El/Fe] of order 1 dex. + This scatter gradually decreases at higher metallicities until a mean element abundance is reached which corresponds to the [EI/Fe] ratio of the stellar yields integrated over the initial mass function (IMF)., This scatter gradually decreases at higher metallicities until a mean element abundance is reached which corresponds to the [El/Fe] ratio of the stellar yields integrated over the initial mass function (IMF). + The aim of our stochastic halo formation model is to understand the trends seen in the observations and to investigate how the metal-poor interstellar medium (SM) in the halo evolves chemically., The aim of our stochastic halo formation model is to understand the trends seen in the observations and to investigate how the metal-poor interstellar medium (ISM) in the halo evolves chemically. + Our fully 3D-code. contrary to I-zone chemical evolution models. enables us to resolve local inhomogeneities in. the ISM with a spatial resolution of 50 pe.," Our fully 3D-code, contrary to 1-zone chemical evolution models, enables us to resolve local inhomogeneities in the ISM with a spatial resolution of 50 pc." + All in all. we model a volume of (2.5 kpe)?. divided into 50° cells.," All in all, we model a volume of (2.5 $^3$ , divided into $50^3$ cells." + Every cell of our grid contains detailed information about the enclosed ISM and the mass distribution of stars., Every cell of our grid contains detailed information about the enclosed ISM and the mass distribution of stars. + We consider simultaneously the evolution of nine elements. the o-elements O. Mg. Si and Ca. the iron-peak elements Cr. Mn. Fe and Ni and the r-process element Eu.," We consider simultaneously the evolution of nine elements, the $\alpha$ -elements O, Mg, Si and Ca, the iron-peak elements Cr, Mn, Fe and Ni and the r-process element Eu." + Our initial conditions assume a halo ISM consisting of a homogeneously distributed single gas phase with primordial abundances and a density of 0.25 particles per em?. which gives a total mass of about LOSAL; in a volume of (2.5 kpe)?.," Our initial conditions assume a halo ISM consisting of a homogeneously distributed single gas phase with primordial abundances and a density of 0.25 particles per $^3$, which gives a total mass of about $10^8 \, \mathrm{M}_{\sun}$ in a volume of (2.5 $^3$." + We adopt a constant time-step of 10° years since it has to be longer than the dynamical evolution of a supernova (SN) remnant and shorter than the lifetime of the most massive stars., We adopt a constant time-step of $10^6$ years since it has to be longer than the dynamical evolution of a supernova (SN) remnant and shorter than the lifetime of the most massive stars. + At each time-step 200000 cells are chosen randomly and independently of each other and of the state of the enclosed ISM., At each time-step 000 cells are chosen randomly and independently of each other and of the state of the enclosed ISM. + Each selected cell may create a star with a probability proportional to the square of the local ISM density (Larson 1988))., Each selected cell may create a star with a probability proportional to the square of the local ISM density (Larson \cite{la88}) ). + The number of stars formed per time-step is the product of the number of cells tested with the probability of star formation in each cell., The number of stars formed per time-step is the product of the number of cells tested with the probability of star formation in each cell. + Various combinations of these parameters. are possible to achieve a given SER: the choice of 200000 cells proved computationally convenient., Various combinations of these parameters are possible to achieve a given SFR; the choice of 000 cells proved computationally convenient. + The absolute value of the SFR influences the of the enrichment process (cf., The absolute value of the SFR influences the of the enrichment process (cf. + Sect. 5.1)).," Sect. \ref{mixing}) )," + but the evolution of |El/Fe|-ratios as function of [Fe/H]., but the evolution of [El/Fe]-ratios as function of [Fe/H]. + Therefore. the main results of this paper are insensitive to the values of these parameters.," Therefore, the main results of this paper are insensitive to the values of these parameters." + The mass of a newly formed star is chosen randomly from a Salpeter IMF., The mass of a newly formed star is chosen randomly from a Salpeter IMF. + The lower and upper mass limits of the IMF are taken to be (TAL: and 50M;. respectively.," The lower and upper mass limits of the IMF are taken to be $0.1 \, \mathrm{M}_{\sun}$ and $50 \, \mathrm{M}_{\sun}$, respectively." + About 5000 stars are formed on average during each step., About 5000 stars are formed on average during each step. + Newly born stars inherit the abundance pattern of the ISM out of which they form. carrying therefore information about the state of the ISM at the place and time of their birth.," Newly born stars inherit the abundance pattern of the ISM out of which they form, carrying therefore information about the state of the ISM at the place and time of their birth." + To determine the lifetime of a star an approximation to the metallicity dependent mass-lifetime relation of the (cf., To determine the lifetime of a star an approximation to the metallicity dependent mass-lifetime relation of the (cf. + Schaller et al. 1992;;, Schaller et al. \cite{sl92}; + Schaerer et al. 1993a::, Schaerer et al. \cite{sr93a}; + Schaereret al. 1993b:: , Schaerer et al. \cite{sr93b}; ; +Charbonnel et al. 1993)), Charbonnel et al. \cite{cb93}) ) + is used. given by where T is the lifetime in units of 10 yr. Z the metallicity in units of solar metallicity Z: and A the mass in units of solar masses M;.," is used, given by where $T$ is the lifetime in units of $10^6$ yr, $Z$ the metallicity in units of solar metallicity $Z_{\sun}$ and $M$ the mass in units of solar masses $\mathrm{M}_{\sun}$." + Stars in a range of 10—50M; will explode as core-collapse supernovae (SNe II). resulting in an enrichment of the neighbouring ISM.," Stars in a range of $10-50 \, \mathrm{M}_{\sun}$ will explode as core-collapse supernovae (SNe II), resulting in an enrichment of the neighbouring ISM." + Stellar vields are taken from Thielemann et al. (1996)), Stellar yields are taken from Thielemann et al. \cite{th96}) ) + and Nomoto et al. (1997)), and Nomoto et al. \cite{no97}) ) + for all elements except Eu., for all elements except Eu. + Since there are no theoretical predictions of stellar Eu yields. we use the indirectly deduced yields of Tsujimoto Shigeyama (1998)) which assume that r-process elements originate from SNe II (see the discussion of stellar yields in Sect. 3)).," Since there are no theoretical predictions of stellar Eu yields, we use the indirectly deduced yields of Tsujimoto Shigeyama \cite{ts98}) ) which assume that r-process elements originate from SNe II (see the discussion of stellar yields in Sect. \ref{nucleo}) )." + We linearly interpolate the stellar yields given in these papers. since we use a finer mass-grid in our simulation.," We linearly interpolate the stellar yields given in these papers, since we use a finer mass-grid in our simulation." + For SNe with masses below 13M; stellar yields are not available.," For SNe with masses below $13 \, \mathrm{M}_{\sun}$ stellar yields are not available." + Since the nucleosynthesis models show declining yields towards low progenitor masses. we have for the interpolation arbitrarily set the yields of à LOAL: SN to one thousandth of those of a 13M; SN.," Since the nucleosynthesis models show declining yields towards low progenitor masses, we have for the interpolation arbitrarily set the yields of a $10 \, +\mathrm{M}_{\sun}$ SN to one thousandth of those of a $13 \, \mathrm{M}_{\sun}$ SN." + The interpolation gives IMF averaged values of the |EVFe] ratios. which are in good agreement with the observed mean values of metal-poor stars in all elements except Ca. which shows a [Ca/Fe] ratio that is about 0.3 dex lower than the observed mean.," The interpolation gives IMF averaged values of the [El/Fe] ratios, which are in good agreement with the observed mean values of metal-poor stars in all elements except Ca, which shows a [Ca/Fe] ratio that is about 0.3 dex lower than the observed mean." + We do not include supernovae (SNe) of Type Ia. since we are only interested in the very early enrichment of the halo ISM. which ts dominated by SNe of Type II.," We do not include supernovae (SNe) of Type Ia, since we are only interested in the very early enrichment of the halo ISM, which is dominated by SNe of Type II." + Intermediate mass stars will evolve to planetary nebulae. returning only slightly enriched material in the course of their evolution.," Intermediate mass stars will evolve to planetary nebulae, returning only slightly enriched material in the course of their evolution." + This locally influences the enrichment. pattern. of the gas. since metal-poor material is returned into the evolved and enriched ISM.," This locally influences the enrichment pattern of the gas, since metal-poor material is returned into the evolved and enriched ISM." + It will not change the element abundances [EUH] significantly. but can affect the local element-to-iron ratios [E/Fe| considerably.," It will not change the element abundances [El/H] significantly, but can affect the local element-to-iron ratios [El/Fe] considerably." + Low mass stars do not evolve significantly during the considered time., Low mass stars do not evolve significantly during the considered time. + In our model. they serve to lock up part of the gas mass. affecting therefore the local element abundances [EI/H]| in the ISM.," In our model, they serve to lock up part of the gas mass, affecting therefore the local element abundances [El/H] in the ISM." + Since the explosion energy of a core-collapse supernova (SN II) depends only slightly on the mass of its progenitor (Woosley Weaver 1905:: Thielemann et al. 1996)).," Since the explosion energy of a core-collapse supernova (SN II) depends only slightly on the mass of its progenitor (Woosley Weaver \cite{ww95}; Thielemann et al. \cite{th96}) )," + every SN IL sweeps up a constant mass of about 5«104M: of gas (Ryan et al. 1906:," every SN II sweeps up a constant mass of about $5 \times 10^4 +\, \mathrm{M}_{\sun}$ of gas (Ryan et al. \cite{ry96};" + Shigeyama Tsujimoto 1998))., Shigeyama Tsujimoto \cite{sh98}) ). + In our model the radius of the SN remnant then is computed from the local density of the ISM and lies typically between 100 pe and 200 pe., In our model the radius of the SN remnant then is computed from the local density of the ISM and lies typically between 100 pc and 200 pc. + The ejecta of the SN II and all the swept up. enriched material are condensed in a spherical shell which is assumed to be chemically well mixed.," The ejecta of the SN II and all the swept up, enriched material are condensed in a spherical shell which is assumed to be chemically well mixed." + The material in the shell subsequently mixes with the ISM of the cells where the expansion of the remnant stopped., The material in the shell subsequently mixes with the ISM of the cells where the expansion of the remnant stopped. + The interior of the remnant. where all the material was swept up. is assumed to be filled with about 5M; of dilute gas from the SN event with the corresponding metal abundances.," The interior of the remnant, where all the material was swept up, is assumed to be filled with about $5 \, \mathrm{M}_{\sun}$ of dilute gas from the SN event with the corresponding metal abundances." + This gas ts unable to form stars until it is swept up by another SN event and mixed with the surrounding ISM., This gas is unable to form stars until it is swept up by another SN event and mixed with the surrounding ISM. + Thus this material contributes to the enrichment only aftersome delay., Thus this material contributes to the enrichment only aftersome delay. + The star formation rate of cells influencedby the remnant will rise. since their density 1s higher than the average density of a cell and the probability to form a star is assumed to be," The star formation rate of cells influencedby the remnant will rise, since their density is higher than the average density of a cell and the probability to form a star is assumed to be" +"the RCS clusters haviug 670$ 0.5) and/or with very different masses. + Those are tlie ones merging (or being tidallv destroved) within 40 Myr of forming., Those are the ones merging (or being tidally destroyed) within 40 Myr of forming. + Using available observational evidence. de la Fuente Marcos de la Fuente Marcos (2009b) have demonstrated that (he population of binary open clusters is statistically significant and that the fraction of candidate binary clusters in the Milkv. Way disk is comparable to that in the Magellanie Clouds. ~10%..," Using available observational evidence, de la Fuente Marcos de la Fuente Marcos (2009b) have demonstrated that the population of binary open clusters is statistically significant and that the fraction of candidate binary clusters in the Milky Way disk is comparable to that in the Magellanic Clouds, $\sim$." + Out of this population. nearly of them can be," Out of this population, nearly of them can be" +is initially surprising until we notice that the errors are large. we note that we have applied. the cosmic variance terms to all the data points ancl these are significant. particularly for the BOS sample ancl the Jresse Macdox sample.,"is initially surprising until we notice that the errors are large, we note that we have applied the cosmic variance terms to all the data points and these are significant, particularly for the B93 sample and the Tresse Maddox sample." + We thus suspect that the coincidence of these various estimators may be due o dillerences in the mean density of these survey volumes which masks a difference in their sampling of he star-formation rate., We thus suspect that the coincidence of these various estimators may be due to differences in the mean density of these survey volumes which masks a difference in their sampling of the star-formation rate. + This assertion is strengthened when we see that the /fea estimate of the. star-ormation rate from the BOS sample itself is further rclow the radio estimate than the Presse Maddox »oint is above it., This assertion is strengthened when we see that the $H\alpha$ estimate of the star-formation rate from the B93 sample itself is further below the radio estimate than the Tresse Maddox point is above it. + An additional star-formation indicator is the far infrared., An additional star-formation indicator is the far infrared. + Several authors (Scoville Young 1983: Vhronson Telesco 1986: Condon 1992: RowanRobinson et al., Several authors (Scoville Young 1983; Thronson Telesco 1986; Condon 1992; Rowan--Robinson et al. + 1997) have derived. relations to convert from. 60. gun luminosity to star formation rate., 1997) have derived relations to convert from 60 $\mu$ m luminosity to star formation rate. + “Phese calculations assume some proportion of 16 optical luminosity produced. by voung stars. is absorbed. and. re-emitted in the infrared. C, These calculations assume some proportion of the optical luminosity produced by young stars is absorbed and re-emitted in the infrared. ( +Phis same extinction factor should. naturally be applied to the gaar-formation rates caleulated from the UV.),This same extinction factor should naturally be applied to the star-formation rates calculated from the UV.) + From such calculations itis of course possible to deduce rw FIRRacljo correlation., From such calculations it is of course possible to deduce the FIR/Radio correlation. + Condon (1992) deduced rw EIRRaclio correlation assuming an obscuration factor of 2/3..," Condon (1992) deduced the FIR/Radio correlation assuming an obscuration factor of 2/3.," +.J) recently: Cram et al. (, recently Cram et al. ( +1998). seems to indicate a close agreement between the radio SER estimate and the farinfrared one obtained considering 100 per cent reprocessing of starlight in the [aur-infrared.,1998) seems to indicate a close agreement between the radio SFR estimate and the far–infrared one obtained considering $\sim100$ per cent reprocessing of starlight in the far-infrared. + In general it does appear that the extinction fraction is high., In general it does appear that the extinction fraction is high. + It would in fact be possible o use the FIlt/Itadio correlation to determine the extinction fraction for any assumed. underlving IME. us could then be feed self consistently into the UV uxl Jia SER estimates.," It would in fact be possible to use the FIR/Radio correlation to determine the extinction fraction for any assumed underlying IMF, this could then be feed self consistently into the UV and $H\alpha$ SFR estimates." + Such an analysis is bevond re scope of this paper., Such an analysis is beyond the scope of this paper. + Instead we use the ELItadio correlation simply o convert local estimates of the GOs luminosity. ensity [rom 890 to L4AGIIz luminosity density and ren use the 1ΚΙ calibration above which is independent. of extinction., Instead we use the FIR/Radio correlation simply to convert local estimates of the $60\mu$ m luminosity density from S90 to 1.4GHz luminosity density and then use the 1.4GHz calibration above which is independent of extinction. + We plot in Figure 5..6 je star-lormation rate estimated thus from the 890 uminosityv. densities for both swarm” LAS galaxies and for all ΗΛ galaxies.," We plot in Figure \ref{fig:sfr1}, \ref{fig:sfr2} the star-formation rate estimated thus from the S90 luminosity densities for both “warm” IRAS galaxies and for all IRAS galaxies." +" It is not clear that the ""cool LRAS galaxies trace star-formation as do he warm Ας galaxies. since the cool emission is from cirrus clouds which may be illuminated. by older stellar populations (similarly the UV density of quiescent or weakly star-forming galaxies might also be dominated by old stars)"," It is not clear that the “cool” IRAS galaxies trace star-formation as do the warm IRAS galaxies, since the cool emission is from cirrus clouds which may be illuminated by older stellar populations (similarly the UV density of quiescent or weakly star-forming galaxies might also be dominated by old stars)." + We have estimated the 1.4 Gllz luminosity density rom a sample of radio star-burst galaxies 2< 1.35. demonstrating that the optical selection criteria applied. to this sample are not. important to this determination.," We have estimated the 1.4 GHz luminosity density from a sample of radio star-burst galaxies $z<0.35$ , demonstrating that the optical selection criteria applied to this sample are not important to this determination." + Phe small volume of this survey at 2< prevents us from having accurate estimates of he luminosity density from low racio lamiinosity star-orming galaxies., The small volume of this survey at $z<0.05$ prevents us from having accurate estimates of the luminosity density from low radio luminosity star-forming galaxies. + Nevertheless we demonstrate that a number of reasonable a priori luminosity functions can be used to estimate the luminosity density missed., Nevertheless we demonstrate that a number of reasonable a priori luminosity functions can be used to estimate the luminosity density missed. + These corrections are small. for the sample as a whole. though larger and more disparate for a higher redshift sub-sample.," These corrections are small for the sample as a whole, though larger and more disparate for a higher redshift sub-sample." + The 1.4 11 luminosity density increases as we move to higher redshifts. though the strength of this elfect is dependent on the assumed luminosity function and may not be conclusive with a sample of this volume.," The 1.4 GHz luminosity density increases as we move to higher redshifts, though the strength of this effect is dependent on the assumed luminosity function and may not be conclusive with a sample of this volume." + Overall the 1.4 Giz luminosity density agrees with that obtained. from 1.4. Cillz measurements of the RSA sample of Condona£., Overall the 1.4 GHz luminosity density agrees with that obtained from 1.4 GHz measurements of the RSA sample of Condon. + The l4Cllz estimator of star-formation rates should be unallectecl by extinction. whereas. local estimates from the UV. and. {ία should. be.," The 1.4GHz estimator of star-formation rates should be unaffected by extinction, whereas local estimates from the UV and $H\alpha$ should be." + We were thus surprised. to find the estimate [rom the radio broadly consistent with these other estimates. particularly since the local estimate from the Concdon luminosity density was considerably higher. than [rom optical measures.," We were thus surprised to find the estimate from the radio broadly consistent with these other estimates, particularly since the local estimate from the Condon luminosity density was considerably higher than from optical measures." + Since the luminosity density estimated from 4/46. within the BOS sample produces a much lower estimate of the star-formation rate than the 1.4CHIz estimate and the (optimistic) cosmic, Since the luminosity density estimated from $H\alpha$ within the B93 sample produces a much lower estimate of the star-formation rate than the 1.4GHz estimate and the (optimistic) cosmic +at the Cerro-Vololo lnteramerican Observatory.,at the Cerro-Tololo Interamerican Observatory. + The. /- band. exposures consist of 150 seconds. per pointing. and each individual image covers an area of order one-quarter of a square degree.," The $I$ -band exposures consist of 150 seconds per pointing, and each individual image covers an area of order one-quarter of a square degree." + We selected. a total of 13.8 deg? of imaging cata Crom the survey for our work. rejecting images that were obtained during poor photometric conditions or which exhibited. poor tracking or poor focus.," We selected a total of 13.8 $^2$ of imaging data from the survey for our work, rejecting images that were obtained during poor photometric conditions or which exhibited poor tracking or poor focus." + The data were calibrated. Uat-licldecl. and de-fringed as described in Alonier et ((2002).," The data were calibrated, flat-fielded, and de-fringed as described in Monier et (2002)." + Object catalogs were created from the reduced. Z-band data using the SIExtractor package (Bertin Arnouts 1996)., Object catalogs were created from the reduced $I$ -band data using the SExtractor package (Bertin Arnouts 1996). + Aclelitional details regarding the quality of the imaging. star-galaxy separation. cosmic rav rejection. point-spread function correction. and. masking of cosmetic defects. (e.g... large stellar blooms. dilfraction spikes) will be presented in a companion paper (Llowell /Drainerd. in. preparation).," Additional details regarding the quality of the imaging, star-galaxy separation, cosmic ray rejection, point-spread function correction, and masking of cosmetic defects (e.g., large stellar blooms, diffraction spikes) will be presented in a companion paper (Howell Brainerd, in preparation)." + In the companion paper we will also present an analysis of the observed ealaxy-ealaxy lensing signal in this data set., In the companion paper we will also present an analysis of the observed galaxy-galaxy lensing signal in this data set. + For the purposes of our present. study. we are simply interested in using the D'ECHO galaxies as the framework for a set of Monte. Carlo simulations of galaxv-galaxy. lensing by non-spherical haloes.," For the purposes of our present study, we are simply interested in using the BTC40 galaxies as the framework for a set of Monte Carlo simulations of galaxy-galaxy lensing by non-spherical haloes." + That is. here we will address the following question: Civen a data set like that obtained from the D'TCH0. what should one expect to observe for the ealaxy-ealaxy lensing signal if the dark matter haloes of the galaxies are non-spherical?," That is, here we will address the following question: Given a data set like that obtained from the BTC40, what should one expect to observe for the galaxy-galaxy lensing signal if the dark matter haloes of the galaxies are non-spherical?" + The information fron the BLC4O images that we use here consists solely of the centroids of the galaxies ancl their Z-band. apparent magnitudes., The information from the BTC40 images that we use here consists solely of the centroids of the galaxies and their $I$ -band apparent magnitudes. + These. along with other quantities. are used as input parameters for our Monte Carlo simulations.," These, along with other quantities, are used as input parameters for our Monte Carlo simulations." + Also. in order to ultimately match the data that will be presented in our companion paper. here we use only DTC0. galaxies with ISxJig:22.5.," Also, in order to ultimately match the data that will be presented in our companion paper, here we use only BTC40 galaxies with $18 \le I_{AB} \le 22.5$." + While the completeness Limit of the data is somewhat fainter than {νε=5. in. practice the D'T€40 galaxies with τρ22.5 are too small for accurate shape determinations.," While the completeness limit of the data is somewhat fainter than $I_{AB} = 22.5$, in practice the BTC40 galaxies with $I_{AB} > 22.5$ are too small for accurate shape determinations." + The observed shapes of the D/TCH0 galaxies have been alectec by the presence of a spatially-varving anisotropic point spread function., The observed shapes of the BTC40 galaxies have been affected by the presence of a spatially-varying anisotropic point spread function. + Because of this. and because of the fact that shape determinations become increasingly. noisy at faint [lux levels. we do not use the observed shapes of the BPCAO galaxies in our Monte. Carlo simulations.," Because of this, and because of the fact that shape determinations become increasingly noisy at faint flux levels, we do not use the observed shapes of the BTC40 galaxies in our Monte Carlo simulations." + Instead. in order to describe the shape of the luminous galaxy. each Alonte Carlo galaxy is assigned an intrinsic image ellipticity. Gu—(ab)/(e|5). that is drawn from the probability cistribution derived by Ebboels (1998) from 94 archival LIST lield survey images: llere r=(a2b-)/(2ab). Aisa normalising constant. and e and b are. respectively. the semi-major and semi-minor axes of the intrinsic image ellipses.," Instead, in order to describe the shape of the luminous galaxy, each Monte Carlo galaxy is assigned an intrinsic image ellipticity, $\epsilon_{\rm in} \equiv (a-b)/(a+b)$, that is drawn from the probability distribution derived by Ebbels (1998) from 94 archival HST field survey images: Here $\tau = (a^2 - b^2)/(2ab)$, $\cal{A}$ is a normalising constant, and $a$ and $b$ are, respectively, the semi-major and semi-minor axes of the intrinsic image ellipses." + We assume that the projected shapes of the haloes of he IYEC40 galaxies are elliptical but. unlike ουρία et ((2004) ancl Mandelbaunm et ((2006b). we do not assume hat there is a linear relationship between the shape of the uminous galaxy and the shape of its projected dark matter ido.," We assume that the projected shapes of the haloes of the BTC40 galaxies are elliptical but, unlike Hoekstra et (2004) and Mandelbaum et (2006b), we do not assume that there is a linear relationship between the shape of the luminous galaxy and the shape of its projected dark matter halo." + While the assumption (enge=λέπωμ may have some validity for elliptical galaxies. it is definitely. false for. clisk galaxies (which make up a substantial fraction of the lens opulation).," While the assumption $\epsilon_{\rm halo} = +\lambda \epsilon_{\rm light}$ may have some validity for elliptical galaxies, it is definitely false for disk galaxies (which make up a substantial fraction of the lens population)." + Agustsson Drainerd. (2006) showed that the observed. ellipticities of disk galaxies embedded within CDM haloes were largely uncorrelated with the cllipticities of their projected. haloes (see their Figure 6)., Agustsson Brainerd (2006) showed that the observed ellipticities of disk galaxies embedded within CDM haloes were largely uncorrelated with the ellipticities of their projected haloes (see their Figure 6). + Vhis is due to the fact that one always views a random projection of the dark matter halo on the αν., This is due to the fact that one always views a random projection of the dark matter halo on the sky. + Therefore. a high inclination angle for the disk (svhich maximises the ellipticity of the luminous galaxy image) does not. in general. correlate with a projection that. maximises the projected. ellipticity of the halo.," Therefore, a high inclination angle for the disk (which maximises the ellipticity of the luminous galaxy image) does not, in general, correlate with a projection that maximises the projected ellipticity of the halo." + In. order το assign projected. axis ratios. f. to the haloes of our Monte Carlo ealaxies. then. we use the probability distribution obtained by Agustsson Drainerd (2006) for the projected axis ratios of CDAL ealaxy haloes.," In order to assign projected axis ratios, $f$, to the haloes of our Monte Carlo galaxies, then, we use the probability distribution obtained by Agustsson Brainerd (2006) for the projected axis ratios of CDM galaxy haloes." + The halo of each galaxy in our simulations is therefore assigned a value of f that is clrawn at random from this clistribution (see Figure 2)., The halo of each galaxy in our simulations is therefore assigned a value of $f$ that is drawn at random from this distribution (see Figure 2). + Next we must make a choice as to how to orient. the luminous galaxies within their dark matter haloes., Next we must make a choice as to how to orient the luminous galaxies within their dark matter haloes. + The only svmmetry axes that can be used in an observational cata set to detect anisotropic galaxy-galaxy lensing are. of course. the symmetry axes of the luminous galaxies themselves.," The only symmetry axes that can be used in an observational data set to detect anisotropic galaxy-galaxy lensing are, of course, the symmetry axes of the luminous galaxies themselves." + Lf mass and light are not reasonably well aligned. within the lens ealaxies. a detection of anisotropic galaxy-galaxy lensing is hopeless since we cannot directly observe the orientations of the symmetry axes of the dark matter haloes.," If mass and light are not reasonably well aligned within the lens galaxies, a detection of anisotropic galaxy-galaxy lensing is hopeless since we cannot directly observe the orientations of the symmetry axes of the dark matter haloes." + Pherefore. in our simulations we will assume that the intrinsic symmetry axes of the luminous galaxies and their dark matter haloes are aligned with cach other.," Therefore, in our simulations we will assume that the intrinsic symmetry axes of the luminous galaxies and their dark matter haloes are aligned with each other." + This assumption maximises the degree of anisotropy in the galaxy-galaxy lensing signal that one should expect to see and it presents a best case scenario for detecting the elfect., This assumption maximises the degree of anisotropy in the galaxy-galaxy lensing signal that one should expect to see and it presents a best case scenario for detecting the effect. + Neither spectroscopic redshifts πο photometric redshifts are available for the BVC40 ealaxies., Neither spectroscopic redshifts nor photometric redshifts are available for the BTC40 galaxies. + Therefore. we must assign redshifts to the galaxies in order to carry out our Monte Carlo simulations.," Therefore, we must assign redshifts to the galaxies in order to carry out our Monte Carlo simulations." + Following the prescriptions of BBS and Wright (2002). we adopt a redshift distribution of the form ‘Taking 3=1.5 vields good agreement with the recdshift surveys of Lebovvre. et ((1996) and. Lebovyre et. ((2004). and we then have," Following the prescriptions of BBS and Wright (2002), we adopt a redshift distribution of the form Taking $\beta = 1.5$ yields good agreement with the redshift surveys of LeFèvvre et (1996) and LeFèvvre et (2004), and we then have" +where all parameters are evaluated at the heating peak.,where all parameters are evaluated at the heating peak. + Eq. (27)), Eq. \ref{eq:gamma}) ) +" shows the competition between the ohmic heating (the first term), and cooling through thermal diffusion (the second term)."," shows the competition between the ohmic heating (the first term), and cooling through thermal diffusion (the second term)." + Changing the surface temperature affects the growth rate by changing the crust temperature at the heating location., Changing the surface temperature affects the growth rate by changing the crust temperature at the heating location. +" If the crust temperature is much greater than Tei, the temperature sensitivity of the resistivity η becomes negligible and the heating feedback effect is lost, thereby stabilizing the system."," If the crust temperature is much greater than $T_{melt}$, the temperature sensitivity of the resistivity $\eta$ becomes negligible and the heating feedback effect is lost, thereby stabilizing the system." + Increasing the current amplitude gives more thermal energy to drive the instability., Increasing the current amplitude gives more thermal energy to drive the instability. + The growth rate is somewhat insensitive to the choice of L., The growth rate is somewhat insensitive to the choice of $L$. +" However, the relationship between the magnetic field and the current (eq. ("," However, the relationship between the magnetic field and the current (eq. (" +"12)) indicates that for a fixed current amplitude jo, larger values of L correspond to larger magnetic fields.","12)) indicates that for a fixed current amplitude $j_0$, larger values of $L$ correspond to larger magnetic fields." +" To obtain crust models with realistic magnetic field amplitudes, the electric current must be concentrated in a relatively small region of the crust."," To obtain crust models with realistic magnetic field amplitudes, the electric current must be concentrated in a relatively small region of the crust." +" Finally, the instability growth rate is highly dependent on the heating location"," Finally, the instability growth rate is highly dependent on the heating location" +interferometry observations. and its high-velocity molecular outflow.,"interferometry observations, and its high-velocity molecular outflow." + Their best-fitting disk model has an inner radius of 0.01 AU. outer radius of 500 AU. and a mass M=0.012Moe.," Their best-fitting disk model has an inner radius of 0.01 AU, outer radius of 500 AU, and a mass $M = 0.012 M_{\sun}$." + Elias 29 was previously observed in X-rays with ASCA. andXMM-Newton.," Elias 29 was previously observed in X-rays with ASCA, and." +". In the oobservation (Imanishietal... 2001)). the source quiescent phase is characterised by a temperature of 4.3 keV and luminosity of 2.0x10°""s7!.. fully consistent with the values derived from the subsequent oobservations by Ozawaetal.(2005):: AT=(3.6—5.1) keV. NCH)=(44-5.3)x107 em. Z=(0.8—1.3)Ze. and Lx=2.8«10°s7!.."," In the observation \citealp{ikt01}) ), the source quiescent phase is characterised by a temperature of 4.3 keV and luminosity of $2.0 \times 10^{30}$, fully consistent with the values derived from the subsequent observations by \citet{ogm05}: $kT = (3.6-5.1)$ keV, $N({\rm H}) = (4.4-5.3) \times +10^{22}$ $^{-2}$, $Z=(0.8-1.3)~Z_{\sun}$, and $L_{\rm X} = 2.8 \times +10^{30}$." + The source was seen flaring during one of the ASCA observations Kamataetal.. 1997)) and during the oobservation., The source was seen flaring during one of the ASCA observations \citealp{kkt+97}) ) and during the observation. + The two flares had similar intensity and duration with an e-folding time of ~10 ks (Tsuboretal.. 20001: etal.. 2001)., The two flares had similar intensity and duration with an $e$ -folding time of $\sim 10$ ks \citealp{tik+00}; ; \citealp{ikt01}) ). + The program is a nominal 500 ks observation of the p- star-forming region performed by the EPIC camera on board the ssatellite., The program is a nominal 500 ks observation of the $\rho$ -Ophiuchi star-forming region performed by the EPIC camera on board the satellite. + The observation was performed over 9.4days. starting 8 March. 2005 (orbits 0961-0965).," The observation was performed over 9.4days, starting 8 March 2005 (orbits 0961–0965)." + Details of the observations and data reduction procedure are given in Pillitterietal. (2007)., Details of the observations and data reduction procedure are given in \citet{psf+07}. +. The preliminary data reduction was done with SAS software version 6.5 in order to obtain lists of photon events calibrated both in energy and astrometry for the three instruments. MOSI. MOS2. and PN. for each orbit.," The preliminary data reduction was done with SAS software version 6.5 in order to obtain lists of photon events calibrated both in energy and astrometry for the three instruments, MOS1, MOS2, and PN, for each orbit." + The data were filtered in the energy band 0.3-10., The data were filtered in the energy band 0.3–10. + keV. and only events with «4 and =0 were retained for the spectral analysis.," keV, and only events with $<4$ and $=0$ were retained for the spectral analysis." + The spectral analysis was performed using the package V11.2. after rebinning the spectra to à minimum of 20 source counts per (variable width) spectral bin.," The spectral analysis was performed using the package V11.2, after rebinning the spectra to a minimum of 20 source counts per (variable width) spectral bin." + Figure 1. shows the light curve of Elias 29 from the three instruments. PN. MOSI. and MOS2. and the six time intervals that we selected for our spectral analysis.," Figure \ref{fig:lc} shows the light curve of Elias 29 from the three instruments, PN, MOS1, and MOS2, and the six time intervals that we selected for our spectral analysis." +" On the basis of the PN data. we selected 5 time intervals with low background (hereafter ""segl"" to ""seg57). plus one time interval covering the strong flare at about 94 ks from the beginning of the observation."," On the basis of the PN data, we selected 5 time intervals with low background (hereafter “seg1” to “seg5”), plus one time interval covering the strong flare at about 94 ks from the beginning of the observation." +" During ""segl"". the MOSI camera was very likely hit by a micro-meteorite (which compromised one of the chips) and the instrument was switched off for the rest of this segment of the observation. during the flare and part of ""seg2""."," During “seg1”, the MOS1 camera was very likely hit by a micro-meteorite (which compromised one of the chips) and the instrument was switched off for the rest of this segment of the observation, during the flare and part of “seg2”." +" MOS? data are available for all the segments of observation. but are insufficient during the flare. thus. we did not include the ""flare"" time interval in the joint spectral analysis of PN and MOS data."," MOS2 data are available for all the segments of observation, but are insufficient during the flare, thus, we did not include the “flare” time interval in the joint spectral analysis of PN and MOS data." +" In addition. we only used PN and MOS?2 data for ""segl"" and ποσο,"," In addition, we only used PN and MOS2 data for “seg1” and “seg2”." + The spectra were initially modelled by an absorbed one-temperature plasma model., The spectra were initially modelled by an absorbed one-temperature plasma model. + The results of the six spectral fits for the PN data alone are reported in Table 1. and the results of the (five) joint fits to the PN. ΜΟΡΙ. and MOS2 data in Table 2..," The results of the six spectral fits for the PN data alone are reported in Table \ref{tab:psfit} and the results of the (five) joint fits to the PN, MOS1, and MOS2 data in Table \ref{tab:psfit_mos}." + For each time-interval. the values of the spectral parameters derived from the simultaneous fitting are very similar to the values derived from the PN data alone.," For each time-interval, the values of the spectral parameters derived from the simultaneous fitting are very similar to the values derived from the PN data alone." + The error bars in the best-fit parameters improve marginally. but y values worsen. likely because of calibration uncertainties.," The error bars in the best-fit parameters improve marginally, but $\chi^2$ values worsen, likely because of calibration uncertainties." +" The spectra and the fits for ""seg1"" and “seg?” are shown in and the spectrum for the flare in reffig:psflare..", The spectra and the fits for “seg1” and “seg2” are shown in \\ref{fig:psfit} and the spectrum for the flare in \\ref{fig:psflare}. + The average values of the source's spectral parameters while quiescent (N(H)=6.8κ107 em. KT=3.7 keV. and Z20.8Ze) are very similar to the values derived from previous observations. so is its quiescent luminosity 10? s7!.. with no evidence of long-term variability.," The average values of the source's spectral parameters while quiescent $N({\rm H}) = 6.8 \times 10^{22}$ $^{-2}$, $kT = 3.7$ keV, and $Z=0.8~Z_{\sun}$ ) are very similar to the values derived from previous observations, so is its quiescent luminosity $L_{\rm X} \sim 10^{30}$ , with no evidence of long-term variability." + The X-ray flare is similar to other events previously observed from this source., The X-ray flare is similar to other events previously observed from this source. + During the flare. the source counts first increased impulsively by a factor of ~8 and then decreased exponentially with a decay time of ~6 ks.," During the flare, the source counts first increased impulsively by a factor of $\sim 8$ and then decreased exponentially with a decay time of $\sim 6$ ks." + The source spectrum during the flare is shown in reffig:psflare.. together with the spectral fit.," The source spectrum during the flare is shown in \\ref{fig:psflare}, together with the spectral fit." + As presented in reftab:psfit.. the fitted value of the plasma temperature does not appear to change significantly during the flare. possibly due to the stringent processing criteria applied to the data that resulted in the events of the flare peak being discarded.," As presented in \\ref{tab:psfit}, the fitted value of the plasma temperature does not appear to change significantly during the flare, possibly due to the stringent processing criteria applied to the data that resulted in the events of the flare peak being discarded." + From reftab:psfit and 2.. it is apparent that the best-fit values of N(H). kT. and Z for the different time intervals do not show significant variations. since they are all consistent. with each other within 2c.," From \\ref{tab:psfit} and \ref{tab:psfit_mos}, it is apparent that the best-fit values of $N({\rm H})$, $kT$, and $Z$ for the different time intervals do not show significant variations, since they are all consistent with each other within $2\sigma$." +" This 1s also apparent by comparing the PN and MOS? spectra from ""segl"" and ""seg2"" in reffig:psfit.. where the overall spectral shape and amplitude are very similar during the two time intervals (in both instruments)."," This is also apparent by comparing the PN and MOS2 spectra from “seg1” and “seg2” in \\ref{fig:psfit}, where the overall spectral shape and amplitude are very similar during the two time intervals (in both instruments)." +" On closer inspection. however. a significant difference between the two time intervals becomes apparent: during time interval ""seg2"". a visible excess of emission around 6.4 keV. the energy of the Fe fluorescent line. is present both in the PN and MOS2 data."," On closer inspection, however, a significant difference between the two time intervals becomes apparent: during time interval “seg2”, a visible excess of emission around 6.4 keV, the energy of the Fe fluorescent line, is present both in the PN and MOS2 data." + To quantify this excess and monitor its variation. we repeated the spectral fits of the spectra with an absorbed IT plasma model and an additional Gaussian line component at 6.4 keV. The position and width (10 eV')) of this component were constrained during the fit. while its normalisation was left free to vary.," To quantify this excess and monitor its variation, we repeated the spectral fits of the spectra with an absorbed 1T plasma model and an additional Gaussian line component at 6.4 keV. The position and width (10 ) of this component were constrained during the fit, while its normalisation was left free to vary." + The other parameters of the absorbed IT plasma model (absorbing column density. temperature. and normalisation of the thermal spectrum) were also free parameters in the fit.," The other parameters of the absorbed 1T plasma model (absorbing column density, temperature, and normalisation of the thermal spectrum) were also free parameters in the fit." + The spectra and spectral fits to the six PN spectra in the energy range AE=4—8 keV are shown in reffig:psine., The spectra and spectral fits to the six PN spectra in the energy range $\Delta E = 4 - 8$ keV are shown in \\ref{fig:ps_line}. +".T hestrongexcessemissionató.AkeVinthespectrao f""seg2"""," The strong excess emission at 6.4 keV in the spectra of “seg2” is well accounted for by the fitted line, while it is clear that no such additional line at 6.4 keV is needed to fit the data from “seg1”." + is Theresults from the spectral fits to the PN data with the additional line at 6.4 keV are summarised in Table 3..., The four other spectra are somewhat in between these two extremes in regard to an excess of emission at 6.4 keV. Theresults from the spectral fits to the PN data with the additional line at 6.4 keV are summarised in Table \ref{tab:psfit_line}. . + As, As +"ranging from 2 GHz up to 43 GHz (Fey&Charlot1997:Keller-etal.2002) show the jet extending up to 40 milli-areseconds (at 2 GHz) to the north-northwest. directly toward the ""counter- at 0.3"" observed by O'Deaetal.(1988).","ranging from 2 GHz up to 43 GHz \citep{FC97,KVZC98,H01,J01,W02} show the jet extending up to 40 milli-arcseconds (at 2 GHz) to the north-northwest, directly toward the ``counter-feature'' at $0.3\arcsec$ observed by \citet{OBC88}." +. These more recent and more sensitive observations (as well as the deep 1.7 GHz observations presented here) show no sign of a southern milli-arcsecond jet. suggesting that the early VLBI results may have simply mis-identified the core.," These more recent and more sensitive observations (as well as the deep 1.7 GHz observations presented here) show no sign of a southern milli-arcsecond jet, suggesting that the early VLBI results may have simply mis-identified the core." +" With a highly superluminal milli-aresecond jet extending to the north-northeast. a bright VLA feature directly in its path at 0.3"". and an aresecond VLA jet oppositely directed by ~180°. the connection between the jets on these scales is an intriguing puzzle."," With a highly superluminal milli-arcsecond jet extending to the north-northeast, a bright VLA feature directly in its path at $0.3\arcsec$, and an arcsecond VLA jet oppositely directed by $\simeq 180^\circ$, the connection between the jets on these scales is an intriguing puzzle." + Here we report the results of observations designed to fill the gap in resolution between the previous VLBI and VLA observations of this source., Here we report the results of observations designed to fill the gap in resolution between the previous VLBI and VLA observations of this source. + The observations are described in82.. and in we suggest and analyze two general models to explain the jet trajectory of this highly superluminal blazar.," The observations are described in, and in we suggest and analyze two general models to explain the jet trajectory of this highly superluminal blazar." +" Throughout this paper we assume a cosmology with Hy270 km s&! Mpe!. 0,=0.3. and O4=0.7. and we choose a spectral index convention: Sj,x»vt""."," Throughout this paper we assume a cosmology with $H_0 = 70$ km $^{-1}$ $^{-1}$ , $\Omega_m = 0.3$, and $\Omega_\Lambda = 0.7$, and we choose a spectral index convention: $S_\nu\propto\nu^{+\alpha}$." + On August I]. 2001 we made deep VLBI observations of PKS [510-089 using the National Radio Astronomy Observatory’s (NRAO) VLBA plus a single VLA antenna (VLBA+tY1I) at 1.7 and 5.0 GHz.," On August 11, 2001 we made deep VLBI observations of PKS $-$ 089 using the National Radio Astronomy Observatory's (NRAO) VLBA plus a single VLA antenna $+$ Y1) at 1.7 and 5.0 GHz." + The observations were taken m dual-polarization mode so that we could study the linear polarization of the jet as a probe of the underlying magnetic field structure., The observations were taken in dual-polarization mode so that we could study the linear polarization of the jet as a probe of the underlying magnetic field structure. + The data were correlated on the VLBA correlator and were processed with NRAO’s Astronomical Imaging Processing System. AIPS. (Bridle&Greisen1994;Greisen1988) and the Caltech DIFMAP package (Shepherd.Pearson.&Taylor1994.1995) using standard techniques for VLBI polarization observations (e.g.Cotton1993:Roberts.Wardle.&Brown 1994).," The data were correlated on the VLBA correlator and were processed with NRAO's Astronomical Imaging Processing System, AIPS, \citep{BG94,G88} + and the Caltech DIFMAP package \citep{SPT94,SPT95} using standard techniques for VLBI polarization observations \citep[e.g.][]{C93,RWB94}." + The feed leakage terms were corrected using the strong. unpolarized source OQ208.," The feed leakage terms were corrected using the strong, unpolarized source OQ208." + Figure | displays our naturally weighted and tapered images of PKS 1510-089 at 1.7 GHz., Figure \ref{f:1510-1} displays our naturally weighted and tapered images of PKS $-$ 089 at 1.7 GHz. + The tapered image was made using a Gaussian weight taper in the (u.v)-plane with a weight factor of 0.3 at a radius of 10 MA.," The tapered image was made using a Gaussian weight taper in the (u,v)-plane with a weight factor of 0.3 at a radius of 10 $\lambda$." + The images show a strong core with a jet extending to the north-northeast for approximately 150 milli-areseconds (mas) before fading., The images show a strong core with a jet extending to the north-northeast for approximately 150 milli-arcseconds (mas) before fading. +" The strong ""counter-feature"" seen by O'Deaetal.(1988). is a prominent feature in both the naturally weighted and tapered maps.", The strong “counter-feature” seen by \citet{OBC88} is a prominent feature in both the naturally weighted and tapered maps. +We do not present polarization maps of our 5 GHz data here. although an intensity map of the milli-aresecond jet is included as part of figure 2..,"We do not present polarization maps of our 5 GHz data here, although an intensity map of the milli-arcsecond jet is included as part of figure \ref{f:1510-2}." + We note that. with three times the resolution of the 1.7 GHz images. the 5 GHz images resolve out most of the extended emission.," We note that, with three times the resolution of the 1.7 GHz images, the 5 GHz images resolve out most of the extended emission." + We do make use of the 5 GHz data to measure the spectral index of the milli-arcsecond scale jet., We do make use of the 5 GHz data to measure the spectral index of the milli-arcsecond scale jet. + Figure 2. is a multi-frame figure showing the jet from aresecond to milli-aresecond scales., Figure \ref{f:1510-2} is a multi-frame figure showing the jet from arcsecond to milli-arcsecond scales. + The first frame (left) is a reprocessed version of the 5 GHz VLA image obtained by O'Deaetal.(1988)., The first frame (left) is a reprocessed version of the 5 GHz VLA image obtained by \citet{OBC88}. +. The second frame (center) is our tapered 1.7 GHz VLBA image with a wider field of view to show that there is no hint of jet emission to the south., The second frame (center) is our tapered 1.7 GHz VLBA image with a wider field of view to show that there is no hint of jet emission to the south. + The third frame (right) is our naturally weighted 5 GHz VLBA image of the milli-arcsecond jet., The third frame (right) is our naturally weighted 5 GHz VLBA image of the milli-arcsecond jet. + At first glance the feature appears to be almost circular in shape. approximately 100 mas in diameter (7500 parsees at >=0.360).," At first glance the feature appears to be almost circular in shape, approximately 100 mas in diameter $\simeq 500$ parsecs at $z=0.360$ )." + The interior of the feature has a sloping brightness profile that increases toward the outside edge., The interior of the feature has a sloping brightness profile that increases toward the outside edge. + The outside edge itself is defined by a sharp brightness gradient and ts distinetly curved. almost semi-circular in shape.," The outside edge itself is defined by a sharp brightness gradient and is distinctly curved, almost semi-circular in shape." + The edge toward the core is less bright and is not clearly defined., The edge toward the core is less bright and is not clearly defined. + The feature is strongly polarized in a narrowly confined region along part of its outside edge., The feature is strongly polarized in a narrowly confined region along part of its outside edge. + Here the fractional polarization climbs well above50%.. and it approaches the theoretical maximum for synchrotron radiation (71% for a=—0.6).," Here the fractional polarization climbs well above, and it approaches the theoretical maximum for synchrotron radiation $71$ for $\alpha=-0.6$ )." + Indeed. at the very outside edge of the feature. the theoretical maximum appears to be exceeded in places: however. polarization and intensity levels have sharp gradients there. and uncertainty in the resulting fractional polarization can be large.," Indeed, at the very outside edge of the feature, the theoretical maximum appears to be exceeded in places; however, polarization and intensity levels have sharp gradients there, and uncertainty in the resulting fractional polarization can be large." + Based on the noise levels in our tapered maps. we can say that the polarization at the very outside edge exceeds at the confidence level.," Based on the noise levels in our tapered maps, we can say that the polarization at the very outside edge exceeds at the confidence level." + The magnetic field must be almost perfectly ordered (as viewed in projection) at this point to explain such high levels of polarization., The magnetic field must be almost perfectly ordered (as viewed in projection) at this point to explain such high levels of polarization. + This provides an important constraint on models for this feature., This provides an important constraint on models for this feature. +" The polarization vectors in the map have been corrected for the integrated rotation measure of —1541 rad/m (Simard-Normandin.Kronberg.&Button1984) which rotates the electric. vectors by 28"" at this frequency.", The polarization vectors in the map have been corrected for the integrated rotation measure of $-15\pm1$ $^2$ \citep{SKB81} which rotates the electric vectors by $28^\circ$ at this frequency. + The resulting polarization angles in this feature agree well with those measured by O'Deaetal.(1988) at 15 GHz., The resulting polarization angles in this feature agree well with those measured by \citet{OBC88} at 15 GHz. + The intrinsic polarization vectors are very nearly perpendicular to the curved outside edge of the feature., The intrinsic polarization vectors are very nearly perpendicular to the curved outside edge of the feature. + The projected magnetic field (907 to the polarization vectors) is therefore parallel to and curving around the outside edge of the feature., The projected magnetic field $90^\circ$ to the polarization vectors) is therefore parallel to and curving around the outside edge of the feature. +" O'Deaetal.(1988) measure an integrated spectral index for the 0.3"" feature of a~—0.6 between the closely spaced frequencies of 15 and 22 GHz. and they note that its integratec flux is 26 mJy at 22 GHz."," \citet{OBC88} measure an integrated spectral index for the $0.3\arcsec$ feature of $\alpha \sim -0.6$ between the closely spaced frequencies of 15 and 22 GHz, and they note that its integrated flux is $26$ mJy at $22$ GHz." + Comparing to our integrated flux of 0.13 Jy at 1.7 GHz. we find the spectral index to indeed be à2—0.6X:0.1 over more than a decade in frequency.," Comparing to our integrated flux of $0.13$ Jy at 1.7 GHz, we find the spectral index to indeed be $\alpha = -0.6\pm0.1$ over more than a decade in frequency." + At —0.6. the spectral index of the feature is less steep than the milli-arcsecond scale jet for which Homanetal.(2002). find a2—0.90.1 from multi-epoch VLBA observations at 15 and 22 GHz.," At $-0.6$, the spectral index of the feature is less steep than the milli-arcsecond scale jet for which \citet{H02} find $\alpha = -0.9\pm0.1$ from multi-epoch VLBA observations at 15 and 22 GHz." + Fitting simple models to our 1.7 and 5 GHz data. we find a spectral index further out (R~20—30 mas) in the aresecond Jet of a2—0.84:0.1.," Fitting simple models to our 1.7 and 5 GHz data, we find a spectral index further out $R\sim20-30$ mas) in the milli-arcsecond jet of $\alpha = -0.8\pm0.1$." + From figure |.. there seems to be little doubt that the 0.3” feature is fed directly by the milli-arcsecond jet.," From figure \ref{f:1510-1}, there seems to be little doubt that the $0.3\arcsec$ feature is fed directly by the milli-arcsecond jet." + In this section we explore the nature of this feature and its relation to the and aresecond scale Jets., In this section we explore the nature of this feature and its relation to the milli-arcsecond and arcsecond scale jets. + Due to its very high. proper motion. we know the axis of the milli-aresecond jet makes a small angle with our line of sight.," Due to its very high proper motion, we know the axis of the milli-arcsecond jet makes a small angle with our line of sight." + For the purposes of this discussion we take this alignment angle. Óvrg4. to be 37. which ts the optimum angle for the superluminal motion of 20c observed by Homanetal.(2001 )..," For the purposes of this discussion we take this alignment angle, $\theta_{VLBA}$, to be $3^\circ$, which is the optimum angle for the superluminal motion of 20c observed by \citet{H01}. ." + The motion in the milli-aresecond jet appears to bestraight along a structural position angle of —28° (Homanetal.2001)., The motion in the milli-arcsecond jet appears to bestraight along a structural position angle of $-28^\circ$ \citep{H01}. +". This motion points directly at the apex of the 0.3"" feature which also has a structural position angle of 287. However. the pathof the jet from a couple milli-areseconds to 0.3” is not entirely straight. and we note that the third panel in figure 2 shows"," This motion points directly at the apex of the $0.3\arcsec$ feature which also has a structural position angle of $-28^\circ$ However, the pathof the jet from a couple milli-arcseconds to $0.3\arcsec$ is not entirely straight, and we note that the third panel in figure \ref{f:1510-2} shows" +We have performed a series of high-resolution RID simulations in 2D to caleulate the jet outflow for physical parameters tvpical of those expected for subenergetic GRD's.,We have performed a series of high-resolution RHD simulations in 2D to calculate the jet outflow for physical parameters typical of those expected for subenergetic GRB's. + From these we have calculated allerelow light curves al various frequencies. covering low radio (75 MIIz) up to N-ray (1.5 keV) and for observer angles from 0 (to 7/2 rad.," From these we have calculated afterglow light curves at various frequencies, covering low radio (75 MHz) up to X-ray (1.5 keV) and for observer angles from 0 to $\pi/2$ rad." + The data for all light curves from (his paper are publicly available via/cosmo.nyu.edu/alterglowlibrary.. that also provides results [rom a more extensive probe of parameter space.," The data for all light curves from this paper are publicly available via, that also provides results from a more extensive probe of parameter space." + We summarize the light curves via smooth power law fits that capture features such as the jet break for small observer angles. (he early time rise due to relativistic beaming for high observer angles ancl the rise and decay of the counterjet.," We summarize the light curves via smooth power law fits that capture features such as the jet break for small observer angles, the early time rise due to relativistic beaming for high observer angles and the rise and decay of the counterjet." + The results here present the most accurate calculations to date of light curve predictions of the standard afterelow jet theory as it applies to short GRBs. fully accounting for aspects such as jet spreading. observer position aud arrival time effects.," The results here present the most accurate calculations to date of light curve predictions of the standard afterglow jet theory as it applies to short GRB's, fully accounting for aspects such as jet spreading, observer position and arrival time effects." + Although we do not diseuss this in detail in this work. the light curves show that SGRB / underluninous afterglows should in principle be observable (at least in the radio) even lor observers outside (he jet cone.," Although we do not discuss this in detail in this work, the light curves show that SGRB / underluminous afterglows should in principle be observable (at least in the radio) even for observers outside the jet cone." + The light curves in this paper and in the on-line database should prove useful for detectability estimates using future radio telescopes such as SIXÀ and LOFAR., The light curves in this paper and in the on-line database should prove useful for detectability estimates using future radio telescopes such as SKA and LOFAR. + Such estimates will also benefit the gravitational waves commnmunitv. since the amount of information that can be extracted. [from GW measurements increases significantly when EM counterparts are observed as well.," Such estimates will also benefit the gravitational waves community, since the amount of information that can be extracted from GW measurements increases significantly when EM counterparts are observed as well." + Furthermore. GW observations can aid the search for EEM counterparts.," Furthermore, GW observations can aid the search for EM counterparts." + In general. (he afterglow light curves are well described by smooth power law fits with up to three breaks. although sometimes the rising phase lor high observer angles is problematic.," In general, the afterglow light curves are well described by smooth power law fits with up to three breaks, although sometimes the rising phase for high observer angles is problematic." + The effects of increasing circumburst densitv aud jet energy. are as expected [rom theoretical models., The effects of increasing circumburst density and jet energy are as expected from theoretical models. + The jet break for small observer angles varies greatly between [requencies. confirming a result Irom VanEertenetal.(2010b).," The jet break for small observer angles varies greatly between frequencies, confirming a result from \cite{vanEerten2010b}." +. Increasing (he observer angle postpones the jet break (il really splits the break into (wo separate breaks. but the second break is the strongest).," Increasing the observer angle postpones the jet break (it really splits the break into two separate breaks, but the second break is the strongest)." + This work was supported in part by NASA under Grant No., This work was supported in part by NASA under Grant No. + 09-ATP09-0190. issued through the Astrophysics Theory Program (ATP)., 09-ATP09-0190 issued through the Astrophysics Theory Program (ATP). + The software used in this work was in part developed by the DOE-supported ASCT/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago., The software used in this work was in part developed by the DOE-supported ASCI/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. +We finally conclude by pointing out that both orbital cases explored in this paper are rather exceptional.,We finally conclude by pointing out that both orbital cases explored in this paper are rather exceptional. + First of all. we ouly considered galaxy models that were initially not tumbling nor rotating.," First of all, we only considered galaxy models that were initially not tumbling nor rotating." + In addition. most cluster ealaxies neither rest in the cluster center nor move ou circular orbits. but they move on clongated orbits with very different pericentric aud apoceutric distances frou the clusters center: m a triaxial cluster many orbits are boxes and some orbits can be chaotic.," In addition, most cluster galaxies neither rest in the cluster center nor move on circular orbits, but they move on elongated orbits with very different pericentric and apocentric distances from the cluster's center; in a triaxial cluster many orbits are boxes and some orbits can be chaotic." + These latter cases can be properly investigated onlv by direct mmuerical simulation of the stellar motions inside the galaxies. coupled with the mmuerical integration of the equations of the motion of the galaxies tlemselves.," These latter cases can be properly investigated only by direct numerical simulation of the stellar motions inside the galaxies, coupled with the numerical integration of the equations of the motion of the galaxies themselves." + Iu. addition. a statistically significant ealaxy population made by the stun of galaxies with different masses. scale-lengths. and flattcnines. should be cousidered.," In addition, a statistically significant galaxy population made by the sum of galaxies with different masses, scale-lengths, and flattenings, should be considered." + We would like to thank Maeda Arnaboldi. Cüuseppe Bertin. Danicl Pfeuniger for useful discussions. and the anouviuous Referee for helpful comunents.," We would like to thank Magda Arnaboldi, Giuseppe Bertin, Daniel Pfenniger for useful discussions, and the anonymous Referee for helpful comments." + VAL is erateful to Ceneva Observatory for allowing the use of their GRAVITOR beowulf cluster., V.M. is grateful to Geneva Observatory for allowing the use of their GRAVITOR beowulf cluster. + Ucre we give the explicit solution of eqs. (, Here we give the explicit solution of eqs. ( +8) for assigned initial conditions (429.59) and (Uy.Ju).,"8) for assigned initial conditions $(\varphi_0,\dphi_0)$ and $(\vartheta_0,\dtheta_0)$." + As shown in CGO. the two mixed equations of the second order Gvhere the 1 cocficicuts ly.do.By.Bo are given in eqs. ," As shown in CG98, the two mixed equations of the second order (where the 4 coefficients $A_1,A_2,B_1,B_2$ are given in eqs. [" +151. can be separated in two ideutical biquadratic equations. cach of them involving only one of the two variables ο and .,"8]), can be separated in two identical biquadratic equations, each of them involving only one of the two variables $\varphi$ and $\vartheta$." + For example. the equation for 5 can be written as where asοο 0=Lofts. nd the functions Oc(r) aud q(r) are given in Sect.," For example, the equation for $\varphi$ can be written as where $u\equiv\Iu/\It$, $v\equiv\Id/\It$, and the functions $\Omegac(r)$ and $q(r)$ are given in Sect." + 3.2., 3.2. + The standard substitution in eq. (, The standard substitution in eq. ( +A.2) leads to the characteristic equation wiAw?D|B=0. whose solutions. can bo written- as uote that in case of a stable equilibrium for the galaxy configuration (Cas asstuued in this paper). the roots A+ are positive. and that from eqs. C,"A.2) leads to the characteristic equation $\omega^4 -A\omega^2 + B=0$, whose solutions can be written as note that in case of a stable equilibrium for the galaxy configuration (as assumed in this paper), the roots $\lambdapm$ are positive, and that from eqs. (" +À.3)-(À.1) w»Q..,A.3)-(A.4) $\omega\propto\Omegac$. + Thus. the eeucral solution of eqs. (," Thus, the general solution of eqs. (" +8) can be written as where the four amplitudes αιδισ aud phases ay.by.609.dy aust be determined by imposing the [initial conditions at f=0.,"8) can be written as where the four amplitudes $a,b,c,d$ and phases $a_0,b_0,c_0,d_0$ must be determined by imposing the 4 initial conditions at $t=0$." + The remaining four constraints are provided bv the request that eqs. (, The remaining four constraints are provided by the request that eqs. ( +A.6) satisfv eqs.CAT) at anytime: the ideutities involving amplitudes can be also written in terms of C aud By instead of A aud By.,A.6) satisfy eqs.(A.1) at anytime: the identities involving amplitudes can be also written in terms of $C$ and $B_2$ instead of $A$ and $B_1$. + We can now proceed to impose the initial conditions ou eqs.(A.6)., We can now proceed to impose the initial conditions on eqs.(A.6). + The easiest wav is to define the 6 new quantities note that r; andr are known., The easiest way is to define the 6 new quantities note that $\rop$ and $\rom$ are known. + Evaluating eqs. (, Evaluating eqs. ( +A.6) at f—0. and using eqs. (,"A.6) at $t=0$, and using eqs. (" +A.7)-(A.8) one obtains The first 1 equations above cau be solved for the uukuowns eX. dY. cU. dV in terms of re. (Ju.09). Go.So): then the two independent phases and amplitudes are obtained as The remaining quantities are finally deteruumed from eqs. (,"A.7)-(A.8) one obtains The first 4 equations above can be solved for the unknowns $cX$, $dY$, $cU$, $dV$ in terms of $r_{\pm}$, $(\vartheta_0,\dtheta_0)$, $(\varphi,\dphi_0)$: then the two independent phases and amplitudes are obtained as The remaining quantities are finally determined from eqs. (" +A.7)-(A.9).,A.7)-(A.9). + As in eqs. (, As in eqs. ( +11). (12) and (19) let use assume that where i is defined as in eq. (,"11), (12) and (19) let use assume that where $m$ is defined as in eq. (" +13). and fj is a normalization coustaut for deusitv.,"13), and $\rhon$ is a normalization constant for density." + The total mass of the model (when finite) is given by where For example. in eqs. (," The total mass of the model (when finite) is given by where For example, in eqs. (" +"11). (12). and (19) ME=1/(3. 3). M= 1/30. and M=x l. respectively,","11), (12), and (19) $\M = 1/(3-\gamma)$ , $\M +=1/30$ , and $\M =\pi /4$ , respectively." + Froii. potential theory. the general expression for o.(€) is found using the," From potential theory, the general expression for $\phig (\csiv)$ is found using the" +0.5 (cf.,$-0.5$ (cf. + the references cited above). a strikinely clillerent enrichment level than in the Alilky Was stellar halo. and a strong indicator ofa different formation history (c.g. Durrell. llarris. Pritchet 2001).," the references cited above), a strikingly different enrichment level than in the Milky Way stellar halo, and a strong indicator of a different formation history (e.g. Durrell, Harris, Pritchet 2001)." + Although there have been many AIDE studies. of halo stars in Local Group members. galaxies beyond. the Local Group have only. recently been investigated. through HSTAWVEPC? photometry anc for only a small number of cases: the giant. LE/SO NGC 5128 (Soria ct al.," Although there have been many MDF studies of halo stars in Local Group members, galaxies beyond the Local Group have only recently been investigated through /WFPC2 photometry and for only a small number of cases: the giant E/S0 NGC 5128 (Soria et al." + 1996: Larris. llarris. Poole 1999 hereafter referred. to as LILI: Harris Llarris 2000. LILIOO: Larris Harris 2002. HIEIO2: Marleau et al.," 1996; Harris, Harris, Poole 1999 hereafter referred to as HHP; Harris Harris 2000, HH00; Harris Harris 2002, HH02; Marleau et al." + 2000). the edge-on SO NGC 3115 (Elson LOOT: Ixundu Whitmore 1998). and. two dwarf ellipticals in the MSI eroup (Caldwell et al.," 2000), the edge-on S0 NGC 3115 (Elson 1997; Kundu Whitmore 1998), and two dwarf ellipticals in the M81 group (Caldwell et al." + 1998)., 1998). + Furthermore. Rejkuba et al. (," Furthermore, Rejkuba et al. (" +2002) have demonstrated the existence. of a significant intermediate-age AGB population in parts of the NGC 5128 ido. based on deep C. V. and A. color-magnitude and color-color diagrams of halo stars resolved by VLT.,"2002) have demonstrated the existence of a significant intermediate-age AGB population in parts of the NGC 5128 halo, based on deep $U$, $V$, and $K_{s}$ color-magnitude and color-color diagrams of halo stars resolved by VLT." + A remarkable result. emerging from the £S7/WEPC2 xhotometrv. of the old-halo red eint. stars in NGC 5128 is he dominance of moderately. metal-rich stars in the range ] « m/l) « 0.0 (LILLP.. ΕΕ ΕΕ LI," A remarkable result emerging from the /WFPC2 photometry of the old-halo red giant stars in NGC 5128 is the dominance of moderately metal-rich stars in the range $-1$ $<$ [m/H] $<$ 0.0 (HHP, HH00, and HH02)." +LLO0 anc L102 suggested that the relatively high. mean abundance and small fraction (~ 10'4)) of metal-poor stars with mj/ll E lcan ogive stronge constraints on the total mass ofdwarl galaxies hat could. be accreted by NGC 5128 and. then disrupted to form its faint stellar halo., HH00 and HH02 suggested that the relatively high mean abundance and small fraction $\sim$ ) of metal-poor stars with [m/H] $<$ $-1$ can give strong constraints on the total mass of dwarf galaxies that could be accreted by NGC 5128 and then disrupted to form its faint stellar halo. + To date. however. there are only a few attempts a physical interpretation of this material.," To date, however, there are only a few attempts at physical interpretation of this material." +" LILLOO discussed a one-zone model of chemical evolution of this galaxy. anc suggested that it experienced. two fairly distinct stages of halo formation: an carly “accreting box” stage when the galaxy is assembling through infall of star-forming gas clumps. and then a major stage of ""closed-box evolution when the star formation proceeds in the galaxy with little eas infall."," HH00 discussed a one-zone model of chemical evolution of this galaxy and suggested that it experienced two fairly distinct stages of halo formation: an early “accreting box” stage when the galaxy is assembling through infall of star-forming gas clumps, and then a major stage of “closed-box” evolution when the star formation proceeds in the galaxy with little gas infall." + IILIO2. extended this basic. picture further to a more generalized. accretine-box formation model. in which he infall rate of unenriched. gas is envisaged to start at a high rate and then dies away exponentially. while star ormation continues throughout until the gas supply is exhausted.," HH02 extended this basic picture further to a more generalized accreting-box formation model, in which the infall rate of unenriched gas is envisaged to start at a high rate and then dies away exponentially, while star formation continues throughout until the gas supply is exhausted." + With appropriate choices of eas infall rate ancl he elfeetive chemical vield. excellent overall matches to the observed. MDEs can be obtained.," With appropriate choices of gas infall rate and the effective chemical yield, excellent overall matches to the observed MDFs can be obtained." + Recently. Beasley ct al. (," Recently, Beasley et al. (" +2002a. b) have further discussed. the origin of the stellar ido MDE within the context of a semi-analvtie model of ealaxy formation (CLALEOIUM). based on the Cold Dark Alatter (CDM). picture.,"2002a, b) have further discussed the origin of the stellar halo MDF within the context of a semi-analytic model of galaxy formation (GALFORM), based on the Cold Dark Matter (CDM) picture." +" In this model. star formation can ake place in two modes. a ""quiescent mode within the relatively unenriched. pregalactic clouds. and a “starburst” mode whenever two roughly equal clouds suddenly. merge."," In this model, star formation can take place in two modes, a “quiescent” mode within the relatively unenriched pregalactic clouds, and a “starburst” mode whenever two roughly equal clouds suddenly merge." + They demonstrated that the global metallicity clistribution within moclel galaxies comparable to NGC 5128 in size is broadly consistent with the observed MDE. although the model is unable to provide any information on the spatial clistribution or radial change in the MDE.," They demonstrated that the global metallicity distribution within model galaxies comparable to NGC 5128 in size is broadly consistent with the observed MDF, although the model is unable to provide any information on the spatial distribution or radial change in the MDF." + These previous studies are based. on one-zone models of chemical evolution and thus cannot spatially resolve the various clistinet stellar compements (Le. halo. bulge. and disc) in a galaxy.," These previous studies are based on one-zone models of chemical evolution and thus cannot spatially resolve the various distinct stellar components (i.e., halo, bulge, and disc) in a galaxy." + Accordingly. comparisons of these models with the MDEs observed at. ¢lilferent. places in NCC 5128 jwe limited value.," Accordingly, comparisons of these models with the MDFs observed at different places in NGC 5128 have limited value." + Numerica simulations which enable us o resolve spatially the halo. bulge. and disc components and thereby to. investigate he MDE for each of these components should be very heplul for better understanding he formation of galactic stellw haloes.," Numerical simulations which enable us to resolve spatially the halo, bulge, and disc components and thereby to investigate the MDF for each of these components should be very helpful for better understanding the formation of galactic stellar haloes." + The purpose of this paper is to investigate the origin of he MDE of the stellar halo o£ OC 5128 based on numerica simulations of elliptical galaxy formation., The purpose of this paper is to investigate the origin of the MDF of the stellar halo of NGC 5128 based on numerical simulations of elliptical galaxy formation. +" We here adopt the asic ""merger"" approach (Loomre 1977) in which elliptica ealaxies are proposed to be formed by major merging of two spiral galaxies.", We here adopt the basic “merger” approach (Toomre 1977) in which elliptical galaxies are proposed to be formed by major merging of two spiral galaxies. + Within the context of this assumption. we investigate the final MDE of the outer halo component. of 1ο merger remnant (ic.. the giant IE galaxy) as well as its ependence on the input. parameters of the progenitor cliscs (c.g.. the MDEs of disces. bulge-to-disc-ratio. and halo mass raction of the disc).," Within the context of this assumption, we investigate the final MDF of the outer halo component of the merger remnant (i.e., the giant E galaxy) as well as its dependence on the input parameters of the progenitor discs (e.g., the MDFs of discs, bulge-to-disc-ratio, and halo mass fraction of the disc)." + Comparing the simulated. MDEs with 16 observed. ones for NGC 5128. we discuss the following xus: (1) how the dynamics of galaxy merging is important or the formation of the gl stellar halo. (2) how the initial AIDE of a disc (or bulge) in a merger controls the final NDE of the stellar halo. (3) whether the bulge-to-disc ratio of a merger progenitor spiral is important for the determination of the stellar halos AIDE. (4) what initial conditions of galaxy mergers in the present simulations can best give the AIDE. similar to the observed one. (5) the relevance of the AIDE for the globular cluster system. which is cillerent from he field-halo stars. and (6) whether. on the grounds of the merger picture. we should always expect the MDESs of stellar woes in elliptical galaxies (12) to be svstematically dilferen (more metal-rich) from those in late-tvpe spirals (Sp).," Comparing the simulated MDFs with the observed ones for NGC 5128, we discuss the following points: (1) how the dynamics of galaxy merging is important for the formation of the gE stellar halo, (2) how the initial MDF of a disc (or bulge) in a merger controls the final MDF of the stellar halo, (3) whether the bulge-to-disc ratio of a merger progenitor spiral is important for the determination of the stellar halo's MDF, (4) what initial conditions of galaxy mergers in the present simulations can best give the MDF similar to the observed one, (5) the relevance of the MDF for the globular cluster system, which is different from the field-halo stars, and (6) whether, on the grounds of the merger picture, we should always expect the MDFs of stellar haloes in elliptical galaxies (E) to be systematically different (more metal-rich) from those in late-type spirals (Sp)." + The plan of the paper is as follows: In the nex section. we describe our numerical. models. for stellar halo ormation in galaxy mergers.," The plan of the paper is as follows: In the next section, we describe our numerical models for stellar halo formation in galaxy mergers." + In 83. we present the numerica results mainlv on the final MDEs of merger remnants (1.6.. elliptical galaxies) for variously dilferent merger models.," In 3, we present the numerical results mainly on the final MDFs of merger remnants (i.e., elliptical galaxies) for variously different merger models." + In Ed. we predict a possible. relationship between MDEs. of stellar haloes ancl physical properties of their host elliptica ealaxies.," In 4, we predict a possible relationship between MDFs of stellar haloes and physical properties of their host elliptical galaxies." + In this section. we also discuss the origin of M31s metal-rich stellar halo.," In this section, we also discuss the origin of M31's metal-rich stellar halo." + We summarize our conclusions in €5., We summarize our conclusions in 5. + In the model calculations. we numerically investigate dynamical evolution of major galaxy mergers between spiral galaxies whose primary components are dark matter haloes. stellar disces. stellar haloes. and globular clusters (GC's).," In the model calculations, we numerically investigate dynamical evolution of major galaxy mergers between spiral galaxies whose primary components are dark matter haloes, stellar discs, stellar haloes, and globular clusters (GCs)." + In the present study. we do not include gaseous components hus no star formation) in the simulations so that all of the halo stars in the mergerὃν remnant come from the pre-existinge μαellar components of the progenitor spirals.," In the present study, we do not include gaseous components (thus no star formation) in the simulations so that all of the halo stars in the merger remnant come from the pre-existing stellar components of the progenitor spirals." + The density profiles of dark matter and cise Components in a spiral follow o. Fall-Efstathiou (1980) model., The density profiles of dark matter and disc components in a spiral follow the Fall-Efstathiou (1980) model. + The total mass and the, The total mass and the +BAL tvpe.,$BM$ type. +" In this case the value of statistics /=2.99. which is greater than /,. therefore we conclude that velocity dispersion decreases with DÀ tvpe."," In this case the value of statistics $t=2.99$, which is greater than $t_{cr}$, therefore we conclude that velocity dispersion decreases with $BM$ type." + This effect is almost at 30 level., This effect is almost at $\sigma$ level. + In Fig., In Fig. + 5c the dependence on the cluster richness and (the velocity dispersion is presented., 5c the dependence on the cluster richness and the velocity dispersion is presented. + The value /=e/co(a)1.31 in the case of p angle and /=1.18. when considering the orientation of galaxy. planes.," The value $t=a/\sigma(a)= 1.31$ in the case of $p$ angle and $t=1.18$, when considering the orientation of galaxy planes." + We analvzed the alignment of galaxies belonging to 247 Abell clusters containing al least LOO members., We analyzed the alignment of galaxies belonging to 247 Abell clusters containing at least 100 members. + Using statistical tests we confirmed suggestion of Godlowskiet(2005) that non randomness of galaxy orientation in clusters increases significantly with the eluster richness., Using statistical tests we confirmed suggestion of \citet{Godlowski05} that non randomness of galaxy orientation in clusters increases significantly with the cluster richness. + Such confirmation follows from the analvses of all three investigated angles 9p. 1j and p.," Such confirmation follows from the analyses of all three investigated angles $\delta_D$, $\eta$ and $p$." + These angles are connected with the orientation of galaxies and therefore with the distribution of galaxy angular momenta., These angles are connected with the orientation of galaxies and therefore with the distribution of galaxy angular momenta. + The effect increases if we restricted the cluster membership to galaxies brighter (han ma2+3. which suggest that this effect is really connected with clusters.," The effect increases if we restricted the cluster membership to galaxies brighter than $m_3+3$, which suggest that this effect is really connected with clusters." + The observed dependency on the alienment of galaxies in clusters and richness of the cluster leads to the conclusion that angular momentum of the cluster increases with the mass of the structure., The observed dependency on the alignment of galaxies in clusters and richness of the cluster leads to the conclusion that angular momentum of the cluster increases with the mass of the structure. + Usually this dependence is presented as empirical relation J~M?oE (Wesson1979.19823:Carrasco1982:Brosche1986).," Usually this dependence is presented as empirical relation $J\sim M^{5/3}$ \citep{Wesson79,Wesson83,Carrasco82,Brosche86}." +. The aim of this relation has been discussed for a long time., The aim of this relation has been discussed for a long time. + One of the first explanation was proposed by Muradyan(1975) in terms of the Ambarzumian’s superdense cosmogony. while Mackrossan(1987) involved termodyvnanmical consideration for its explanation.," One of the first explanation was proposed by \citet{Muradyan75} in terms of the Ambarzumian's superdense cosmogony, while \citet{Mackrossan87} involved termodynamical consideration for its explanation." + Wesson(1983) argued that this is a consequence of self similarity of Newtonian problem applied to rotating &ravitationallyv bound svstems., \citet{Wesson83} argued that this is a consequence of self similarity of Newtonian problem applied to rotating gravitationally bound systems. +The relation was used for pointing out its possible role in the unification of the eravitation and particle physics (Wesson 1981).,The relation was used for pointing out its possible role in the unification of the gravitation and particle physics \citep{Wesson81}. +. Catelan&Theuns(1996) joined the, \citet{Catelan96} joined the +Here I use the methods aud software described above to compare the survey capabilities of two proposed observatories:SNAP wotlc represeit the state of the art in orbiting imaging observatories late in the decade. with a 1 deg?> CCD FCIV behiud a 2-meter teescope.,"Here I use the methods and software described above to compare the survey capabilities of two proposed observatories: would represent the state of the art in orbiting imaging observatories late in the decade, with a 1 $^{2}$ CCD FOV behind a 2-meter telescope." + The (LSST) would lisewlse represent the state of the art iu large grouucd-base survey telescopes. with z7 deg? FOV behiud au s.|-ueter primary iirror.," The ) would likewise represent the state of the art in large ground-based survey telescopes, with $\approx +7$ $^{2}$ FOV behind an 8.4-meter primary mirror." + In erms of imaging throiehput. each tustriment wotld be z2 orders of nae.itucle faster than present-day counterparts.," In terms of imaging throughput, each instrument would be $\approx2$ orders of magnitude faster than present-day counterparts." + ΤΙe space aud erouud observaories. howeve*. have ve‘y distiuct. strenetls. alle would likely be [οςsed on very different science goals.," The space and ground observatories, however, have very distinct strengths, and would likely be focused on very different science goals." + The asstuumect claracteristies of the two observatories are cetailec in Table 1.., The assumed characteristics of the two observatories are detailed in Table \ref{obschars}. +" The tm»ortaut differences to note aeC For wavelengths beyoud 1 jan. I posit eitherLSST or to beequipped with a mosaic of 16 2kx2kx15,un. HeCdTe array detectors. with Le read noise aud 0.02 e/s dark current."," The important differences to note are: For wavelengths beyond 1 $\mu$ m, I posit either or to beequipped with a mosaic of 16 $\times$ $\times15\mu$ m HgCdTe array detectors, with 4e read noise and 0.02 e/s dark current." + The HeCdTe pixels are assumed to have a dead. zone on each edge., The HgCdTe pixels are assumed to have a dead zone on each edge. + I presume for now that the NIB arrays would have the same focal ratio andCosimic-ray rates as the posited CCD arrays., I presume for now that the NIR arrays would have the same focal ratio andcosmic-ray rates as the posited CCD arrays. + Figure 6 compares tle speed for a photometric point-source survey ou relative to SNAP., Figure \ref{ptsrc} compares the speed for a photometric point-source survey on relative to . +Carbon is one of the most common elements. but we know surprisingly little about its origin.,"Carbon is one of the most common elements, but we know surprisingly little about its origin." + What we do know. however. is that it is ubiquitous throughout the Universe. and can be found in just about any astrophysical environment.," What we do know, however, is that it is ubiquitous throughout the Universe, and can be found in just about any astrophysical environment." + We also know that life. as we know it. requires the existence of carbon. nitrogen. oxygen and a few other elements.," We also know that life, as we know it, requires the existence of carbon, nitrogen, oxygen and a few other elements." + Understanding the origin of carbon may therefore tell us something about the probability of finding carbon-based life elsewhere in the Galaxy. te.. beyond the solar neighbourhood.," Understanding the origin of carbon may therefore tell us something about the probability of finding carbon-based life elsewhere in the Galaxy, i.e., beyond the solar neighbourhood." + The stellar origin of carbon is mainly due to the Triple- reaction (Salpeter1952) but this reaction may occur in various types of stars., The stellar origin of carbon is mainly due to the Triple-Alpha reaction \cite{Salpeter52} but this reaction may occur in various types of stars. + Carbon Stars (C-stars) have been recognised as a class of astronomical object for more than a century and have several times been suggested as the main carbon sources in the Universe., Carbon Stars (C-stars) have been recognised as a class of astronomical object for more than a century and have several times been suggested as the main carbon sources in the Universe. + Already in the work by Burbidge et al. (, Already in the work by Burbidge et al. ( +1957) — it was suggested that carbon was provided by mass-loss from red giants and supergiants.,1957) \nocite{Burbidge57} it was suggested that carbon was provided by mass-loss from red giants and supergiants. + Later Dearborn (1978) suggested that low-mass stars may be a significant source of carbon in planetary nebulae., Later Dearborn (1978) \nocite{Dearborn78} suggested that low-mass stars may be a significant source of carbon in planetary nebulae. + Recent theoretical work on stellar evolution of low and intermediate mass (LIM) stars also. low-mass stars as significant producers of carbon. although the quantative results may differ (Marigo2001:Izzardetal.2004:Gavilán2005:Karakas&Lattanzio2007 ).," Recent theoretical work on stellar evolution of low and intermediate mass (LIM) stars also low-mass stars as significant producers of carbon, although the quantative results may differ \cite{Marigo01,Izzard04,Gavilan05,Karakas07}." +. Aodels of chemical evolution (CEMs) are in general in good agreement with observed abundances if a delayed carbon release from LIM-stars is assumed., Models of chemical evolution (CEMs) are in general in good agreement with observed abundances if a delayed carbon release from LIM-stars is assumed. + Timmes et al. (, Timmes et al. ( +1995) used the nucleosynthetie yields by Woosley Weaver (1995. from hereon cited as WW95) and Renzini Voli (1981). which led to à very significant contribution of carbon from LIM-stars to the Galactic Disc. and more recent work (using other sets of yields for LIM-stars) have led to quite similar results (Chiappinietal.2003:Akerman2004:Carigi2005;Gavilanetal. 2005).,"1995) \nocite{Timmes95} used the nucleosynthetic yields by Woosley Weaver (1995, from hereon cited as WW95) and Renzini Voli (1981), which led to a very significant contribution of carbon from LIM-stars to the Galactic Disc, and more recent work (using other sets of yields for LIM-stars) have led to quite similar results \cite{Chiappini03,Akerman04,Carigi05,Gavilan05}." +. However. Maeder (1992) — argued that radiatively driven winds from high-mass (HM) stars should provide huge amounts of helium and carbon.," However, Maeder (1992) \nocite{Maeder92} argued that radiatively driven winds from high-mass (HM) stars should provide huge amounts of helium and carbon." + In such case. these stars would be the main contributors. and in CEMs the of LIM-stars would have to be much less significant to avoid over-production. of carbon compared. with. observed. abundances.," In such case, these stars would be the main contributors, and in CEMs the of LIM-stars would have to be much less significant to avoid over-production of carbon compared with observed abundances." + Garnett et al. (, Garnett et al. ( +1995). observed that the C/O-ratio increased with increasing O/H in dwarf irregular galaxies. which they interpreted as consistent with carbon being produced in with metallicity-dependent yields. as in the models by Maeder (1992) and Portinart et al. (,"1995) \nocite{Garnett95} observed that the C/O-ratio increased with increasing O/H in dwarf irregular galaxies, which they interpreted as consistent with carbon being produced in with metallicity-dependent yields, as in the models by Maeder (1992) and Portinari et al. (" +1998).,1998). + Following that idea. argued that the rising C/O-trend with metallicity that they found in Galactic-dise stars was the result of carbon being produced in HM-stars rather than LIM-stars.," Following that idea, argued that the rising C/O-trend with metallicity that they found in Galactic-disc stars was the result of carbon being produced in HM-stars rather than LIM-stars." + Recent observations have revealed a declining trend for the C/O ratio in the solar neighbourhood at early times (Akermanetal.2004:Fabbianetal. 2009a).," Recent observations have revealed a declining trend for the C/O ratio in the solar neighbourhood at early times \cite{Akerman04,Fabbian09}." +. C/O vs. O/H shows a negative slope roughly until. the anticipated onset of dise formation. Le. during the first billion. years of Galactic evolution. which is in disagreement (see.e.g.Chiappinietal.2003:Gavilánetal.2005) with the predictions of CEMs do not include any modifications of the carbon and oxygen yields.," C/O vs. O/H shows a negative slope roughly until the anticipated onset of disc formation, i.e., during the first billion years of Galactic evolution, which is in disagreement \cite[see, e.g.][]{Chiappini03,Gavilan05} with the predictions of CEMs do not include any modifications of the carbon and oxygen yields." + connected to the first generations of stars in the Milky Way. and may therefore haveof early chemical evolution.," connected to the first generations of stars in the Milky Way, and may therefore have early chemical evolution." + For instance. the underabundance of essentially metal-free LIM-stars in the halo. which ts often claimed to be a result of a top-heavy initial mass function (IMF) at early times (see.e.g..Abeletal.2002:Tumlinson2006:Karlssonetal.2008.andreferences therein). is one such problem.," For instance, the underabundance of essentially metal-free LIM-stars in the halo, which is often claimed to be a result of a top-heavy initial mass function (IMF) at early times \cite[see, e.g.,][and references therein]{Abel02,Tumlinson06,Karlsson08}, is one such problem." + If the IMF has evolved from being initially top-heavy. to the form that is observed in the solar neighbourhood today. it is possible that this may affect the evolution of the C/O ratio as well.," If the IMF has evolved from being initially top-heavy, to the form that is observed in the solar neighbourhood today, it is possible that this may affect the evolution of the C/O ratio as well." + Chiappini et al. (, Chiappini et al. ( +2000) have considered an evolving IMF. but concluded that it did not improve the agreement with observational constraints.,"2000) have considered an evolving IMF, but concluded that it did not improve the agreement with observational constraints." + However. their study did not focus on the early chemical evolution and abundance trends at very low metallicity.," However, their study did not focus on the early chemical evolution and abundance trends at very low metallicity." + In this paper. the origin of carbon is investigated once again. using a set of multi-zone CEMs for the Milky Way.," In this paper, the origin of carbon is investigated once again, using a set of multi-zone CEMs for the Milky Way." + Several nucleosynthetic prescriptions are considered. as well as the effects of an evolving IMF.," Several nucleosynthetic prescriptions are considered, as well as the effects of an evolving IMF." +rredshift and luminosity distributions.,redshift and luminosity distributions. + The aand ecorrelations are derived in Section 6., The and correlations are derived in Section 6. + A discussion and summary follows in Section T., A discussion and summary follows in Section 7. + The GUSBAD catalog (Schmidt2006) is based on observations with the BATSE LAD detectors which provide output in lour enerev channels. viz.," The GUSBAD catalog \citep{sch06} is based on observations with the BATSE LAD detectors which provide output in four energy channels, viz." + 20—50 keV (eh 1). 50—100 key (ch 2). 100—300 keV (ch 3). and >300 keV (ch 4).," $20-50$ keV (ch 1), $50-100$ kev (ch 2), $100-300$ keV (ch 3), and $> 300$ keV (ch 4)." + The catalog lists peak photon fluxes for channels 2 and 3 (together., The catalog lists peak photon fluxes for channels 2 and 3 together. +" These were derived assuming a Band spectrum with a=—1.0. 9=—2.0. and £z,=200 keV. For the present study. we have derived for each GRB peak photon fluxes in each channel based on the two brightest illuminated LAD detectors."," These were derived assuming a Band spectrum \citep{ban93} with $\alpha = -1.0$, $\beta = -2.0$, and $E_0 = 200$ keV. For the present study, we have derived for each GRB peak photon fluxes in each channel based on the two brightest illuminated LAD detectors." + At (he outset of this study. it was not clear whether the four channels of the BATSE LAD detectors could be used for low-resolution spectrophotometry.," At the outset of this study, it was not clear whether the four channels of the BATSE LAD detectors could be used for low-resolution spectrophotometry." + We decided to use only GRBs with a 50—300 keV peak photon flux 7? exceeding 0.50 ph em7s ! je. twice the effective photon this limit of the GUSDAD catalog.," We decided to use only GRBs with a $50-300$ keV peak photon flux $P$ exceeding 0.50 ph $^{-2}$ $^{-1}$, i.e. twice the effective photon flux limit of the GUSBAD catalog." + This still leaves a large sample of 1319 GRBs., This still leaves a large sample of 1319 GRBs. + The Euclidean value of iis simply —(Pj/Prin)y3/2⋅The value of {for uniformly. distributed objects having any Iuminosity function in Euclidean space is 0.5., The Euclidean value of is simply $= (P/P_{lim})^{-3/2}$.The value of for uniformly distributed objects having any luminosity function in Euclidean space is $0.5$. + This value derives [rom the fact that volumes are ~A275 and areas ~A7., This value derives from the fact that volumes are $\sim R^3$ and areas $\sim R^2$. + This will not apply in non-Euclidean space. so for cosmological objects the Euclidean value of wwill deviate [rom 0.5. the more so the larger the tvpical redshift. 1.e.. il is a cosmological distance indicator.," This will not apply in non-Euclidean space, so for cosmological objects the Euclidean value of will deviate from $0.5$, the more so the larger the typical redshift, i.e., it is a cosmological distance indicator." + Concern has been expressed in the literature about the use of particularly when sample thresholds vary (Banc1992:Pelrosian1993:Hartmann.1993).," Concern has been expressed in the literature about the use of particularly when sample thresholds vary \citep{ban92,pet93,har93}." +". The problem of varxing threshold can be handled if each object has its own value of £7, as in the GUSDAD catalog.", The problem of varying threshold can be handled if each object has its own value of $P_{lim}$ as in the GUSBAD catalog. + In our present study. the adopted constant limit of 0.50 ph ? Lis larger than all individual limits in the catalog.," In our present study, the adopted constant limit of 0.50 ph $^{-2}$ $^{-1}$ is larger than all individual limits in the catalog." + All well delinecl samples above a given flux limit are subject to the Eddington effect (Eddington1913. 1940).," All well defined samples above a given flux limit are subject to the Eddington effect \citep{edd13,edd40}." +. Random errors in (he fluxes of individual objects if positive may, Random errors in the fluxes of individual objects if positive may +"have used projections of their 3D map, that showed the clumpy structure of the ejecta, as well as hints of the ring-like structure of the ejecta.","have used projections of their 3D map, that showed the clumpy structure of the ejecta, as well as hints of the ring-like structure of the ejecta." +" They also created an interactive 3D map, that enables the reader to zoom, pan, rotate and fly around and through their 3D map."," They also created an interactive 3D map, that enables the reader to zoom, pan, rotate and fly around and through their 3D map." +" Stereo pairs, together with those others visualization methods, confirmed the presence of the ring structure, and ruled out any perspective effects due to the projection of the 3D map on a 2D plane."," Stereo pairs, together with those others visualization methods, confirmed the presence of the ring structure, and ruled out any perspective effects due to the projection of the 3D map on a 2D plane." +" The stereo pairs are very efficient in this ring to the reader, compared to, e.g., a montage of slices."," The stereo pairs are very efficient in this ring to the reader, compared to, e.g., a montage of slices." +" This is a big advantage in the case of SNR. N132D, for which the actual shape of the ejecta has been subject to interpretation since the discovery of the remnant (seeLasker1980;Morseetal.1995;VogtandDopita 2011)."," This is a big advantage in the case of SNR N132D, for which the actual shape of the ejecta has been subject to interpretation since the discovery of the remnant \citep[see][]{Lasker80,Morse95,Vogt10c}." +". Everyone can the ring, and the impression of depth given by stereo pairs is a valuable complement to the interactive 3D map."," Everyone can the ring, and the impression of depth given by stereo pairs is a valuable complement to the interactive 3D map." + Those stereo pairs have been created with using the sTi technique described in Sect. ??.., Those stereo pairs have been created with using the sTi technique described in Sect. \ref{Sec:tools}. +" The whole code, that takes as an input the data cube in a format, contains less than 50 lines, of which only 10 are actually responsible for plotting the data."," The whole code, that takes as an input the data cube in a format, contains less than 50 lines, of which only 10 are actually responsible for plotting the data." + Stereo pairs can also be used for the visualization of theoretical data sets., Stereo pairs can also be used for the visualization of theoretical data sets. +" In this example, we use stereoscopy to reveal the structure of a simulated relativistic Active Galactic Nucleus (AGN) jet (WagnerandBicknell 2011)."," In this example, we use stereoscopy to reveal the structure of a simulated relativistic Active Galactic Nucleus (AGN) jet \citep[][]{Wagner10}." +". The jet simulations were grid-based hydrodynamic simulations which produced multivariate data of thermodynamic quantities, e.g., density, temperatu pressure, velocity components and tracers, as functions of 3 rectilinear spatial coordinates."," The jet simulations were grid-based hydrodynamic simulations which produced multivariate data of thermodynamic quantities, e.g., density, temperature, pressure, velocity components and tracers, as functions of 3 rectilinear spatial coordinates." +" The resolution of the simulations was 512? cells, each cell representing a physical volume of (2pc)?."," The resolution of the simulations was $512^3$ cells, each cell representing a physical volume of $(2 \mathrm{pc})^3$." +" Volume rendered images of the double jet structure areshown in the two stereo pairs, Fig."," Volume rendered images of the double jet structure areshown in the two stereo pairs, Fig." + 5 and Fig. 6.., \ref{fig:jetlong} and Fig. \ref{fig:jetshort}. +" In these renderings, the ray-traced variable was proportional to the 1.8th power of the density and the tracer variable of the jet, which is a measure of the radio emissivity of a jet plasma."," In these renderings, the ray-traced variable was proportional to the 1.8th power of the density and the tracer variable of the jet, which is a measure of the radio emissivity of a jet plasma." + Figure 5. shows that stereo pairs do not necessarily need to be made up of square images., Figure \ref{fig:jetlong} shows that stereo pairs do not necessarily need to be made up of square images. +" In this case, the upright rectangular stereo pair allows one to inspect the 3D structure of the jet along the full length of its propagation axis."," In this case, the upright rectangular stereo pair allows one to inspect the 3D structure of the jet along the full length of its propagation axis." +" In particular, one can see the deformations of the central jet stream as it becomes unstable due deceleration and entrainment in the lobes (Bicknell1984)."," In particular, one can see the deformations of the central jet stream as it becomes unstable due deceleration and entrainment in the lobes \citep{Bicknell1984}." +. The structure of the jet lobes along the line of sight is also clearer in the stereo pairs than in either of the 2D images on their own., The structure of the jet lobes along the line of sight is also clearer in the stereo pairs than in either of the 2D images on their own. +" In the edge-on stereo pairs of Fig. 6,,"," In the edge-on stereo pairs of Fig. \ref{fig:jetshort}," + the use of stereoscopy enables one to identify the locations of lower and higher concentrations of jet plasma within the volume of the lobe., the use of stereoscopy enables one to identify the locations of lower and higher concentrations of jet plasma within the volume of the lobe. +" Globally, one obtains a less ambiguous picture of the true shape and structural characteristics of the complex flow."," Globally, one obtains a less ambiguous picture of the true shape and structural characteristics of the complex flow." +" The viewer obtains a strong sense of depth in the image, despite the contracted view at small angles of the line of sight to the jet axis."," The viewer obtains a strong sense of depth in the image, despite the contracted view at small angles of the line of sight to the jet axis." + The relativistic AGN jet simulation were performed with the code (Fryxelletal. 2000).., The relativistic AGN jet simulation were performed with the code \citep[][]{Fryxell00}. . +" The stereo pairs were produced with the software, developed at the"," The stereo pairs were produced with the software, developed at the" +For cach galaxy we simultaucously fit a single eaussiau profile to the three different SIT lines. forcing the three les to share a common centroid aud width but allowine the normalization (depth) of each line to vary freely,"For each galaxy we simultaneously fit a single gaussian profile to the three different SiII lines, forcing the three lines to share a common centroid and width but allowing the normalization (depth) of each line to vary freely." + Iu all four galaxies the results strongly favor the picket fence model with an implied covering factor of optically-thick. clouds of about for LBAO213|12 aud LBAO926|15. for LDAOSOS|39. aud for LDAOO921|10.," In all four galaxies the results strongly favor the picket fence model with an implied covering factor of optically-thick clouds of about for LBA0213+12 and LBA0926+45, for LBA0808+39, and for LBA0921+45." + We show these fits for the case of LBAQ921|15 in Figure Tn principle. the sielitlines that avoid the clouds could be optically-thin to the metal lines but /still be opticalh-thick to the Lyinan continuum (equation 1).," We show these fits for the case of LBA0921+45 in Figure In principle, the sightlines that avoid the clouds could be optically-thin to the metal lines but still be optically-thick to the Lyman continuum (equation 1)." + Thus. coufirmation that there is significant escapiug lonizing radiation will require direct Observations below the Lyman οσο in these cases.," Thus, confirmation that there is significant escaping ionizing radiation will require direct observations below the Lyman edge in these cases." + Iu the mean time we can consider whether there is other evidence for the escape of ionizing radiation in these four LBAs., In the mean time we can consider whether there is other evidence for the escape of ionizing radiation in these four LBAs. + In O09 we highlighted the relative weakness of the extinction-corrected Πο eiissiou-Ime im most of the LBAs with DCOs. aud speculated that a sjeuificaut fraction of the ioniziug radiation nüght be escaping.," In O09 we highlighted the relative weakness of the extinction-corrected $\alpha$ emission-line in most of the LBAs with DCOs, and speculated that a significant fraction of the ionizing radiation might be escaping." + This information is listed in Table 2 where we compare the star-formation rates derived from the extinetion-corrected Πα cuussiou-line (SFR yy.) to that obtained from the sun of the total-IR and far UV huuinositv (SP Rp)., This information is listed in Table 2 where we compare the star-formation rates derived from the extinction-corrected $\alpha$ emission-line $SFR_{H\alpha}$ ) to that obtained from the sum of the total-IR and far- UV luminosity $SFR_{IRUV}$ ). + It is noteworthy that three of the four objects above in which we have interred au incomplete coveriug of the f£u-U source by neutral clouds have the highest ratios of VSPΠεμ(SPR: LBA02P13|12 (a ratio of 8.2). LDAOSOS|39 (3.0). and LDBAO0921|15 (3.2).," It is noteworthy that three of the four objects above in which we have inferred an incomplete covering of the far-UV source by neutral clouds have the highest ratios of $SFR_{IRUV}/SFR_{H\alpha}$: LBA0213+12 (a ratio of 8.2), LBA0808+39 (3.0), and LBA0921+45 (3.2)." + All three of these coutain à DC'O., All three of these contain a DCO. +" Iu contrast. the mean ratio of SFRrey/SER, for the other five galaxies is 1.1."," In contrast, the mean ratio of $SFR_{IRUV}/SFR_{H\alpha}$ for the other five galaxies is 1.4." + Tow do these results compare to what is secu at high redsluft?, How do these results compare to what is seen at high redshift? + There are four eravitationally-leused ligh-z ealaxies that have been observed with spectral resolution and signal-to-noise similar to our sauple., There are four gravitationally-lensed high-z galaxies that have been observed with spectral resolution and signal-to-noise similar to our sample. +Low-mass X-rav binaries (LAINBs) are binary star svstenis that are composed of a compact primary (a neutron star or a black hole) that accretes the outer gaseous lavers of a (sub-) solar-mass companion star.,Low-mass X-ray binaries (LMXBs) are binary star systems that are composed of a compact primary (a neutron star or a black hole) that accretes the outer gaseous layers of a (sub-) solar-mass companion star. + Neutron star primaries can reveal themselves by showing coherent X-ray pulsations when the accretion Ilow is funnelled onto the magnetic poles of the neutron star. or by displaving twpe-l N-ray. bursts caused by unstable thermonuclear burning of the accreted matter on the surface of the neutron star.," Neutron star primaries can reveal themselves by showing coherent X-ray pulsations when the accretion flow is funnelled onto the magnetic poles of the neutron star, or by displaying type-I X-ray bursts caused by unstable thermonuclear burning of the accreted matter on the surface of the neutron star." + Many neutron star LAINBs are transient ane alternate active accretion outbursts with long episodes of quiescence., Many neutron star LMXBs are transient and alternate active accretion outbursts with long episodes of quiescence. +" Whereas outbursts typically last a only few weeks and generate. 0.5.10. Καν N-ray luminosities of Ly~107ores ‘tee.Chenetal.1997).. the quiescent: phase mav extend to many decades and is characterised by a much lower quiescent Luminosity of L,~1075*eres.+ (0.5.10keV:Heinkeetal. 2009)."," Whereas outbursts typically last a only few weeks and generate 0.5–10 keV X-ray luminosities of $L_X\sim10^{36-38}~\lum$ \citep[e.g.,][]{chen97}, the quiescent phase may extend to many decades and is characterised by a much lower quiescent luminosity of $L_q\sim10^{31-33}~\lum$ \citep[0.5--10 keV;][]{heinke2009}." +. Phe cause of the quicscent X-ray emission has been subject of debate (e.g..Campana2003).," The cause of the quiescent X-ray emission has been subject of debate \citep[e.g.,][]{campana2003}." +. Spectrally. one can distinguish a soft thermal component at energies below ~2 keV. and a hard non-thermal emissiontail that dominates the quicscent X-ray spectrum above —29 Καν. The soft quiescent: spectral component is. generally interpreted as heat being radiated from the surface of the cooling neutron star (Brownctal.1998:C'olpi2001).," Spectrally, one can distinguish a soft thermal component at energies below $\sim2$ keV, and a hard non-thermal emissiontail that dominates the quiescent X-ray spectrum above $\sim2-3$ keV. The soft quiescent spectral component is generally interpreted as heat being radiated from the surface of the cooling neutron star \citep{brown1998,colpi2001}." +. As such. the quiescent thermal emission provides a measure of the neutron star's interior temperature.," As such, the quiescent thermal emission provides a measure of the neutron star's interior temperature." + Llowever. Iow-level accretion onto the surface of the neutron star might also produce a thermal X-ray spectrum (Zampierietal.1995).," However, low-level accretion onto the surface of the neutron star might also produce a thermal X-ray spectrum \citep[][]{zampieri1995}." +. The hard non-thermal emission is usually miocellect as a simple power law with a photon index of P~12. ancl its fractional contribution to the total 0.510 keV. [lux may vary anywhere from 0.1004. (Jonkeretal.2004).," The hard non-thermal emission is usually modelled as a simple power law with a photon index of $\Gamma \sim1-2$, and its fractional contribution to the total 0.5–10 keV flux may vary anywhere from $0-100\%$ \citep[][]{jonker2004}." +.. ]t has been attributed. e.g. to shock emission. generated in the interaction of a residual accretion. Dow with the magnetic field. of the neutron star. or the re-activation of a radio pulsar in quiescence (Campanactal. 1998)..," It has been attributed e.g., to shock emission generated in the interaction of a residual accretion flow with the magnetic field of the neutron star, or the re-activation of a radio pulsar in quiescence \citep{campana1998}. ." + ]t remains an unanswered question if. and how. the two spectral components are related.," It remains an unanswered question if, and how, the two spectral components are related." +" The contour plots have been obtained after smoothing the distribution with a Gaussian beam with size &—4"" or ~1.2 ppc. as indicated by the circle in the upper right corner of the figure."," The contour plots have been obtained after smoothing the distribution with a Gaussian beam with size $\sigma=4\arcsec$ or $\sim +1.2$ pc, as indicated by the circle in the upper right corner of the figure." + The lowest contour level corresponds to a local density of PMS stars twice as high as the average PMS stars density over the entire field., The lowest contour level corresponds to a local density of PMS stars twice as high as the average PMS stars density over the entire field. + The step between contour levels is constant and corresponds to a factor of 1.5., The step between contour levels is constant and corresponds to a factor of $1.5$. + We also show with small circles the positions of 55 young massive stars brighter than ~2«10 LL.. and with an implied mass >15 (e.g. Iben 1967)., We also show with small circles the positions of 55 young massive stars brighter than $\sim 2 \times 10^4$ $_\odot$ and with an implied mass $> 15$ (e.g. Iben 1967). + A striking feature in this figure is the difference in. the spatial distribution of the three types of stars., A striking feature in this figure is the difference in the spatial distribution of the three types of stars. +" Many older PMS stars are distributed along the rim of the gas shell to the S and W of the cluster's centre (hereafter named ""southern are”) and. except for the centre itself. they appear to avoid regions where younger PMS stars are located."," Many older PMS stars are distributed along the rim of the gas shell to the S and W of the cluster's centre (hereafter named “southern arc”) and, except for the centre itself, they appear to avoid regions where younger PMS stars are located." + As for massive stars. albeit more abundant near the centre of 3346. they also appear at various other locations in the field that are not occupied by PMS objects.," As for massive stars, albeit more abundant near the centre of 346, they also appear at various other locations in the field that are not occupied by PMS objects." + The careful reader could be worried that several old PMS stars seem to lie along the southern are. since nebular emission might in. principle contamimate their photometry and give us an Inaccurate measurement of their Ho excess emission.," The careful reader could be worried that several old PMS stars seem to lie along the southern arc, since nebular emission might in principle contaminate their photometry and give us an inaccurate measurement of their $\alpha$ excess emission." + However. as already mentioned in HI. we have carefully inspected the images and removed from the list of bona-fide PMS stars all objects whose Ha photometry might be contaminated by gas filaments.," However, as already mentioned in II, we have carefully inspected the images and removed from the list of bona-fide PMS stars all objects whose $\alpha$ photometry might be contaminated by gas filaments." + While it is possible that some of the Ha emission that we detect is due to diffuse nebular emission in the HII region not powered by the accretiol process (see ID. if the emission is extended and uniform over an area comparable to that of the point spread function. its contribution cancels out with the rest of the background when we perform the photometry (see Sabbi et al.," While it is possible that some of the $\alpha$ emission that we detect is due to diffuse nebular emission in the HII region not powered by the accretion process (see I), if the emission is extended and uniform over an area comparable to that of the point spread function, its contribution cancels out with the rest of the background when we perform the photometry (see Sabbi et al." + 2007 anc III for details on the photometry)., 2007 and II for details on the photometry). + Obviously. the subtraction would not work if the emissior were not uniform. as for example in the case of a filament that projects over the star but that does not cover completely the background annulus.," Obviously, the subtraction would not work if the emission were not uniform, as for example in the case of a filament that projects over the star but that does not cover completely the background annulus." + For this reason. after applying a unsharp-masking algorithm to highlight and sharpen the details of the Ha frames. we have carefully inspected all sources with excess Ha emission and have marked as suspicious and excluded from our bona-fide sample all those with filaments contamination within 073 of the star. for a total of 62 objects.," For this reason, after applying an unsharp-masking algorithm to highlight and sharpen the details of the $\alpha$ frames, we have carefully inspected all sources with excess $\alpha$ emission and have marked as suspicious and excluded from our bona-fide sample all those with filaments contamination within $0\farcs3$ of the star, for a total of 62 objects." + Although some of them might have intrinsic Ha excess emission. we prefer to adopt a conservative approach and remove all dubious cases.," Although some of them might have intrinsic $\alpha$ excess emission, we prefer to adopt a conservative approach and remove all dubious cases." + A detailed example of how well this powerful technique works can be found in Beccart et al. (, A detailed example of how well this powerful technique works can be found in Beccari et al. ( +2010).,2010). + Therefore. we are confident that the tight distribution of older PMS stars along the rim of the gas shell is not an artefact and suggests instead that these objects have very low velocities or at least a very small velocity spread.," Therefore, we are confident that the tight distribution of older PMS stars along the rim of the gas shell is not an artefact and suggests instead that these objects have very low velocities or at least a very small velocity spread." + Observed values of the velocity dispersions of stars in young clusters and associations typically fall in the range 1-10kkmss7! (e.g. van Altena et al., Observed values of the velocity dispersions of stars in young clusters and associations typically fall in the range $1 - 10$ $^{-1}$ (e.g. van Altena et al. + 1988: Jones Walker 1988: Mengel et al., 1988; Jones Walker 1988; Mengel et al. + 2009; Bosch. Terlevich Terlevich 2009; Rochau et al.," 2009; Bosch, Terlevich Terlevich 2009; Rochau et al." + 2010)., 2010). +" The thickness of the projected distribution of the older PMS in 3346 is of order —20"" or -6 ppc.", The thickness of the projected distribution of the older PMS in 346 is of order $\sim 20\arcsec$ or $\sim 6$ pc. + With a median estimated age of ~20 MMvr. this implies à small value of the projected velocity spread. namely Z0.5 ss!. corresponding to a three dimensional velocity dispersion of =| kkmss along the gaseous rim.," With a median estimated age of $\sim +20$ Myr, this implies a small value of the projected velocity spread, namely $\la 0.5$ $^{-1}$, corresponding to a three dimensional velocity dispersion of $\la 1$ $^{-1}$ along the gaseous rim." + This picture is consistent with the very low velocity dispersion (<3kkm s!) of the ionised gas measured by Smith (2008) in this field from high-resolution echelle spectroscopy., This picture is consistent with the very low velocity dispersion $< 3$ km $^{-1}$ ) of the ionised gas measured by Smith (2008) in this field from high-resolution echelle spectroscopy. + If there is a higher velocity component. 1t must be linked to the systematic motion of the gas shell.," If there is a higher velocity component, it must be linked to the systematic motion of the gas shell." + The match between the location of many old PMS objects (about — of them) and the rim of the gas shell also suggests that the shell itself reflects the distribution of the gas out of which these stars formed and that it has not (yet) been significantly affected by the stellar winds and by the ionising radiation of the much younger massive stars at the centre of the field., The match between the location of many old PMS objects (about $\sim$ of them) and the rim of the gas shell also suggests that the shell itself reflects the distribution of the gas out of which these stars formed and that it has not (yet) been significantly affected by the stellar winds and by the ionising radiation of the much younger massive stars at the centre of the field. + Furthermore. the fact that the distribution of these massive objects and of the younger PMS stars does not appear to trace in any way the geometry of the gas shell indicates quite convinemely that we are seeing two rather different and unrelated generations of stars.," Furthermore, the fact that the distribution of these massive objects and of the younger PMS stars does not appear to trace in any way the geometry of the gas shell indicates quite convincingly that we are seeing two rather different and unrelated generations of stars." + From the apparent shape of the rim of the gas shell. Gouliermis et al. (," From the apparent shape of the rim of the gas shell, Gouliermis et al. (" +2008) recently argued that there is a relationship between the central 3346 cluster and the southern arc.,2008) recently argued that there is a relationship between the central 346 cluster and the southern arc. + They suggested that the latter outlines the ionisation front of the cloud that is caused by the powerful stellar winds of the young massive stars at its centre., They suggested that the latter outlines the ionisation front of the cloud that is caused by the powerful stellar winds of the young massive stars at its centre. + In their scenario. the photoronisation process of the central OB stars would provide the primary source of mechanical energy that triggers star formation in this region.," In their scenario, the photoionisation process of the central OB stars would provide the primary source of mechanical energy that triggers star formation in this region." +.. not only ts the rim of the gas shell unaffected by the central OB stars. but it is also much older (and 1t may be much farther away from the OB stars than what the projected distance might seem to suggest).," not only is the rim of the gas shell unaffected by the central OB stars, but it is also much older (and it may be much farther away from the OB stars than what the projected distance might seem to suggest)." + This discrepancy outlines the risks of drawing conclusions on triggered star formation based primarily on the morphology of structures projected on the sky., This discrepancy outlines the risks of drawing conclusions on triggered star formation based primarily on the morphology of structures projected on the sky. + As Watson. Hanspal Mengistu (2010) have recently shown. only studied appear to have a significant number of YSOs associated with their photodisociation fronts. implying that triggered star formation mechanisms acting on the boundary of the expanding HII region are not common.," As Watson, Hanspal Mengistu (2010) have recently shown, only studied appear to have a significant number of YSOs associated with their photodisociation fronts, implying that triggered star formation mechanisms acting on the boundary of the expanding HII region are not common." + A more quantitative characterisation of the relative distribution of younger and older PMS objects and massive stars Is offered by the maps shown in reffigd.., A more quantitative characterisation of the relative distribution of younger and older PMS objects and massive stars is offered by the maps shown in \\ref{fig4}. +" The (0.0) position in that figure corresponds. to RA-059g, DEC=—72°10°32” (J2000). with North up and East to the left."," The (0,0) position in that figure corresponds to $=0^{\rm h} 59^{\rm m} 8^{\rm s}$, $=-72^\circ +10\arcmin 32\arcsec$ (J2000), with North up and East to the left." + In panel a) we show all young stars using different symbols (blue pentagrams. red dots and yellow dots respectively for massive young stars. younger PMS stars and older PMS objects). whereas panel b) gives the number," In panel a) we show all young stars using different symbols (blue pentagrams, red dots and yellow dots respectively for massive young stars, younger PMS stars and older PMS objects), whereas panel b) gives the number" +ol the inverse of the filter (ransmission function. (,of the inverse of the filter transmission function. ( +This latter kernel does not normalize to one. since it also includes the effect of equivalent width censorship.),"This latter kernel does not normalize to one, since it also includes the effect of equivalent width censorship.)" + We then applied these (wo kernels to a series of functions of the form treated each curve as a probability distribution. aud computed (he likelihood that the observed sample ofLya huninosities could be drawn from (hat distribution.," We then applied these two kernels to a series of functions of the form treated each curve as a probability distribution, and computed the likelihood that the observed sample of$\alpha$ luminosities could be drawn from that distribution." + Figure 5 displays our best-fit fanction. both belore (the dashed line) and after the equivalent-width censorship (solid red line).," Figure \ref{lumfun_z3} displays our best-fit function, both before (the dashed line) and after the equivalent-width censorship (solid red line)." + Also plotted are the best-fit curves for the 2=3.1 LAEs found by Gr07 (in green) and Ouchietal.(2008.inblue).., Also plotted are the best-fit curves for the $z=3.1$ LAEs found by Gr07 (in green) and \citet[][in blue]{ouchi+08}. + The parameters of these Iunctions are listed in Table 8.., The parameters of these functions are listed in Table \ref{sch_lf}. + Note that for the current study. we have fixed the faànt-end slope of our function to a=—1.65.," Note that for the current study, we have fixed the faint-end slope of our \citet{schechter} function to $\alpha = -1.65$." + This is the most-likelv value inferred from the Gr07 data. once continuun sublraction has been applied to their f(Iuxes.and it is also consistent. with ihe recent 2$ 0 after background subtraction. +" We fitted cach long term lighteurve with a line of constant intensity. in order to ascertain the source variability,"," We fitted each long term lightcurve with a line of constant intensity, in order to ascertain the source variability." + All four targets were observed with NAILNewton: NB163 was caught in outburst once iu 2006. December. aud twice in 2008. February.," All four targets were observed with XMM-Newton; XB163 was caught in outburst once in 2006, December, and twice in 2008, February." + We obtained source and background spectra in the 0.310 keV band from the pu imstruneut: the backeround regions were circular. with the same size as the source region. ou the same CCD. aud at simular offset angles.," We obtained source and background spectra in the 0.3–10 keV band from the pn instrument; the background regions were circular, with the same size as the source region, on the same CCD, and at similar offset angles." + The appropriate response matrix aud ancillary response file was obtained for each source., The appropriate response matrix and ancillary response file was obtained for each source. + We neglected the MOS detectors to avoid pileup., We neglected the MOS detectors to avoid pileup. + We present a iuerged. 0.37 keV ACTS image of the central region of ΑΙ in Fie 1: our BITC's are circled and labeled.," We present a merged, 0.3–7 keV ACIS image of the central region of M31 in Fig \ref{4bhim}; our BHCs are circled and labeled." + We note that NB163 looks rather faint in this mereccl muage. as it is a recurrent transient. and quicscent for much of the time.," We note that XB163 looks rather faint in this merged image, as it is a recurrent transient, and quiescent for much of the time." + These merged observations cover an »roxinuatelv circular region with 20/ radius., These merged observations cover an approximately circular region with $'$ radius. + We detected 133. N-rav sources in this recion. id found 128 elobular clusters from the RBC.," We detected 433 X-ray sources in this region, and found 428 globular clusters from the RBC." + Therefore we expect chance comceideuces of X-ray sources within 1” of the GC ceuters for 0.13 out of [28 CC's., Therefore we expect chance coincidences of X-ray sources within $''$ of the GC centers for 0.13 out of 428 GCs. + Figue 2 shows the 0.310 keV lone term lightcurves of our four DIICs: ACTS aud TRC observations are represeuted by crosses aud circles respectively., Figure \ref{4bhlcs} shows the 0.3–10 keV long term lightcurves of our four BHCs; ACIS and HRC observations are represented by crosses and circles respectively. + Superposed on each lehtcurve is the best fit line of constant intensity: we give the bIuninosity. uucertaiuties aud \7 / deerces of freedom (dof) iu the caption.," Superposed on each lightcurve is the best fit line of constant intensity; we give the luminosity, uncertainties and $\chi^2$ / degrees of freedom (dof) in the caption." + Spectra were 8erouped to have a imi of Ww| counts por bin. and analyzed with NSPEC version 12.6.," Spectra were grouped to have a minimum of 20 counts per bin, and analyzed with XSPEC version 12.6." + Each spectrmu was fitted with four uodels that were represeutative of various spectral states exhibited. by LAINBs (seeeg.72?)..," Each spectrum was fitted with four models that were representative of various spectral states exhibited by LMXBs \citep[see e.g.][]{vdk94,mr06}." + The ow accretion rate state conunuon to neutron star and black hole LAINBs is dominated bv inverse Compton scattering of cool photous ou iot electrons. aud low state NBs have electron eniperatures ~LOO300 keV (seee.g.2): it is well represented by power law enmüssiou iu the 0.310 keV band. with P. —1.L 2.," The low accretion rate state common to neutron star and black hole LMXBs is dominated by inverse Compton scattering of cool photons on hot electrons, and low state XBs have electron temperatures $\sim$ 100–300 keV \citep[see e.g.][]{mr06}; it is well represented by power law emission in the 0.3–10 keV band, with $\Gamma$ $\sim$ 1.4–2." + We fitted cach spectrua with two models to represent Coniptonization: a simple power Law model. aud a model.," We fitted each spectrum with two models to represent Comptonization: a simple power law model, and a model." + The black hole high state was represcuted by a disk blackbody (?).., The black hole high state was represented by a disk blackbody \citep{mr06}. + A blackbody || power law model is represcutative of high accretion rate neutron stars: we expect a blackbody with ki ~1 2 keV. contributing ~LO-50% of the flux (scee.g.?)..," A blackbody + power law model is representative of high accretion rate neutron stars; we expect a blackbody with $T$ $\sim$ 1–2 keV, contributing $\sim$ of the flux \citep[see e.g.][]{white86}. ." + Each model is attenuated by line of sight absorption., Each model is attenuated by line of sight absorption. + The properties of cach spectrum are provided iu Table Ll. ΕΕ a power law eunüssion model.," The properties of each spectrum are provided in Table \ref{spectab}, assuming a power law emission model." + For each spectrum we indicate the observation used. aud the uuniber of net source counts: we then eive the cohunn deusitv. power law index. (P /dof aud 0.3.10 keV. luminosity for the best fit power law inodel: uncertainties are quoted at the confidence level.," For each spectrum we indicate the observation used, and the number of net source counts; we then give the column density, power law index, $\chi^2$ /dof and 0.3–10 keV luminosity for the best fit power law model; uncertainties are quoted at the confidence level." + XDOS2 was observed in 19 ACTS and 35 TRC observations. due toits high off-axis augle. but appears to be persistently bright.," XB082 was observed in 13 ACIS and 35 HRC observations, due toits high off-axis angle, but appears to be persistently bright." + Its 0.3.10 keV huninosity varied by a factor ~3. up to 232 «1075 erg C.," Its 0.3–10 keV luminosity varied by a factor $\sim$ 3,up to $\sim$ $\times$ $^{38}$ erg $^{-1}$." + Tt was also observed in the 2001 NATAL observation of the ND core. with a goo exposure tine of ~27 ks.," It was also observed in the 2001 XMM-Newton observation of the M31 core, with a good exposure time of $\sim$ 27 ks." +" The power law enüssou model vielded the vest fit to the NADENewton pu spectrum: A] (absorqlon). — 3.90.5 «107au) atomic ,7, substantially. Πσ]ο than the Galactic absorption along the line- (Ny = <1PU atom 2): Caldwell ο al. ("," The power law emission model yielded the best fit to the XMM-Newton pn spectrum; $N_{\rm H}$ (absorption) = $\pm$ 0.5 $\times$ $^{21}$ atom $^{-2}$, substantially higher than the Galactic absorption along the line-of-sight $N_{\rm H}$ = $\times 10^{20}$ atom $^{-2}$ ); Caldwell et al. (" +2011) noted that Bo 82 was particularly red. rence the absorbing material is Likely to reside in the cluster.,"2011) noted that Bo 82 was particularly red, hence the absorbing material is likely to reside in the cluster." + The photon index P — 1.2040.09: he unabsorbed 0.310 keV hunuinositv Lysiy = 2.60.2 «1075 ove 1; and 4? /dof = 127/117.," The photon index $\Gamma$ = $\pm$ 0.09; the unabsorbed 0.3–10 keV luminosity $L_{0.3-10}$ = $\pm$ $\times 10^{38}$ erg $^{-1}$, and $\chi^2$ /dof = 127/147." + The observed ploton index is lower than the expected range for black holes (P —1.41.7): however. fixine —]1.L resulted iu a good fit with V2 /dof «1: we prescut a A2 /dof = 1 (4? = 117) contour plot for D vs Ay in Fig. L. ," The observed photon index is lower than the expected range for black holes $\Gamma$ $\sim$ 1.4–1.7); however, fixing $\Gamma$ =1.4 resulted in a good fit with $\chi^2$ /dof $<$ 1; we present a $\chi^2$ /dof = 1 $\chi^2$ = 147) contour plot for $\Gamma$ vs $N_{\rm H}$ in Fig. \ref{contplot}. ." +The best fit model described a hot. optically thin corona. with kT; —51 keV aud r 71. for V? /dof = 127/115: however. these parameters could not be constrained. as ki. lies well outsidethe NMNE-Newtou pass band.," The best fit model described a hot, optically thin corona, with $T_{\rm e}$ $\sim$ 54 keV and $\tau$ $\sim$ 1, for $\chi^2$ /dof = 127/145; however, these parameters could not be constrained, as $T_{\rm e}$ lies well outsidethe XMM-Newton pass band." +LIudeed. electron temperatures of 100 or 300 keV,"Indeed, electron temperatures of 100 or 300 keV" +"Alunooz. Aladau. Loeb errors on the Au, and the mass-to-light ratio of satellites are improved: (3) the degree of cosmic variance between cilferent high-resolution MW simulations is understood: and (4) new high-resolution simulations are developed to include xwvons and. feedback. processes.","oz, Madau, Loeb errors on the $M_{300}$ and the mass-to-light ratio of satellites are improved; (3) the degree of cosmic variance between different high-resolution MW simulations is understood; and (4) new high-resolution simulations are developed to include baryons and feedback processes." + Progress is already. being made on some of these fronts., Progress is already being made on some of these fronts. + αςΕΛ (Ixaiser2002).. he Dark Energy Survey (DarkEnergySurveyCollaboration 2005).. SkvMappoer (Ixeller2007).. and the Large Synoptic Survey Telescope. (Ivezicetal.2008) will. intensively obe for satellites populating the galactic neighborhood.," PanSTARRS \citep{Kaiser02}, the Dark Energy Survey \citep{DESC05}, SkyMapper \citep{Keller07}, and the Large Synoptic Survey Telescope \citep{Ivezic08} will intensively probe for satellites populating the galactic neighborhood." + Additionally. Ishivamaetal.(2009) have compared subhalo »opulations for many cillerent simulations of galactic halos and. found: more scatter than anticipated by Springelοἱal.(2008) using a smaller sample. but their work has not vet resolved. the. progenitors that. formed ultra-[aint. svystenis.," Additionally, \citet{Ishiyama09} have compared subhalo populations for many different simulations of galactic halos and found more scatter than anticipated by \citet{Springel08} using a smaller sample, but their work has not yet resolved the progenitors that formed ultra-faint systems." + Once developed. high-resolution cosmological simulations with barvons and feedback will test. much more specific models of reionization and open an avenue for comparisons with new observables. in. addition to those explored. here. such as the bhalf-light radius. which promises to holed interesting clues about the high-redshift formation physics of MW. satellites.," Once developed, high-resolution cosmological simulations with baryons and feedback will test much more specific models of reionization and open an avenue for comparisons with new observables, in addition to those explored here, such as the half-light radius, which promises to hold interesting clues about the high-redshift formation physics of MW satellites." + With these. improvements. our basic methodology can be used in the future to further probe reionization and the process of star formation in the early universe.," With these improvements, our basic methodology can be used in the future to further probe reionization and the process of star formation in the early universe." + We thank Mike Ixublen. Louie Strigari. Raja Gubathakurta. and Cerey Gilmore for useful discussions.," We thank Mike Kuhlen, Louie Strigari, Raja Guhathakurta, and Gerry Gilmore for useful discussions." + J.D. acknowledges support from NASA through Llubble Fellowship grant LISTT-11E-01194.01., J.D. acknowledges support from NASA through Hubble Fellowship grant HST-HF-01194.01. + This NNXUSALAAGresearch was supported in part ον NASA erants and LA CX.L.). LIST-AR-11268.01- and NNXOSAVG68G. (PAL). anc by Harvard. University funds.," This research was supported in part by NASA grants NNX08AL43G and LA (A.L.), HST-AR-11268.01-A1 and NNX08AV68G (P.M.), and by Harvard University funds." +refS:results.. the shape of the overall distribution 1s robust against these issues.,", the shape of the overall distribution is robust against these issues." + The left-hand plot of Figure 5. shows that the number of regions in the RMS sample peaks around 3 x 10L..., The left-hand plot of Figure \ref{F:discussion_nplots} shows that the number of regions in the RMS sample peaks around 3 $\times$ $^{4}$. + There are few sources which are identified as regions but have a luminosity derived from the SED lower than the limit for formation of an region (L~550L.... spectral type ~B3.2000).," There are few sources which are identified as regions but have a luminosity derived from the SED lower than the limit for formation of an region \citep[ L~$\sim$~550~\lsol{}, spectral type $\sim$." +" Inspection of these sources suggest that they are correctly identified as regions. but suffer from individual distance determination issues,"," Inspection of these sources suggest that they are correctly identified as regions, but suffer from individual distance determination issues." + While the models used by the SED fitter do not include additional sources of heating of the dust inside the tontsed zone. in particular Lyman alpha (e.g.Hoareetal..1991).. the SEDs of regions are similar to those of YSOs except at radio wavelengths. which the models do not probe.," While the models used by the SED fitter do not include additional sources of heating of the dust inside the ionised zone, in particular Lyman alpha \citep[e.g.][]{Hoare1991}, the SEDs of regions are similar to those of YSOs except at radio wavelengths, which the models do not probe." + As the primary concern of this work is the bolometric flux. the fits are acceptable for this purpose.," As the primary concern of this work is the bolometric flux, the fits are acceptable for this purpose." + The most luminous region observed by WoodChurchwell(1989) has a luminosity of ~3 x 10°L.... while no RMS source has a luminosities above 10°L...," The most luminous region observed by \citet{Wood1989a} has a luminosity of $\sim$ 3 $\times$ $^{6}$, while no RMS source has a luminosities above $^{6}$." + However. some of the Wood&Churchwell(1989) sources are now known to contain multiple objects and in some cases the RMS kinematic distance neasurements are significantly less than the ones used by those authors.," However, some of the \citet{Wood1989a} sources are now known to contain multiple objects and in some cases the RMS kinematic distance measurements are significantly less than the ones used by those authors." + For example Wood&Churchwell(1989) use d = 9.7 kpe for GO45.4543+00.0600 but the RMS kinematic distance to this source 1s 7.3 kpe. which would change their L44 x 10° to 8.2 x 10°La.," For example \citet{Wood1989a} use d = 9.7 kpc for G045.4543+00.0600 but the RMS kinematic distance to this source is 7.3 kpc, which would change their 1.44 $\times$ $^{6}$ to 8.2 $\times$ $^{5}$." + The SED fit for this source gives L = (3.7 + 1.0) x 10° but MIPSGAL rather than IRAS far-IR fluxes are used and the MIPSGAL image shows multiple bright regions nearby (see Figure 12))., The SED fit for this source gives L = (3.7 $\pm$ 1.0) $\times$ $^{5}$ but MIPSGAL rather than IRAS far-IR fluxes are used and the MIPSGAL image shows multiple bright regions nearby (see Figure \ref{F:discussion_hiis}) ). + The SED does not fit the point well. but this source exhibits significant surrounding low-level emission in the MIPSGAL image and strong radio emission.," The SED does not fit the point well, but this source exhibits significant surrounding low-level emission in the MIPSGAL image and strong radio emission." + Both of these factors could increase the observed SCUBA flux above that consistent with the SED models based on the lower wavelength emission. which is well fit.," Both of these factors could increase the observed SCUBA flux above that consistent with the SED models based on the lower wavelength emission, which is well fit." + In comparing the luminosity distributions of YSOs and regions (Figure 5)). the difference in the peak of these distributions is apparent.," In comparing the luminosity distributions of YSOs and regions (Figure \ref{F:discussion_nplots}) ), the difference in the peak of these distributions is apparent." +" Indeed. a Kolmogorov-Smirnov (KS) test of the cumulative distribution functions. indicates that the probability of these distributions being the same is of the order 108,"," Indeed, a Kolmogorov-Smirnov (KS) test of the cumulative distribution functions, indicates that the probability of these distributions being the same is of the order $^{-26}$ ." + It is unlikely that this is due to an under-detection of B spectral type regions in the sample as the RMS radio observations (Urquhartetal..2007a.2009) were deep enough to detect regions down to spectral type Bl to distances of 20 kpe assuming an electron temperature of 107 K. In addition. many of these MYSOs are visible at near-IR wavelengths. so are unlikely to be heavily embedded hyper-compact (HC) regions.," It is unlikely that this is due to an under-detection of B spectral type regions in the sample as the RMS radio observations \citep{Urquhart2007a,Urquhart2009} were deep enough to detect regions down to spectral type B1 to distances of 20 kpc assuming an electron temperature of $^{4}$ K. In addition, many of these MYSOs are visible at near-IR wavelengths, so are unlikely to be heavily embedded hyper-compact (HC) regions." + Main-sequence stars with a spectral type of B3 (L > 550L.) or earlier are capable of producing regions. and evolutionary tracks indicate that core hydrogen burning should have started in YSOs of spectral type B3 or earlier despite the fact that aceretion is still ongoing (e.g.Yorke&Sonnhalter.2002).," Main-sequence stars with a spectral type of B3 (L $\geq$ ) or earlier are capable of producing regions, and evolutionary tracks indicate that core hydrogen burning should have started in YSOs of spectral type B3 or earlier despite the fact that accretion is still ongoing \citep[e.g.][]{Yorke2002}." +. It has therefore been unclear until recently why MYSOs. where the central source is massive enough to form an region but no region 1s observed. are detected at all. rather than all young massive stars transitioning directly from intermediate mass YSOs to regions às they gain mass (Hoare&Franco.2007)..," It has therefore been unclear until recently why MYSOs, where the central source is massive enough to form an region but no region is observed, are detected at all, rather than all young massive stars transitioning directly from intermediate mass YSOs to regions as they gain mass \citep[][]{Hoare2007b}." + Some mechanism must either quench or mask the existence of an region (e.g.Walmsley.1995:Keto.2003).. or increase the radius of the star such that the stellar Το. and thus UV flux. are decreased (e.g.Hosokawaetal..2010).," Some mechanism must either quench or mask the existence of an region \citep[e.g.][]{Walmsley1995,Keto2003}, or increase the radius of the star such that the stellar $_{eff}$, and thus UV flux, are decreased \citep[e.g.][]{Yorke2008,Hosokawa2009,Hosokawa2010}." +. Ascertaming further how selection effects influence the difference in the distribution of RMS YSOs and regions will require the luminosity functions of these sources. which will be the subject of a future paper (Mottram et al..," Ascertaining further how selection effects influence the difference in the distribution of RMS YSOs and regions will require the luminosity functions of these sources, which will be the subject of a future paper (Mottram et al.," + 2010. in prep.).," 2010, in prep.)." + After preforming tests of the influence of the input parameters to the model SED fitter of Robitailleetal.(2007).. we have obtained the lummosities of 1173 young RMS sources. of which 1069 have unique kinematic distances and good fits.," After preforming tests of the influence of the input parameters to the model SED fitter of \citet{Robitaille2007a}, we have obtained the luminosities of 1173 young RMS sources, of which 1069 have unique kinematic distances and good fits." + The lummmosity distributions of these sources in terms of their RMS classification have been presented. and show that there are few MYSOs with L > 10°L.. though we detect regions up to ~7 x 1Ο... a difference which we find to be statistically significant.," The luminosity distributions of these sources in terms of their RMS classification have been presented, and show that there are few MYSOs with L $\geq$ $^{5}$, though we detect regions up to $\sim$ 7 $\times$ $^{5}$, a difference which we find to be statistically significant." + We also find that using the SED fitter to obtain bolometric flux measurements is more consistent and has less scatter. than either using simple trapezium rule integration or greybody fits for mid-IR bright young massive stars.," We also find that using the SED fitter to obtain bolometric flux measurements is more consistent and has less scatter, than either using simple trapezium rule integration or greybody fits for mid-IR bright young massive stars." + Finally. we obtained the flux ratios consistent with our SED fits. which allow us to estimate the bolometric flux. of 280 sources for which far-IR fluxes could not be obtained.," Finally, we obtained the flux ratios consistent with our SED fits, which allow us to estimate the bolometric flux, of 280 sources for which far-IR fluxes could not be obtained." + Having obtained the luminosity distributions of YSOs and regions in the RMS sample. we can go on to calculate the luminosity functions forthese sources.," Having obtained the luminosity distributions of YSOs and regions in the RMS sample, we can go on to calculate the luminosity functions forthese sources." + This will be discussed in a forthcoming paper., This will be discussed in a forthcoming paper. +Vixprange the mass is ~510 MM...,range the mass is $\sim 5\times 10^{4}$ $_{\odot}$. + Thus. the )AIM. of extended gas traced by our broad-line NIL; observations represents at least of the total cloud mass.," Thus, the $>$ $_\odot$ of extended gas traced by our broad-line $_3$ observations represents at least of the total cloud mass." + Cores 3 and 6 are not found towards any of the LASS.S. TeV gamma-ray sources., Cores 3 and 6 are not found towards any of the H.E.S.S. TeV gamma-ray sources. + Their values at 7-25 are quite dilferent to the other Cores in the region., Their values at $\sim$ are quite different to the other Cores in the region. + The most likely connection is with the near-3-kpe spiral arm (with heliocentric distance ~2 to 3kkpc). which has an expected value =53.1|4.167 2008)).," The most likely connection is with the near-3-kpc spiral arm (with heliocentric distance $\sim$ 2 to kpc), which has an expected value $=-53.1+4.16l$ )." + Core 3 is possibly associated with the BSILVY spectral type star LID 313632., Core 3 is possibly associated with the IV spectral type star HD 313632. +" Our new detection of a 19Ο. maser towards Core 3 may result from the envelope of LID""nu313632 or signal the presence of star formation.", Our new detection of a $_2$ O maser towards Core 3 may result from the envelope of HD 313632 or signal the presence of star formation. + From the image in Figure 7 a 24jmn feature is seen towards this core., From the image in Figure \ref{fig:IRdata} a $\mu$ m feature is seen towards this core. + For Core 6. the IR. and radio sources LRAS 17555-2408 anc PAIN J1758-2405 are found ~2’ and ~4’ distant.," For Core 6, the IR and radio sources IRAS 17555-2408 and PMN J1758-2405 are found $\sim 2^\prime$ and $\sim 4^\prime$ distant." + For both cores. our detection of NIL; couldsignal some degree of star formation.," For both cores, our detection of $_3$ could signal some degree of star formation." + Finally. Core 6 also Liesjust outside the TeV. emission from LIESS J180(-240€ and dusis unlikely to be associated.," Finally, Core 6 also lies just outside the TeV emission from HESS J1800-240C and thus is unlikely to be associated." + For ppc radius. both of these cores have masses 7600 to MM. and densities 400 to 10° Cma3.," For a pc radius, both of these cores have masses $\sim$ 600 to $_{\odot}$, and densities $\sim$ 400 to $\times 10^{3}$ 3." + These cores are located towards the peak of the TeV gamma-ray source LIESS 1800-240. and are likely associated with the Hirregions €:6.225-0.560. (Core 4) uM €G6.1-0.6 (Corefa) (Lockman1989:Kuchar&C," These cores are located towards the peak of the TeV gamma-ray source HESS J1800-240A and are likely associated with the regions G6.225-0.569 (Core 4) and G6.1-0.6 (Core4a) \citep{lockman,kuchar}." +lark199 Additional. counterparts to Core ta are the LR. source. 17588-2358. also clearly visible in theSpi/zer image (Figure 7)). and a MMlIz OLL maser (Sevensterctal.," Additional counterparts to Core 4a are the IR source, 17588-2358, also clearly visible in the image (Figure \ref{fig:IRdata}) ), and a MHz OH maser \citep{sevenster}." + 1997).. Our detection of LICN(32) towards Core ta may also suggest it is at an earlier evolutionary stage than Core 4., Our detection of $_{3}$ N(3–2) towards Core 4a may also suggest it is at an earlier evolutionary stage than Core 4. +" Assuming a ppc radius we derived a mass and density of 7510 MM. and ng, 745 to ]O0cem for Core ta and Core 4 respectively.", Assuming a pc radius we derived a mass and density of 75 to $_{\odot}$ and $n_{\rm H_2}\sim$ 45 to $\times 10^{3}$ $^{-3}$ for Core 4a and Core 4 respectively. +" Despite the reasonable amount of chumpy molecular gas traced. by. Nanten CO) observations ~25.qJ05 MM. from (() Aharonianctal.""Ie.om10Sb assuming a2 kpe distance). we see no clear indication extended: NIL; emission towards this region."," Despite the reasonable amount of clumpy molecular gas traced by Nanten CO observations (e.g. $\sim 2.5\times 10^{4}$ $_{\odot}$ from $^{12}$ (1–0) \citealt{hess_w28} assuming a 2 kpc distance), we see no clear indication for extended $_3$ emission towards this region." + We note however this region has only half the Alopra exposure compared to the other regions due to the lack of LOPS overlap., We note however this region has only half the Mopra exposure compared to the other regions due to the lack of HOPS overlap. + The Triple Core represents the most complex. of the regions we mapped. and comprises three NIL; peaks aligned in à Sk to NW direction all of which are generally centred on the TeV gamma-ray source HIESS JLS00-240B and the very Hibrnght and energetic Hülregion G5.89-0.39.," The Triple Core represents the most complex of the regions we mapped, and comprises three $_3$ peaks aligned in a SE to NW direction all of which are generally centred on the TeV gamma-ray source HESS J1800-240B and the very IR-bright and energetic region G5.89-0.39." + Our mmm observations are the largest scale mapping in dense molecular gas tracers so far of this enigmatic region., Our mm observations are the largest scale mapping in dense molecular gas tracers so far of this enigmatic region. + Cib.sO-0.39 actually comprises two active star formation sites and Following the nomenclature of Ixim&Woo(2001) they are labeled G5.89-0.39A to the cast. and 65.89-0.39DB. about 2’ to the west.," G5.89-0.39 actually comprises two active star formation sites and following the nomenclature of \citet{kimkoo2001} they are labeled G5.89-0.39A to the east, and G5.89-0.39B about $^\prime$ to the west." + The Triple Core SW. NIL; core is associated with LHücore €15.80-0.39.X. otherwise known as W28-AÀ2 after its strong radio continuum emission.," The Triple Core SW $_3$ core is associated with core G5.89-0.39A, otherwise known as W28-A2 after its strong radio continuum emission." + The ring-like features prominently visible in theSpzer Sim. emission (sco Figure 7)) are centred. on (5.50-90ΑΔ suggesting strong PALL molecular excitation. from. stellar. photons., The ring-like features prominently visible in the $\mu$ m emission (see Figure \ref{fig:IRdata}) ) are centred on G5.89-0.39A suggesting strong PAH molecular excitation from stellar photons. + The Triple Core Central NLL; core is associated. with the UC-Hluregion €15.89-0.39D. from which strong τα RRL appears to be centred (kim&Ίνου2001)— signalling strong ionisation of the surrounding molecular gas., The Triple Core Central $_3$ core is associated with the region G5.89-0.39B from which strong $\alpha$ RRL appears to be centred \citep{kimkoo2001} signalling strong ionisation of the surrounding molecular gas. + “Phe IRL 162a. W65e and W69e emission from our observations also appears prominent towards €15.89-t39D although in uu three lines the emission. is elongated: towards 30.," The RRL $\alpha$, $\alpha$ and $\alpha$ emission from our observations also appears prominent towards G5.89-0.39B although in all three lines the emission is elongated towards G5.89-0.39A." + The strongest HO maser is also seen towards Gmn, The strongest $_2$ O maser is also seen towards G5.89-0.39B. +" From the position-switched observations. strong maser emission with complex structures spanning very wide velocity coverage over are cletectecl towards 550-029Α ancl in G5.89-0.39B.loss €15.89-0.39""--D. is. responsible [ο very energetic and studied. in many molecular lines over aresce to arcmin sc"" ("," From the position-switched observations, strong $_{2}$ O maser emission with complex structures spanning very wide velocity coverage over are detected towards G5.89-0.39A and in G5.89-0.39B. G5.89-0.39B is responsible for very energetic outflows and is extensively studied in many molecular lines over arcsec to arcmin scales. (" +sce e.g. Llarvey2008)).,"see e.g. \citealt{harvey,churchwell,gomez,acord,sollins,thompson,klaassen,kimkoo2001,kimkoo2003,hunter}) )." + Previous small-scale NIL; studies are ciscussecl by Gomez(1991):Wood.(1993):Acordetal.(1997):Hunteretal.," Previous small-scale $_3$ studies are discussed by \citet{gomez, wood, acord,hunter}." +(2008).. The Triple Core NW. NIL; core is found a further 5 distant and may be linked to the M spectral type pulsating star. SSgr or perhaps the natal gas from which this star was born., The Triple Core NW $_3$ core is found a further $^\prime$ distant and may be linked to the M spectral type pulsating star Sgr or perhaps the natal gas from which this star was born. + Core 5 appears to stradcdle the south cast quadrant of the Spam Επ. shell or excitation ring of G5.89-0.39A and LESS «1500-2012. and is resolved. into two components CorelI5 NE and SW.," Core 5 appears to straddle the south east quadrant of the $\mu$ m IR shell or excitation ring of G5.89-0.39A and HESS J1800-240B, and is resolved into two components Core 5 NE and SW." + Local peaks in CO emission overlapping CoreIa5 NE and aare clearly visible (see Figure 6 and and also Lisztotal.na{):Wim&Koo (2003))).," Local peaks in CO emission overlapping Core 5 NE and SW are clearly visible (see Figure \ref{fig:COdata} and and also \citet{liszt,kimkoo2003}) )." + Core 5 NE is the coldest of cores detected with I21xIx. Here we detect only NIL; ((11) emission in mapping. and only very weak (2.2) ancl (3.3) emission inthe deep spectra.," Core 5 NE is the coldest of the cores detected with $\sim12$ K. Here we detect only $_{3}$ (1,1) emission in mapping, and only very weak (2,2) and (3,3) emission inthe deep spectra." +" Lt is also one of the few sites where N(""9) is detected.", It is also one of the few sites where $_{5}$ N(10–9) is detected. + In Core 5 SW we find 7j;—IS Wik and NID; ((2.2) and (3.3) emission being stronger than in the NE.," In Core 5 SW we find $\sim18$ K and $_3$ (2,2) and (3,3) emission being stronger than in the NE." +" ""here is also HIC4N(3 2) emission when looking at the 5 to velocity range in mapping data.", There is also $_{3}$ N(3–2) emission when looking at the 5 to velocity range in mapping data. +" Overall. assuming a (.2ppc core radius. we [ind our NlIl;((1.1) and (2.2) observations trace 7100 to MAL. and density ng, —80 to 300.10 * for the individual cores in the Triple Core and Core 5. complexes."," Overall, assuming a pc core radius, we find our $_{3}$ (1,1) and (2,2) observations trace $\sim$ 100 to $_\odot$ and density $n_{\rm H_2}=$ 80 to $\times 10^{3}$ $^{-3}$ for the individual cores in the Triple Core and Core 5 complexes." + The core masses are in general agreement with their virial masses., The core masses are in general agreement with their virial masses. +" Higher resolution NIL; ((3.8) observations of 615.39- by Gomez(1991) with the VLA suggest a ppc. radius molecular envelope: around. C15.89-0.39D (Triple Core Central) tracing 30 MM. assuming an abundance ratio \wvi,=10 "," Higher resolution $_3$ (3,3) observations of G5.39-0.39B by \citet{gomez} with the VLA suggest a pc radius molecular envelope around G5.89-0.39B (Triple Core Central) tracing $\sim$ $_\odot$ assuming an abundance ratio ${\large \chi}_{\textrm{\tiny{NH}}_{3}} =10^{-6}$ ." +Using our abundance ratio this mass converts to 71500 MM. . about à factor 5 larger than our mass estimate using the NILI;((1.1). and. (2.2) emission.," Using our abundance ratio this mass converts to $\sim$ $_\odot$ , about a factor 5 larger than our mass estimate using the $_3$ (1,1) and (2,2) emission." + This dillerence may arise from the fact that our, This difference may arise from the fact that our +Carina-Sagittarius and Perseus (for a recent review see Valléce 2002. who also reports a likely pitch angle of 12° for this pattern).,"Carina-Sagittarius and Perseus (for a recent review see Valléee 2002, who also reports a likely pitch angle of $^\circ$ for this pattern)." + Additionally. features such as the Orion spur at the Solar neighborhood. have been revealed: (Cieorgelin Georgelin. 1976).," Additionally, features such as the Orion spur at the Solar neighborhood have been revealed (Georgelin Georgelin 1976)." +" Drinamel (2000) laid down. from the comparison. the hypothesis that the αγιος, structure is 10 gas response to the 2-armed. ""stellar? pattern."," Drimmel (2000) laid down, from the comparison, the hypothesis that the 4-armed structure is the gas response to the 2-armed “stellar"" pattern." + Assuming that indeed the Ix band data is by far a better tracer of mass than the optical data of spiral structure. in js work we model the spiral pattern. from the locus and pitch angle of Drimmel (2000) and study its self-consistency. requirement we consider it must. satisfy.," Assuming that indeed the K band data is by far a better tracer of mass than the optical data of spiral structure, in this work we model the spiral pattern from the locus and pitch angle of Drimmel (2000) and study its self-consistency, a requirement we consider it must satisfy." + As the answer garonglv depends on the pattern. speed. this study. should vield a value for this fundamental Galactic parameter.," As the answer strongly depends on the pattern speed, this study should yield a value for this fundamental Galactic parameter." + The value of the pattern speed of the Galaxy. has been a matter of controversy for a long time., The value of the pattern speed of the Galaxy has been a matter of controversy for a long time. +" From the values proposed by Lin. Yuan Shu (1960) of Q,=dL1Bkms|kpe numbers in the range of 10-60 kms+kpe* have been used in the literature."," From the values proposed by Lin, Yuan Shu (1969) of $\Omega_p = 11-13~km~s^{-1}~kpc^{-1}$ , numbers in the range of 10-60 $km~s^{-1}~kpc^{-1}$ have been used in the literature." + In a previous paper (Pichardo et al 2003. hereafter P1). we explored. the gaellar dynamics in a full axisvmmetric model for our Galaxy Lguperimposing our modeling of mass distribution for the Esλα pattern: the locus of Drimmel (2000). the optical locus of Valléee (2002). and a superposition of both.," In a previous paper (Pichardo et al 2003, hereafter P1), we explored the stellar dynamics in a full axisymmetric model for our Galaxy superimposing our modeling of mass distribution for the spiral pattern: the locus of Drimmel (2000), the optical locus of Valléee (2002), and a superposition of both." + Pl did not sume the usual simple perturbing term (a cosine term for 1e potential) that hack been used in the literature in. the =nocdeling of spiral armis: it is precisely the very. prominent Esrival structure in red light what suggests to us that such structure should be considered an important. galactic component worthy of a modeling elfort bevond the simple »erturbinge term., P1 did not assume the usual simple perturbing term (a cosine term for the potential) that had been used in the literature in the modeling of spiral arms: it is precisely the very prominent spiral structure in red light what suggests to us that such structure should be considered an important galactic component worthy of a modeling effort beyond the simple perturbing term. + Pl modelingὃν consists of a superposition of oblate spheroids for the spiral., P1 modeling consists of a superposition of oblate spheroids for the spiral. +" Pwo different: values of Q,=15.20Kms51kpe 5. were tried."," Two different values of $\Omega_p = 15, 20~km~s^{-1}~kpc^{-1}$ , were tried." +" Phe best. self-consistency was achieved: with ©,20kms|kpe or the locus and pitch angle of Drimmel (2000).", The best self-consistency was achieved with $\Omega_p = 20~km~s^{-1}~kpc^{-1}$ for the locus and pitch angle of Drimmel (2000). + Figure 7 οἱ PI. a mosaic of our sell-consisteney test explained odow [ου parameters including the elobal spiral mass and loci. exhibits a remarkably good. response for this case which rules out the other 3 cases in the panel.," Figure 7 of P1, a mosaic of our self-consistency test – explained below – for parameters including the global spiral mass and loci, exhibits a remarkably good response for this case which rules out the other 3 cases in the panel." +" In act. the behavior at Q,=20funs3kpe* is so good hat one can hardlv envision an improvement on general heoretical grounds."," In fact, the behavior at $\Omega_p = 20~km~s^{-1}~kpc^{-1}$ is so good that one can hardly envision an improvement on general theoretical grounds." +" The question that comes to mind. is. given the spiral locus ancl pitch angle of Drimmel (2000). our adopted mass distribution modeling. and the spiral mass iniplied by observations of external galaxies applied to those parameters. now fixed. are there other values of O, which also satisfy our self-consistency criterion to that accuracy?"," The question that comes to mind is, given the spiral locus and pitch angle of Drimmel (2000), our adopted mass distribution modeling, and the spiral mass implied by observations of external galaxies applied to those parameters, now fixed, are there other values of $\Omega_p$ which also satisfy our self-consistency criterion to that accuracy?" +" In this paper. we extend the selfl-consisteney. calculations to a finer range of values of Q,, in order to answer that question."," In this paper, we extend the self-consistency calculations to a finer range of values of $\Omega_p$ in order to answer that question." + Once the best value is found. we put it to the test in two wavs: Calculating the gaseous response to find out whether ib ds consistent with the observed. optical Galactic spiral pattern. which amounts to a test of Drimmel's hypothesis.," Once the best value is found, we put it to the test in two ways: calculating the gaseous response to find out whether it is consistent with the observed optical Galactic spiral pattern, which amounts to a test of Drimmel's hypothesis." +" Finally. we review recent work using independent data sets which are sensitive to the value of Q,."," Finally, we review recent work using independent data sets which are sensitive to the value of $\Omega_p$." + This is another wav of testing our prediction against “nature”. anc not only versus different modeling approaches. as the subjects of those independent. studies are quite cifferent from. our Galactic modeling elfort.," This is another way of testing our prediction against ""nature"", and not only versus different modeling approaches, as the subjects of those independent studies are quite different from our Galactic modeling effort." + A continued. line of work by. Contopolous and collaborators (see. v.g.," A continued line of work by Contopolous and collaborators (see, v.g." + Patsis. Grosbol and. Ποιοί» 1997 ancl references. therein) has provided. the framework to study the response of gaseous disks to spiral perturbations.," Patsis, l and Hiotelis 1997 and references therein) has provided the framework to study the response of gaseous disks to spiral perturbations." + In that paper. a comparison between SPLL models with Population E features observed on B images of normal. erand design galaxies. showed that the 4:1 resonance generates a jfurcation of the arms and interarm: features.," In that paper, a comparison between SPH models with Population I features observed on B images of normal, grand design galaxies, showed that the 4:1 resonance generates a bifurcation of the arms and interarm features." + Furthermore. Contopoulos Crosbol (1986.1988) had shown that the central [amily of periodic orbits do not support a spiral xdtern bevond the position of the 4:1 resonance. which hus determines the extent of the pattern.," Furthermore, Contopoulos l (1986,1988) had shown that the central family of periodic orbits do not support a spiral pattern beyond the position of the 4:1 resonance, which thus determines the extent of the pattern." + Weak spirals can extend their pattern. up to corotation. from linear heory.," Weak spirals can extend their pattern up to corotation, from linear theory." + A phenomenological link between resonances. the angular speed. and the stellar ancl gas patterns in spirals is complemented by the study of Cirosbol and Patsis (2001) using deep Ix. band. surface. photometry to analyze spiral structure in 12 galaxies.," A phenomenological link between resonances, the angular speed, and the stellar and gas patterns in spirals is complemented by the study of l and Patsis (2001) using deep K band surface photometry to analyze spiral structure in 12 galaxies." + They find that the radial extent of he two-armec pattern is consistent with the location of the major resonances: the inner Lindblad resonance (LL). the 4:1 resonance. corotation and the outer Lindblad resonance (OLR).," They find that the radial extent of the two-armed pattern is consistent with the location of the major resonances: the inner Lindblad resonance (ILR), the 4:1 resonance, corotation and the outer Lindblad resonance (OLR)." + For galaxies with a bar perturbation. the extent of he main spiral was better fitted assuming it is limited. by corotation and the OLR.," For galaxies with a bar perturbation, the extent of the main spiral was better fitted assuming it is limited by corotation and the OLR." + Using Mo=75Ains.|Alpe1+. the odtern speed was found to be for the entire sample of the order of 20 kins*Ape1. and remarkably. not a sensitive tunction of morphological type or total mass.," Using $H_0 = 75~km~s^{-1}~Mpc^{-1}$, the pattern speed was found to be for the entire sample of the order of 20 $km~s^{-1}~kpc^{-1}$, and remarkably, not a sensitive function of morphological type or total mass." +" 1n the following section we describe our results. [or he stellar orbital response to the imposed. spiral pattern. hrough which £3, is determined."," In the following section we describe our results for the stellar orbital response to the imposed spiral pattern, through which $\Omega_{p}$ is determined." + As in Pl our axisymmetric Galactic model is that of Allen Santillánn (1991). which includes a bulge and a Iattened isk proposed by Alivamoto Nagai (1975). together with a massive spherical dark halo.," As in P1 our axisymmetric Galactic model is that of Allen Santillánn (1991), which includes a bulge and a flattened disk proposed by Miyamoto Nagai (1975), together with a massive spherical dark halo." + We coupled to this mass istribution a spiral pattern. modeled. as a superposition of inhomogeneous oblate spheroids along a locus that fits 16 IX. band. cata of Drimmel (2000). with a pitch angle of 15.," We coupled to this mass distribution a spiral pattern modeled as a superposition of inhomogeneous oblate spheroids along a locus that fits the K band data of Drimmel (2000), with a pitch angle of $^\circ$." +5 Pl describes in detail the parameters of the spheroids. which brielly are: the minor axis of the spheroids is perpendicular to the Galactic plane and its length is 0.5 kpe: the major semi-axes have a length. of 1 kpe.," P1 describes in detail the parameters of the spheroids, which briefly are: the minor axis of the spheroids is perpendicular to the Galactic plane and its length is 0.5 kpc; the major semi-axes have a length of 1 kpc." + Each spheroid has a similar mass distribution., Each spheroid has a similar mass distribution. + Dillerent. density laws. linear and exponential. were analvzed. finding no important dillerences.," Different density laws, linear and exponential, were analyzed, finding no important differences." + The total mass in the spiral is fixed such that the local ratio of spiral to background (disk) force have a prescribed value., The total mass in the spiral is fixed such that the local ratio of spiral to background (disk) force have a prescribed value. + Seeking sensible values for this ratio. we used the empirical result of Patsis. Contopoulos ancl Cirosbol (1991). where self-consistent mocels for 12 normal spiral galaxies are presented. a sample including Sa. Sb andSe galaxies.," Seeking sensible values for this ratio, we used the empirical result of Patsis, Contopoulos and l (1991), where self-consistent models for 12 normal spiral galaxies are presented, a sample including Sa, Sb andSc galaxies." + Fheir, Their +dC stars.,HdC stars. + The spectra allow a direct comparison between (he winds of the two classes of objects ancl (hus directly address the relationship between the classes., The spectra allow a direct comparison between the winds of the two classes of objects and thus directly address the relationship between the classes. + A second motivation for this study is to investigate the nature of the wind driver., A second motivation for this study is to investigate the nature of the wind driver. + It has been suggested that the winds in RCB stars are dust driven (Clavtonetal.1992)., It has been suggested that the winds in RCB stars are dust driven \citep{cla92}. +. If there also are winds in {heir dustless cousins. the Πας; stars. then another driving mechanism must exist.," If there also are winds in their dustless cousins, the HdC stars, then another driving mechanism must exist." + Spectra in the vicinity of the He I 10330 lline were obtained for the live known HdC stars on 2008 February 4 and 7 ancl April 4 and 6 al (he Gemini South telescope. using (he echelle spectrograph Phoenix. as part of Gemini program GS-2008A-Q-17.," Spectra in the vicinity of the He I 10830 line were obtained for the five known HdC stars on 2008 February 4 and 7 and April 4 and 6 at the Gemini South telescope, using the echelle spectrograph Phoenix, as part of Gemini program GS-2008A-Q-17." +" A log of these and additional observations is given in Table 1,", A log of these and additional observations is given in Table 1. + The sslit was used and provided a resolving power of ~ 50.000.," The slit was used and provided a resolving power of $\sim$ 50,000." + Each star was positioned allernately al two locations along (he slit., Each star was positioned alternately at two locations along the slit. + Total integration times were (vpically a few minutes., Total integration times were typically a few minutes. +" The extreme helium (Elle) star. FQ Aqr. which is expected to have a prominent 10830 απο, was also observed at Gemini South on 2008 April 11."," The extreme helium (EHe) star, FQ Aqr, which is expected to have a prominent 10830 line, was also observed at Gemini South on 2008 April 11." + Elle stars. which are low mass A or D supergiants with strong helium lines and weak or absent hydrogen limes. appear to be hieher temperature counterparts of ROB and Πας stars (Pandeyοἱal.2001:Jeffery.2003).," EHe stars, which are low mass A or B supergiants with strong helium lines and weak or absent hydrogen lines, appear to be higher temperature counterparts of RCB and HdC stars \citep{pan01, jef08}." +. The wind characteristics of the Elle stars are not known., The wind characteristics of the EHe stars are not known. + Spectra of bright main sequence stars of spectral (vpes AOA? were obtained near-smulianeouslv to and at similar airmasses as those of the HWdC and Elle stars in order to remove telluric lines [rom the Πας and Elle stellar spectra aud to provide wavelength calibration via the same tellurie lines., Spectra of bright main sequence stars of spectral types A0–A2 were obtained near-simultaneously to and at similar airmasses as those of the HdC and EHe stars in order to remove telluric lines from the HdC and EHe stellar spectra and to provide wavelength calibration via the same telluric lines. + The wavelength calibration is accurate to better than 3km !.., The wavelength calibration is accurate to better than 3 km $^{-1}$. + A few of the A stars possessed weak 10830, A few of the A stars possessed weak 10830 +The logarithmic. or power-law slope a(r) thus,"The logarithmic, or power-law slope $\alpha(r)$ thus." +"r,..", Fig. + Fig. 2 shows atr) [ον à munber of values of + and r;. where the values have been chosen to cover the range shown by the LSB rotation curve fits [rom IIO4.," \ref{fig:courslope} shows $\alpha(r)$ for a number of values of $\gamma$ and $r_t$, where the values have been chosen to cover the range shown by the LSB rotation curve fits from H04." + Changing > has the effect of changing the shape of the slope-radius relations: changing r; shifts the relations horizontally without allecting the shape for anv particular 5., Changing $\gamma$ has the effect of changing the shape of the slope-radius relations; changing $r_t$ shifts the relations horizontally without affecting the shape for any particular $\gamma$. + Most of the plotted slopes are remarkably ab small radii., Most of the plotted slopes are remarkably at small radii. + An inner asvanptotie value of a=0 is predominant., An inner asymptotic value of $\alpha = 0$ is predominant. + The CDM slope a~—1 can onlv be reproduced with Eqs. (, The CDM slope $\alpha \sim -1$ can only be reproduced with Eqs. ( +"1) and (4) for small values of r, and/or exiremely smallvalues of 5.",1) and (4) for small values of $r_t$ and/or extremely smallvalues of $\gamma$. + Similarly. at large radii the slope converges to a=—2.," Similarly, at large radii the slope converges to $\alpha = -2$." + These are not naturally occurring values for CDM mass profiles. with asvmptotie slopes aS—1 in the inner parts and a=—3 in the outer parts.," These are not naturally occurring values for $\Lambda$ CDM mass profiles, with asymptotic slopes $\alpha \la -1$ in the inner parts and $\alpha=-3$ in the outer parts." +" Equation (1) is really built to mimic the same striking features of rotation curves that led to the introduction of the pseudo-isothermal (SO) halo. namely a solic-body rise in (he inner parts. and a constant (""flat) rotation velocity in the outer parts."," Equation (1) is really built to mimic the same striking features of rotation curves that led to the introduction of the pseudo-isothermal (ISO) halo, namely a solid-body rise in the inner parts, and a constant (“flat”) rotation velocity in the outer parts." + One needs (to make very specific choices of fitting parameters to make this function resemble an NEW profile., One needs to make very specific choices of fitting parameters to make this function resemble an NFW profile. + The LIO4 simulations predict steep slopes. even at the smallest reliably resolved radii. delined by the so-called convergence radius rCON (Poweretal.2003).," The H04 simulations predict steep slopes, even at the smallest reliably resolved radii, defined by the so-called convergence radius $r_{\rm conv}$ \citep{power03}." +. For the IIO4. dwarf ealaxv models Pon=0.352+ kpe or ~0.4 kpe or AhO.7., For the H04 dwarf galaxy models $r_{\rm conv}= 0.3h^{-1}$ kpc or $\sim 0.4$ kpc for $h=0.7$. +" The slope at ra, in the simulations varies between àc—1 and ~—1.3.", The slope at $r_{\rm conv}$ in the simulations varies between $\alpha \sim -1$ and $\sim -1.3$. + Equation (4) can be used to derive the slopes implied by the fits to the observed LSB rotation curves., Equation (4) can be used to derive the slopes implied by the fits to the observed LSB rotation curves. + For (his one needs to choose a radius al which the slopes will be evaluated., For this one needs to choose a radius at which the slopes will be evaluated. + In the rest of this paper 6wo choices will be used., In the rest of this paper two choices will be used. + Firstv. (he radius of the innermost measured point of the rotation curve as given in deBloketal.(2001b) and will beconsidered!..," Firstly, the radius of the innermost measured point of the rotation curve as given in \citet{blok2001b} and \citet{dBB02} will be." + One might argue that at r=ry à different radius is probed for each rotalion curve. so. secondly. a constant radius r—0.4 kpe 2ray Κρὸ for all curves will be used as well.," One might argue that at $r= r_{\rm in}$ a different radius is probed for each rotation curve, so, secondly, a constant radius $r = 0.4$ kpc $ +\simeq r_{\rm conv}$ kpc for all curves will be used as well." +" One should not expect dramatically different results from both choices (hough: the average value of rj, is ~0.45 kpc. very much comparable with roo."," One should not expect dramatically different results from both choices though: the average value of $r_{\rm in}$ is $\sim 0.45$ kpc, very much comparable with $r_{\rm conv}$ ." + Ht should be kept in nund that even though we evaluate the slope at these particular choices for the radius. the," It should be kept in mind that even though we evaluate the slope at these particular choices for the radius, the" +(Llarlaftis et al. 1999).,"(Harlaftis et al, 1999)." + Thus we have shown that using TiO xuds for radial velocity studies can be a very powerful tool., Thus we have shown that using TiO bands for radial velocity studies can be a very powerful tool. + From the new T«. we re-determined the orbital period. using our data and that of Chevalier Hovaisky (1996). Filipenke. Alatheson llo (1995). LHlarlaftis et al (1999) and. Casares et. al (1995). so as to extend the base line.," From the new $_\circ$, we re-determined the orbital period, using our data and that of Chevalier Ilovaisky (1996), Filipenko, Matheson Ho (1995), Harlaftis et al (1999) and Casares et al (1995), so as to extend the base line." + Each Εν was adjusted to the phase convention used here in equation L., Each $_\circ$ was adjusted to the phase convention used here in equation \ref{eq:newephem}. +A period of 0.21216002:0.0000002d. was found to fit all the data. with a T. of 2450274.41562:0.0009.," A period of $\pm$ 0.0000002d was found to fit all the data, with a $_\circ$ of $\pm$ 0.0009." + ‘This gives a new ephemoeris ol. where Ε.Ο is the LHeliocentric Julian Date and E the cvcle number.," This gives a new ephemeris of, where HJD is the Heliocentric Julian Date and E the cycle number." + Phase zero for this ephemeris is taken to be the inferior conjunction of the Iate-type star., Phase zero for this ephemeris is taken to be the inferior conjunction of the late-type star. + From our initial estimate of the magnitude of 0422|32. it appeared that 0422|32 had. become considerably fainter over the 3 vears since it was last observed.," From our initial estimate of the magnitude of J0422+32, it appeared that J0422+32 had become considerably fainter over the 3 years since it was last observed." + Previously. J0422|32 was found to be —0.14 magnitudes brighter when observed. by Casares et al (1995). in December 1994 and 10.33 magnitudes brighter when observed. by Orosz Dailvn (1995). in October 1994.," Previously, J0422+32 was found to be $\sim$ 0.14 magnitudes brighter when observed by Casares et al \shortcite{Casa95} + in December 1994 and $\sim$ 0.33 magnitudes brighter when observed by Orosz Bailyn \shortcite{Oros95} in October 1994." + Vo verily this. we used the Following method.," To verify this, we used the following method." + The Casares et al (1995). observation is the lowest published value to date., The Casares et al \shortcite{Casa95} observation is the lowest published value to date. + We reanalysed the Casares et al (1995) data bv obtaining the frames taken at the ΙΤ in December 1994 from the RGO Astronomy Data Centre., We reanalysed the Casares et al \shortcite{Casa95} data by obtaining the frames taken at the JKT in December 1994 from the RGO Astronomy Data Centre. + These we reduced. in the same manner as the 0422|32 Whotometrv that we obtained in December 1997. from the INT. although a simple Iat-lelding technique was used. as there was no [ringing effect. on these CCD frames.," These we reduced in the same manner as the J0422+32 photometry that we obtained in December 1997 from the INT, although a simple flat-fielding technique was used, as there was no fringing effect on these CCD frames." + >hotometry was carried out on the 1994 data of JO422|32 and 7 stars in the neighbourhood and on the same stars in he 1997 data., Photometry was carried out on the 1994 data of J0422+32 and 7 stars in the neighbourhood and on the same stars in the 1997 data. + Both the frames used. were from a similar hase (ὁ20.67)., Both the frames used were from a similar phase ${\phi\simeq}$ 0.67). + In cach case. J0422|32. was divided by cach of the other 7 stars in the frame and the relative counts compared from the two vears.," In each case, J0422+32 was divided by each of the other 7 stars in the frame and the relative counts compared from the two years." + The 1997 data was found to be 2243 fainter than the 1994 data of L=20.22+0.07 (where the error is the standard deviation caleulated from the ratio between the 1997 and 1994 data for each of the 7 stars), The 1997 data was found to be $\pm$ fainter than the 1994 data of $\pm$ 0.07 (where the error is the standard deviation calculated from the ratio between the 1997 and 1994 data for each of the 7 stars). + ‘This indicates that we observed JO422|32 at an I magnitude of 20.44+0.08., This indicates that we observed J0422+32 at an I magnitude of $\pm$ 0.08. + This is the lowest state that J0422|32 has been observed to date. which indicates that in 1994. it had not vet reached. its quiescent value. following the outburst ancl subsequent mini-outbursts.," This is the lowest state that J0422+32 has been observed to date, which indicates that in 1994, it had not yet reached its quiescent value, following the outburst and subsequent mini-outbursts." + ‘To search for periodicities in the photometry. à. Fourier ransform routine was used.," To search for periodicities in the photometry, a Fourier transform routine was used." + From the power spectrum. we ound no significant evidence for the orbital period reported w others (ee. Filippenko. Matheson IIo. 1995). nor any other period.," From the power spectrum, we found no significant evidence for the orbital period reported by others (e.g. Filippenko, Matheson Ho, 1995), nor any other period." + Llowever. as binning the spectroscopic data on the 5.1 jour period had been so successful. the cata were then jnned into the same S phase bins. of 0.125 of the orbital »iod.," However, as binning the spectroscopic data on the 5.1 hour period had been so successful, the data were then binned into the same 8 phase bins, of 0.125 of the orbital period." + Each bin had a minimum of 5 points in it., Each bin had a minimum of 5 points in it. + The weighted mean relative [lux was calculated and an average shase. for each bin.," The weighted mean relative flux was calculated and an average phase, for each bin." + Plotting relative Dux against phase. an ellipsoidal. modulation. as seen by Beckman ct al (1997). Chevalier llovaisky (1996). Martin et al (1995) ete is therefore evident.," Plotting relative flux against phase, an ellipsoidal modulation, as seen by Beekman et al (1997), Chevalier Ilovaisky (1996), Martin et al (1995) etc is therefore evident." + Llowever. we observe excess flux. between phases 7-0.4-0.6. which may be due to the irradiation of the M star by the inner edge of the accretion disc (e.g. Shahbaz. 1994). although why the X-ray heating should increase curing this low state. is unclear.," However, we observe excess flux between phases $\sim$ 0.4-0.6, which may be due to the irradiation of the M star by the inner edge of the accretion disc (e.g. Shahbaz, 1994), although why the X-ray heating should increase during this low state, is unclear." + From examining the database from the Alb-Sky Monitor on the X-ray Timing Explorer (XP) for J0422|32 around this observation period. the X-ray activity was minimal.," From examining the database from the All-Sky Monitor on the X-ray Timing Explorer (XTE) for J0422+32 around this observation period, the X-ray activity was minimal." + It is however possible. that since JOL22|32 hac declined from outburst in December 1997. the disc opening angle should also have decreased (see e.g. Webb et al. 1999).," It is however possible, that since J0422+32 had declined from outburst in December 1997, the disc opening angle should also have decreased (see e.g. Webb et al, 1999)." + Therefore more X-rays from the inner parts of the dise woulc be able to impinge on the secondary. star. and thus heat the surface between phases 0.4-0.6.," Therefore more X-rays from the inner parts of the disc would be able to impinge on the secondary star, and thus heat the surface between phases 0.4-0.6." + Our interest is to measure the maximum allow«« amplitude in this Ποιονο to constrain the inclination of this system. (see Sec. 5.3)).," Our interest is to measure the maximum allowed amplitude in this light-curve, to constrain the inclination of this system (see Sec. \ref{sec:orbpar}) )." + Clearly. a larger amplitude is possible if we ignore the “X-ray heated! points.," Clearly, a larger amplitude is possible if we ignore the `X-ray heated' points." + We therefore fitted the [ux variation between phases 70.6-1.4., We therefore fitted the flux variation between phases $\sim$ 0.6-1.4. + The maximum Ilux variation is 0.014., The maximum flux variation is 0.014. + Taking into account that only of the Hus observed emanates from the M star, Taking into account that only of the flux observed emanates from the M star +The data in Table 9. thus show that disks are found in wide multiple-svstenis: απσον docs not necessarily destrov a disk.,The data in Table \ref{tab:multiple} thus show that disks are found in wide multiple-systems: multiplicity does not necessarily destroy a disk. + The solu system shows evidence for α fast removal of a disk of plauctesimals a few hundred. Myr. after he Sun formed a disk., The solar system shows evidence for a fast removal of a disk of planetesimals a few hundred Myr after the Sun formed a disk. + The best case is given by the surface of the Moon. where accurate crater countiis LOu high resolution iaging can be combined with aceurate age deteriunations of different parts of the Aloous surface.," The best case is given by the surface of the Moon, where accurate crater counting from high resolution imaging can be combined with accurate age determinations of different parts of the Moon's surface." + The age of the hmar surface is known rou the rocks brought back to earth bw the Apollo wissious: the early history of the Moon was marked bv aimich higher cratering rate than observed today: see for a iscussion Shocuaser&Shocinalser (1999)..., The age of the lunar surface is known from the rocks brought back to earth by the Apollo missions; the early history of the Moon was marked by a much higher cratering rate than observed today; see for a discussion \citet{shoe:99}. . +" This so-caled ""heavy bombardiucut” lasted uutil some Nr attey the formation of the Sun.", This so-called “heavy bombardment” lasted until some Myr after the formation of the Sun. + Thereafter the impact rate decreased exponentialv with time coustauts between ae aud a few- times: PES years (Chyba1990)., Thereafter the impact rate decreased exponentially with time constants between $^7$ and a few times $^8$ years \citep{chyb:90}. +. Other plancts and satellites with little erosion on their surface confi this evidence: Mercury (StromὃνNeukuim 1988).. Maius (Ashotal.|996:Soderblomet1971) Canvinede aud Callisto (Shocimaker&Wolfe1982:Neukumneal.1997:Zahuleet 1998).," Other planets and satellites with little erosion on their surface confirm this evidence: Mercury \citep{stro:88}, Mars \citep{ashx:96, + sode:74} Ganymede and Callisto \citep{shoe:82,neuk:97,zahn:98}." +. The exact timescales are a matter ofehate., The exact timescales are a matter of debate. + Thus there are indications of a cleanup phase of a few hundred Myr throughout the solar svstem: these cleanup processes lay be dynamically connected., Thus there are indications of a cleanup phase of a few hundred Myr throughout the solar system; these cleanup processes may be dynamically connected. + The plotometers on ISO have been used to measure the 60 and 170 gen flux deusities of a sample of 81 12ain-sequence stars with spectral tvpes from A to Ix. On the basis o theevidence prescuted we draw the following conclusions:, The photometers on ISO have been used to measure the 60 and 170 $\mu m$ flux densities of a sample of 84 main-sequence stars with spectral types from A to K. On the basis of theevidence presented we draw the following conclusions: +nuclei.,nuclei. + The mean off-axis angle of the nucleus during the observation was only 38 arcseconds. so the point spread [unction (ealeulated using the standard CIAO tools) is very close to the value.," The mean off-axis angle of the nucleus during the observation was only 38 arcseconds, so the point spread function (calculated using the standard CIAO tools) is very close to the on-axis value." + To estimate source fIuxes. we generated monochromatic point spread functions for the midpoints of the three energv bands using the CLAO tool mkpsf. ancl subtracted a point source from (he raw images at the location of the hard peak. with the maximum amplitude that did not create a dip in the local diffuse flux when the data was then smoothed.," To estimate source fluxes, we generated monochromatic point spread functions for the midpoints of the three energy bands using the CIAO tool mkpsf, and subtracted a point source from the raw images at the location of the hard peak, with the maximum amplitude that did not create a dip in the local diffuse flux when the data was then smoothed." + This procedure was repeated at the location of remaining fIux peaks., This procedure was repeated at the location of remaining flux peaks. + The central region is consistent (within the 1 absolute astrometrie accuracy of the Chandra data) with a pair of hard point sources at the positions of radio nuclei A and D (Scoville et al 19983). with the western nucleus dominant. although the best fit separation for (wo point sources is only 0.77 rather than the 1.17 of the radio posiGons and the decomposition of this small region into multiple point sources and diffuse emission is nol unique.," The central region is consistent (within the 1"" absolute astrometric accuracy of the Chandra data) with a pair of hard point sources at the positions of radio nuclei A and B (Scoville et al 1998), with the western nucleus dominant, although the best fit separation for two point sources is only 0.7"" rather than the 1.1"" of the radio positions and the decomposition of this small region into multiple point sources and diffuse emission is not unique." + We designate the sources in order of total flux., We designate the sources in order of total flux. + The hard band image shows emission concentrated around a nuclear source. X-1. with extended emission around it.," The hard band image shows emission concentrated around a nuclear source, X-1, with extended emission around it." + Point source subtraction suggests the presence of a much weaker second hard nucleus. X-4. together with a diffuse component which we denote as the X-1 halo: its centroid is 0.5 arcseconds east of X-1.," Point source subtraction suggests the presence of a much weaker second hard nucleus, X-4, together with a diffuse component which we denote as the X-1 halo; its centroid is 0.5 arcseconds east of X-1." + X-2. further out from the nucleus. is a hard source detected out to 5 keV: only 23 net counts are seen.," X-2, further out from the nucleus, is a hard source detected out to 5 keV; only 33 net counts are seen." + Its luminosity of 6x10ergs puts it in the interesting category of ULX (ultra-Iuninous X-ray) sources., Its luminosity of $6\times 10^{39}\mbox{erg s$ $}$ puts it in the interesting category of non-nuclear ULX (ultra-luminous X-ray) sources. + X-3. (he soft peak. is not reliably separated from the extended soft circumnuclear emission. aud coincides with the peak of the IIo. emission (Arribas. Colina Clements 2001: MeDowell et al.," X-3, the soft peak, is not reliably separated from the extended soft circumnuclear emission, and coincides with the peak of the $\alpha$ emission (Arribas, Colina Clements 2001; McDowell et al." + 2002)., 2002). + The 210keV luminosity we derive for the nuclear source N-1 and surrounding hard emission (assuming the spectral model derived in the next section) is 6.0x10 eres st. measured [rom a 3 aperture centred on (he nucleus.," The 2–10keV luminosity we derive for the nuclear source X-1 and surrounding hard emission (assuming the spectral model derived in the next section) is $\times +10^{40}$ ergs $^{-1}$, measured from a 3” aperture centred on the nucleus." + Because of the poorly constrained absorption. here ancl below we quote observed Iuminosiüies rather (han absorption-corrected ones unless explicitly stating otherwise.," Because of the poorly constrained absorption, here and below we quote observed luminosities rather than absorption-corrected ones unless explicitly stating otherwise." + The hard luminosity found here compares to the 2JOkeV hnuninositv found by Iwasawa et al. (, The hard luminosity found here compares to the 2–10keV luminosity found by Iwasawa et al. ( +2001). in a 3 arcminute aperture. of 11x107 eres LI. asstuning a similar distance to Arp 220.,"2001), in a 3 arcminute aperture, of $\times 10^{40}$ ergs $^{-1}$, assuming a similar distance to Arp 220." + The background in our observation makes us insensitive to hard enission on 3 areminute scales. and we cannot rule out an extended contribution of (his magnitude.," The background in our observation makes us insensitive to hard emission on 3 arcminute scales, and we cannot rule out an extended contribution of this magnitude." + ILowever. the 3 sigma upper limit to any remaining hard (2-8 keV) flux within | arcminute of the nucleus is 2.6xLOMeres and we speculate tha enussion [rom the nearby southern group max be contributing to the Iwasawa et al result.," However, the 3 sigma upper limit to any remaining hard (2-8 keV) flux within 1 arcminute of the nucleus is $2.6\times10^{40}\mbox{erg s$ $}$ and we speculate that emission from the nearby southern group may be contributing to the Iwasawa et al result." + Deeper observations wilh NMM/Newton would resolve (his issue., Deeper observations with XMM/Newton would resolve this issue. +time scale of the envelope.,time scale of the envelope. +" Second, pulsations tend to be out with the method adopted in stellar numericallyevolution dampedcodes."," Second, pulsations tend to be numerically damped out with the implicit method adopted in stellar evolution codes." +" However, the implicitstudy by Hegeretal.(1997) shows that the predictions of linear stability analysis for basic pulsational properties (i.e., pulsation period and growth rate) can be accurately reproduced in non-linear evolutionary calculations of RSGs by a hydrodynamic stellar evolution code, if the growth rate is sufficiently large and if the adopted time steps are sufficiently small."," However, the study by \citet{Heger97} shows that the predictions of linear stability analysis for basic pulsational properties (i.e., pulsation period and growth rate) can be accurately reproduced in non-linear evolutionary calculations of RSGs by a hydrodynamic stellar evolution code, if the growth rate is sufficiently large and if the adopted time steps are sufficiently small." +" On the other hand, non-linear evolutionary calculations do not require the condition of complete thermal and hydrostatic equilibrium of the star, in contrast to the case of linear stability analysis."," On the other hand, non-linear evolutionary calculations do not require the condition of complete thermal and hydrostatic equilibrium of the star, in contrast to the case of linear stability analysis." + We therefore decide to use an existing stellar evolution code for our analysis of RSG pulsations., We therefore decide to use an existing hydrodynamic stellar evolution code for our analysis of RSG pulsations. + hydrodynamicDetails of our implicit hydrodynamic code are described in (2006) and references therein., Details of our implicit hydrodynamic code are described in \citet{Yoon06} and references therein. +" To start with, we construct non-rotating hydrostatic models at solar metallicity for 11 different initial masses (15, 16, 17, 18, 19, 20, 21, 23, 25, 30, 40 Mo))."," To start with, we construct non-rotating hydrostatic models at solar metallicity for 11 different initial masses (15, 16, 17, 18, 19, 20, 21, 23, 25, 30, 40 )." +" Since the hydrodynamic term in the momentum equation is switched off, pulsations do not appear in these model sequences."," Since the hydrodynamic term in the momentum equation is switched off, pulsations do not appear in these model sequences." + The HR diagrams for some model sequences are shown in Fig. 1.., The HR diagrams for some model sequences are shown in Fig. \ref{fig:hr}. +" Then, we turn on the hydrodynamic term and restart the calculation from the reference models chosen at various evolutionary epochs during the supergiant phase for each model sequence."," Then, we turn on the hydrodynamic term and restart the calculation from the reference models chosen at various evolutionary epochs during the supergiant phase for each model sequence." +" In total, 71 reference models are selected as starting points."," In total, 71 reference models are selected as starting points." +" In Fig. 1,,"," In Fig. \ref{fig:hr}," +" some of the starting points are shown, marked by filled circles and open diamonds."," some of the starting points are shown, marked by filled circles and open diamonds." +" To guarantee enough time resolution for describing pulsations in the hydrodynamic calculations, we limit the time steps such that At<0.01[R/(1000Ryr."," To guarantee enough time resolution for describing pulsations in the hydrodynamic calculations, we limit the time steps such that $\Delta t \le +0.01[R/(1000\mathrm{R_\odot})]^2[(15\mathrm{M_\odot})/M]~\mathrm{yr}$." +" This choice is based on the fact that pulsations5)? [(15M)/M]of a RSG with Minit>15Mo have a period of the order of 1000 days (e.g.Heger 1997),, and obey the relation of PοςR*/M, where P is the R the radius and M the total mass of a RSG pulsation(Goughetperiod,al.1965)."," This choice is based on the fact that pulsations of a RSG with $ M_\mathrm{init} > +15~\mathrm{M_\odot}$ have a period of the order of 1000 days \citep[e.g.][]{Heger97}, and obey the relation of $P \propto R^2/M$, where $P$ is the pulsation period, $R$ the radius and $M$ the total mass of a RSG \citep{Gough65}." +. An example of such calculations is given in Fig. 2.., An example of such calculations is given in Fig. \ref{fig:velocity}. +" As the pulsation amplitude grows gradually, the surface velocity eventually reaches the sound speed."," As the pulsation amplitude grows gradually, the surface velocity eventually reaches the sound speed." +" Since ourcode cannot describe shock waves, we investigate the pulsation properties only with the sub-sonic results."," Since ourcode cannot describe shock waves, we investigate the pulsation properties only with the sub-sonic results." + Fig., Fig. + 1 shows the pulsation period P and the growth rate η of the fundamental mode at different reference points on the HR diagram., \ref{fig:hr} shows the pulsation period $P$ and the growth rate $\eta$ of the fundamental mode at different reference points on the HR diagram. +" Here, the growth rate is defined as η=|v(to+P)/v(to)|, where v(to) denotes a local maximum of the surface velocity located at a certain time f=f."," Here, the growth rate is defined as $\eta = |v(t_0+P)/v(t_0)|$, where $v(t_0)$ denotes a local maximum of the surface velocity located at a certain time $t=t_0$." +" According to this definition, pulsational instability means η>1."," According to this definition, pulsational instability means $\eta > 1$." +" The growth rate obtained here should be considered only indicative, given the limitations of our adopted numerical method."," The growth rate obtained here should be considered only indicative, given the limitations of our adopted numerical method." +" For in our calculations, no pulsation is detected from some example,reference points."," For example, in our calculations, no pulsation is detected from some reference points." +" This does not mean that the considered RSGs are stable against the pulsational instability, but that the growth rate is too small for our code to follow."," This does not mean that the considered RSGs are stable against the pulsational instability, but that the growth rate is too small for our code to follow." +" Also, in our calculations, instant adjustment of convective flux during pulsation is assumed, which is not physical given the similar time scales of convection and tion?.."," Also, in our calculations, instant adjustment of convective flux during pulsation is assumed, which is not physical given the similar time scales of convection and ." +" Despite these uncertainties, our results are qualitatively"," Despite these uncertainties, our results are qualitatively" + , +sviithesis models which greatly aided the paper.,synthesis models which greatly aided the paper. + We also (hank M. Polletta for useful contributions io this We (hank the anonvmous referee for comments which greatly improved this This work was supported bv the Science aud Technology Facilities Research Council ierant numberSpitzer(1AS)..SDSS..," We also thank M. Polletta for useful contributions to this We thank the anonymous referee for comments which greatly improved this This work was supported by the Science and Technology Facilities Research Council [grant number,." +evidence to remnant intracluster light anc CSSs.,evidence to remnant intracluster light and CSSs. + Since disruption ellicieney. depends on environmental factors such as density and cluster mass. we investigate the spatial distribution. kinematics ancl photometric properties of an increased sample of Virgo ancl Fornax redshift-confirmed Iuminous CSSs in three cluster environments.," Since disruption efficiency depends on environmental factors such as density and cluster mass, we investigate the spatial distribution, kinematics and photometric properties of an increased sample of Virgo and Fornax redshift-confirmed luminous CSSs in three cluster environments." + 1n Section 2 we describe Virgo and Fornax observations during 2006 with the ANOmeea multi-fibre spectrograph at the 3.9-m Anelo-Australian Telescope (AAT)., In Section 2 we describe Virgo and Fornax observations during 2006 with the AAOmega multi-fibre spectrograph at the 3.9-m Anglo-Australian Telescope (AAT). + Phe Virgo observations were completed in 2006. between March 28 and April 1.," The Virgo observations were completed in 2006, between March 28 and April 1." + The scientific objectives were to (1) compare the distributions of bright and faint CSSs. in order to test the hypothesis that bright CSSs are simply the bright tail of the GC luminosity distribution (e.g.?):: and (2) test the hypothesis that bright CSSs are the remnant nuclei of tically stripped dlI.N galaxies. and are consequently more. widely distributed than classical GCs — tidal threshing simulations," The scientific objectives were to (1) compare the distributions of bright and faint CSSs, in order to test the hypothesis that bright CSSs are simply the bright tail of the GC luminosity distribution \citep[e.g.][]{Mieske..2004I}; and (2) test the hypothesis that bright CSSs are the remnant nuclei of tidally stripped dE,N galaxies, and are consequently more widely distributed than classical GCs – tidal threshing simulations" +by both temperature and gravity effects.,by both temperature and gravity effects. + We show an example of the computed median ridge lines. with NGC 1851 in Fig. 5..," We show an example of the computed median ridge lines, with NGC 1851 in Fig. \ref{fig_tg}." + Generally. we confirm that the curvature of S3839(CN) as a function of V magnitude is much smaller than the curvature of CH4300.," Generally, we confirm that the curvature of S3839(CN) as a function of V magnitude is much smaller than the curvature of CH4300." + We define our rectified 083839(CN) and 6CH4300 indices as the difference between the original S3839(CN) and CH4300 indices and their respective median ridge lines., We define our rectified $\delta$ S3839(CN) and $\delta$ CH4300 indices as the difference between the original S3839(CN) and CH4300 indices and their respective median ridge lines. + The rectified indices will be used throughout the rest of this paper., The rectified indices will be used throughout the rest of this paper. + To increase our observed sample. we re-reduced the 47 Tuc data we found in the ESO archive with our procedure. which is very similar to the one adopted by the original team that made the observations2003).," To increase our observed sample, we re-reduced the 47 Tuc data we found in the ESO archive with our procedure, which is very similar to the one adopted by the original team that made the observations." +. This way. a direct comparison of the results was possible. showing excellent agreement and therefore providing a useful validation of our adopted procedure.," This way, a direct comparison of the results was possible, showing excellent agreement and therefore providing a useful validation of our adopted procedure." + We also added index measurements for the four clusters in that had MS and SGB stars faint enough to have pristine surface composition. not altered by the first dredge-up mixing episode. which happens at the base of the RGB.," We also added index measurements for the four clusters in that had MS and SGB stars faint enough to have pristine surface composition, not altered by the first dredge-up mixing episode, which happens at the base of the RGB." + We therefore selected from their measurements (their Table À.1) those stars in NGC 362 with «18.5. in M 55 with V<17.5. in M 15 with V« 18.5. and in M 22 with V«172008).," We therefore selected from their measurements (their Table A.1) those stars in NGC 362 with $<$ 18.5, in M 55 with $<$ 17.5, in M 15 with $<18.5$ , and in M 22 with $<$ 17." +. Their definition of indices is exactly the same as ours (Sect. 3))., Their definition of indices is exactly the same as ours (Sect. \ref{sec-index}) ). + We applied a more strict selection in radial velocity. at c (as in Sect. 2.5)).," We applied a more strict selection in radial velocity, at $\sigma$ (as in Sect. \ref{sec-1stqc}) )." + We then removed the temperature and gravity dependency from their measurements (their Table A.1). using the same procedure described in Sect. 3.2..," We then removed the temperature and gravity dependency from their measurements (their Table A.1), using the same procedure described in Sect. \ref{sec-tg}." + do not give the S/N of their spectra. but judging from their errobars (see their Table A.1). they should be of the order of S/Nx 15-20 for M 15. M 22. and M 55. and S/Nx 10-15 for NGC 362 anf NGC 288.," do not give the S/N of their spectra, but judging from their errobars (see their Table A.1), they should be of the order of $\simeq$ 15–20 for M 15, M 22, and M 55, and $\simeq$ 10–15 for NGC 362 anf NGC 288." + In the following sections. we analyse and diseuss these data together with ours.," In the following sections, we analyse and discuss these data together with ours." + The presence of CH and CN bimodalities. Le. two well separated groups of stars with a different strength of these bands. was apparent almost as soon as CH and CN anomalies were discovered in red giants in the 1970s and 1980s.," The presence of CH and CN bimodalities, i.e., two well separated groups of stars with a different strength of these bands, was apparent almost as soon as CH and CN anomalies were discovered in red giants in the 1970s and 1980s." + Some clusters showed clear bimodalities in CN (or in [N/Fe]) and weaker or missing bimodalities in CH (or in [C/Fe]). while some other clusters mstead showed a continuous spread in CN strength.," Some clusters showed clear bimodalities in CN (or in [N/Fe]) and weaker or missing bimodalities in CH (or in [C/Fe]), while some other clusters instead showed a continuous spread in CN strength." + Various studies identified CN bimodalities among red giants of M 3 and M 132004b).. GC 67521981).. «o Cen1986).. GC 69341986).. NGC 61711988).. M 712005).. M 21990).. M 52002).. NGC 288 and GC 3622008).. NGC 61212008).. NGC 6356. and NGC 65282009).. among others.," Various studies identified CN bimodalities among red giants of M 3 and M 13, NGC 6752, $\omega$ Cen, NGC 6934, NGC 6171, M 71, M 2, M 5, NGC 288 and NGC 362, NGC 6121, NGC 6356, and NGC 6528, among others." + Bimodalities among MS and sub-giant branch stars have also been found in M 711999).. 47 Tuc2005).. and NGC 67522005).," Bimodalities among MS and sub-giant branch stars have also been found in M 71, 47 Tuc, and NGC 6752." +. The interest. related to. the presence of a bimodal distribution — rather than à continuous spread — is clear in the light of the latest theories of self-enrichment for GGC (see also Sect. 1))., The interest related to the presence of a bimodal distribution – rather than a continuous spread – is clear in the light of the latest theories of self-enrichment for GGC (see also Sect. \ref{sec-intro}) ). + First generation stars should have a surface composition. rich in C and poor in N. while the second generation ones. formed from CN(O) cycle processing polluted gas. should have higher N and lower C1952). If we finc a clear bimodality in the data. this supports the idea of two stellargenerations*.," First generation stars should have a surface composition, rich in C and poor in N, while the second generation ones, formed from CN(O) cycle processing polluted gas, should have higher N and lower C. If we find a clear bimodality in the data, this supports the idea of two stellar." +. If a bimodal distribution is found measuring the CH and CN band strengths. we expect that the underlying [C/Fe] and [N/Fe] distributions will turn out to be bimodal as well. since each cluster has the same overall metallicity and all stars in each cluster have roughly the same atmospheric parameters.," If a bimodal distribution is found measuring the CH and CN band strengths, we expect that the underlying [C/Fe] and [N/Fe] distributions will turn out to be bimodal as well, since each cluster has the same overall metallicity and all stars in each cluster have roughly the same atmospheric parameters." + This of course requires confirmation via spectrum synthesis calculations., This of course requires confirmation via spectrum synthesis calculations. + These calculations will be the subject of a future paper., These calculations will be the subject of a future paper. + Indeed. such a bimodality in C and N enhancements has been found e.g.. by in RGB stars in M 13. or by in MS stars in 47 Tuc.," Indeed, such a bimodality in C and N enhancements has been found e.g., by in RGB stars in M 13, or by in MS stars in 47 Tuc." + That such bimodalities have rarely been found among red giants when the Na-O anti-correlations areconsidered deserves further studies., That such bimodalities have rarely been found among red giants when the Na-O anti-correlations areconsidered deserves further studies. + We point out two possible, We point out two possible +Jem which is brought about by the cubic polynomial behaviour of S(7) at depths immediately ereater than Tay.,0em which is brought about by the cubic polynomial behaviour of $S(\tau)$ at depths immediately greater than $\tau_{NL}$. + These two families of boundary conditions are sufficient to ensure Chat the RT problem is self-consistent., These two families of boundary conditions are sufficient to ensure that the RT problem is self-consistent. +" 3em The link between (he values of the specific intensities al any pair of consecutive optical depth points (75.7;4). namely any sinele link of the whole RT chain. is given bw the corresponding RT equations in the integral form. (hat is and . where Ar,=tT,4—75."," 3em The link between the values of the specific intensities at any pair of consecutive optical depth points $(\tau_{L}, \tau_{L+1})$, namely any single link of the whole RT chain, is given by the corresponding RT equations in the integral form, that is 0em and where $\Delta \tau_{L} \equiv \tau_{L+1} - \tau_{L}$." + Equations (6) and (7) are the straightforward representation of the RT process., Equations (6) and (7) are the straightforward representation of the RT process. + Jem At the surface for τη= 0) the set of values {2(0.46).7.=1..ND] are the initial conditions for the inward RT problem. while the set (7.(0.46).7.= 1..ND] is the solution of the outward RT problem. theemergent intensities.," 3em At the surface for $\tau_{0} = 0$ ) the set of values $\lbrace I^{-}(0,\mu_{J}), J = 1,ND\rbrace$ are the initial conditions for the inward RT problem, while the set $\lbrace I^{+}(0,\mu_{J}), J = 1,ND\rbrace$ is the solution of the outward RT problem, theemergent intensities." + At the bottom the sel UE(Tdqu).=L1..NDj) vields the upgoing initial conditions (οἱ.," At the bottom the set $\lbrace I^{+}(\tau_{NL},\mu_{J}), J = 1,ND\rbrace$ yields the upgoing initial conditions (cf." + eq. |, eq. [ +5]): the set {L(tap.qu)J=1.ND} is the result of the inward RT process.,"5]); the set $\lbrace I^{-}(\tau_{NL},\mu_{J}), J = 1,ND\rbrace$ is the result of the inward RT process." + Let us now turi our attention on the cubic spline approximation to the source [unction 5(7)., Let us now turn our attention on the cubic spline approximation to the source function $S(\tau)$. + That is. we will assume a cubic polvnonmial approximation insicle each particular interval (Ty.τι1). defined by two consecutive optical depth points. as the single link of the spline chain.," That is, we will assume a cubic polynomial approximation inside each particular interval $(\tau_{L},\tau_{L+1})$, defined by two consecutive optical depth points, as the single link of the spline chain." + Anvone of these ares of eubic is uniquelv determined by the values of the source funelion and those of its second derivative at the end points (knots) of each interval., Anyone of these arcs of cubic is uniquely determined by the values of the source function and those of its second derivative at the end points (knots) of each interval. +" To impose the continuity of the source function as well as that of its [ist and. second derivative at the end points of each interval (75.745.4) leads to the cubic spline condition Üem where ir,=7,—Tj4 and Avy,y=74— 7,."," To impose the continuity of the source function as well as that of its first and second derivative at the end points of each interval $(\tau_{L},\tau_{L+1})$ leads to the cubic spline condition 0em where $\Delta \tau_{L}\ \equiv\ \tau_{L} - \tau_{L-1}$ and $\Delta \tau_{L+1}\ \equiv\ \tau_{L+1} - \tau_{L}$ ." + Likewise. as a consequence of the," Likewise, as a consequence of the" +In (his paper we show that the hieh entropy relativistic flows thought to accompany cabastrophic stellar endpoint events like binary neutron star mergers (Eichleretal.1989) and collapsars (MacFadyen&Woosley1999) may be a source of interesting lieht element sviithesis.,"In this paper we show that the high entropy relativistic flows thought to accompany catastrophic stellar endpoint events like binary neutron star mergers \citep{schramm} and collapsars \citep{woosley} + may be a source of interesting light element synthesis." + In particular. we find (hat under the right circumstances a significant [raction of the relativistic ejecta can be turned into ?IL.," In particular, we find that under the right circumstances a significant fraction of the relativistic ejecta can be turned into ${^2}{\rm +H}$." + Though this cannot be a cosmologically significant 711 source on account of the small mass and presumed low event rates associated with. e.g. GRBs. it could represent an appreciablefocal enhancement.," Though this cannot be a cosmologically significant ${^2}{\rm H}$ source on account of the small mass and presumed low event rates associated with, e.g., GRBs, it could represent an appreciable enhancement." + Because the collisionless shocking (and subsequent svunchrotron emission) of ulira-relativistic winds is thought to eive rise to observed GRBs. deuterium production in these winds raises the possibilitv of a nucleosvnthetie signature of the GRB environment.," Because the collisionless shocking (and subsequent synchrotron emission) of ultra-relativistic winds is thought to give rise to observed GRBs, deuterium production in these winds raises the possibility of a nucleosynthetic signature of the GRB environment." +The sample of common proper motion pairs to be observed was chosen from the available literature. mainly from the papers of Silvestrietal.(2001). and Wegner&Reid(1991).. and from a cross-correlation of the SIMBAD database and the Villanova White Dwarf Catalog.,"The sample of common proper motion pairs to be observed was chosen from the available literature, mainly from the papers of \cite{sil01} and \cite{weg91}, and from a cross-correlation of the SIMBAD database and the Villanova White Dwarf Catalog." + We selected the pairs taking into account different requirements., We selected the pairs taking into account different requirements. + Firstly. the white dwarf component should be classified as a DA (1.ο.. with the unique presence of Balmer lines). so that the fitting procedure 1s sufficiently accurate to derive realistic values for the effective temperature and surface gravity.," Firstly, the white dwarf component should be classified as a DA (i.e., with the unique presence of Balmer lines), so that the fitting procedure is sufficiently accurate to derive realistic values for the effective temperature and surface gravity." + Secondly. the other component of the pair should be a star of spectral type FG or K for an accurate determination of the metallicity. and moderately evolved or very close to the ZAMS in order to be able to estimate its age.," Secondly, the other component of the pair should be a star of spectral type F, G or K for an accurate determination of the metallicity, and moderately evolved or very close to the ZAMS in order to be able to estimate its age." + The complete list of targets is given in Table I., The complete list of targets is given in Table \ref{tab:1}. + The observations were carried out during different campaigns between the summer of 2005 and the spring of 2007., The observations were carried out during different campaigns between the summer of 2005 and the spring of 2007. + In Table 2. we give details of the telescope-instrument configurations employed. as well as the resolution and spectral coverage of each setup.," In Table \ref{tab:2} we give details of the telescope-instrument configurations employed, as well as the resolution and spectral coverage of each setup." + For the white dwarf members we performed long-slit low-resolution spectroscopic observations covering some of the main Balmer lines (from Hf to H8)., For the white dwarf members we performed long-slit low-resolution spectroscopic observations covering some of the main Balmer lines (from $\beta$ to $8$ ). + WD0315-011 was kindly observed for us by T. Oswalt with the RC spectrograph at the 4 m telescope at Kitt Peak National Observatory with a resoltuion of about 1.5 ΕΝΗΜ., $-$ 011 was kindly observed for us by T. Oswalt with the RC spectrograph at the 4 m telescope at Kitt Peak National Observatory with a resoltuion of about $1.5$ FWHM. + We performed as many exposures as necessary to guarantee a high signal-to-noise ratio final spectrum for each object (after the corresponding- reduction)., We performed as many exposures as necessary to guarantee a high signal-to-noise ratio final spectrum for each object (after the corresponding reduction). + Spectra of high quality are essential to derive the atmospheric parameters with accuracy., Spectra of high quality are essential to derive the atmospheric parameters with accuracy. + We co-added individual 1800s exposures to minimize the effects of cosmic ray impacts on the CCD., We co-added individual 1800 s exposures to minimize the effects of cosmic ray impacts on the CCD. + The white dwarf spectra were reduced using the standard procedures within the single-slit tasks inIRAE., The white dwarf spectra were reduced using the standard procedures within the single-slit tasks in. +.. First. the images were bias- and flatfield-corrected. and then. the spectra were extracted and wavelength calibrated using are lamp observations.," First, the images were bias- and flatfield-corrected, and then, the spectra were extracted and wavelength calibrated using arc lamp observations." + We combined multiple spectra of the same star to achieve a final spectrum of high signal-to-noise ratio (S/N > 100)., We combined multiple spectra of the same star to achieve a final spectrum of high signal-to-noise ratio (S/N $>$ 100). + Before this step. we applied the heliocentric correction of each spectrum. since we were co-adding spectra secured in different days.," Before this step, we applied the heliocentric correction of each spectrum, since we were co-adding spectra secured in different days." + Finally. they were normalized to the continuum.," Finally, they were normalized to the continuum." + The FGK companions were observed with echelle spectrographs. obtaining high signal-to-noise high-resolution spectra (S/N > 150). which are necessary to derive the metallicity with accuracy.," The FGK companions were observed with echelle spectrographs, obtaining high signal-to-noise high-resolution spectra (S/N $>$ 150), which are necessary to derive the metallicity with accuracy." + For the reduction of the FGK stars spectra the procedure followed was similar to the case of white dwarfs but we used the corresponding echelle tasks in IRAF., For the reduction of the FGK stars spectra the procedure followed was similar to the case of white dwarfs but we used the corresponding echelle tasks in IRAF. + In this case. we used the task in order to model and subtract the scattered light.," In this case, we used the task in order to model and subtract the scattered light." + After the corresponding reduction. we carried out a first inspection of the spectra.," After the corresponding reduction, we carried out a first inspection of the spectra." + All the objects in Table 3 were previously classified as DA white dwarfs., All the objects in Table \ref{tab:3} were previously classified as DA white dwarfs. + However. we found that four of them are not of DA type.," However, we found that four of them are not of DA type." + Particularly. WD1750+098 turned out to be of type DC although in the most recent reference (Silvestri et al.," Particularly, $+$ 098 turned out to be of type DC although in the most recent reference (Silvestri et al." + 2001) it appears classified as a DA., 2001) it appears classified as a DA. + We believe that WD1544+008 Is the same star as WD1544+009. which was classified as a DAB white dwarf by Silvestrietal.(2001).," We believe that $+$ 008 is the same star as $+$ 009, which was classified as a DAB white dwarf by \cite{sil01}." +.. However. it was identified as a sdO star by Wegner&Reid(1991).," However, it was identified as a sdO star by \cite{weg91}." +. The same authors also studied WD1043—034 and classified it as a sdB star. although MeCook&Sion(1999). considered it as a DAB white dwarf.," The same authors also studied $-$ 034 and classified it as a sdB star, although \cite{mcc99} considered it as a DAB white dwarf." + Taking into account the different inconsistencies in the literature. we decided to reobserve these objects in order to revise their spectral classifications. if necessary.," Taking into account the different inconsistencies in the literature, we decided to reobserve these objects in order to revise their spectral classifications, if necessary." + The reduced spectra of these two stars were kindly analysed by P. Bergeron. who performed the corresponding fits and derived their temperatures and surface gravities. which turned out to be too low to be white dwarfs.," The reduced spectra of these two stars were kindly analysed by P. Bergeron, who performed the corresponding fits and derived their temperatures and surface gravities, which turned out to be too low to be white dwarfs." + As can be seen in Table 3.. 1449+003 ts an M star.," As can be seen in Table \ref{tab:3}, $+$ 003 is an M star." + This classification was also recently indicated by Farihietal.(2005)., This classification was also recently indicated by \cite{far05}. +. These authors also reported that WD09134+442 and BD +44 1847 are not a physical pair according to their parallaxes., These authors also reported that $+$ 442 and BD $+$ 44 1847 are not a physical pair according to their parallaxes. + It is worth mentioning that some of the previous misclassifications are probably due to the fact that the signal-to-noise ratio of the spectra used was low., It is worth mentioning that some of the previous misclassifications are probably due to the fact that the signal-to-noise ratio of the spectra used was low. +amplitudes (400 km !) and linewidths (2500 kms ! EWIIM).,amplitudes $<$ 400 km $^{-1}$ ) and linewidths $<$ 500 km $^{-1}$ FWHM). + ? found extreme kinematic components al the location of the western nucleus with velocity shifts up to 72000 km ! and line widths of 2000 km ! (FWIIM) providing evidence for warm gas outflows in the narrow line region.," \cite{Holt03} + found extreme kinematic components at the location of the western nucleus with velocity shifts up to $\sim$ 2000 km $^{-1}$ and line widths of $\sim$ 2000 km $^{-1}$ (FWHM) providing evidence for warm gas outflows in the narrow line region." + As mentioned in Section 3.1. we detect emission lines αἱ the locations of the voung star clusters visible in our LST in both the images ancl the lone slit spectra.," As mentioned in Section 3.1, we detect emission lines at the locations of the young star clusters visible in our HST in both the images and the long slit spectra." + Therefore it is interesting to compare the kinematics of the star clusters with those of the other kinematic components in the ealaxy., Therefore it is interesting to compare the kinematics of the star clusters with those of the other kinematic components in the galaxy. + Fieures 7 and 8 compare (he emission line kinematics at the locations of (he clusters with those of the spatially resolved diffuse gas detected in the Ia ancl [OIJA3727 emission lines in the halo of the galaxy along PA 160 and PA 230., Figures 7 and 8 compare the emission line kinematics at the locations of the clusters with those of the spatially resolved diffuse gas detected in the $\alpha$ and $\lambda$ 3727 emission lines in the halo of the galaxy along PA 160 and PA 230. + Intriguingly. we find clear evidence for line splitting in both Ha and {NIL} at the locations of clusters C1/C2 and C4.," Intriguingly, we find clear evidence for line splitting in both $\alpha$ and [NII] at the locations of clusters C1/C2 and C4." + The line splitting is clearly visible in the extracted spectra of these regions shown in Figures 9 aud 10 and also the erev scale representation of the long-slit spectra shown in Figure 1., The line splitting is clearly visible in the extracted spectra of these regions shown in Figures 9 and 10 and also the grey scale representation of the long-slit spectra shown in Figure 11. + Iuportant features of the line splitting regions include the following., Important features of the line splitting regions include the following. +to the gravitational softening length.,to the gravitational softening length. + This way the resolution of the RT calculation is fixed for all halos., This way the resolution of the RT calculation is fixed for all halos. + Figure 3 compares the results from the OTUV run with and without the RT calculation., Figure \ref{fig:fn_rt} compares the results from the OTUV run with and without the RT calculation. +" The transferred stellar spectra are computed by using the v2.0 (Fioc&Rocca-Volmerange1997) based on the mass, formation time, and age of the star particles generated in the simulation."," The transferred stellar spectra are computed by using the v2.0 \citep{Fioc97} based on the mass, formation time, and age of the star particles generated in the simulation." +" We find that the local stellar radiation does not have a significant impact on the shape of f(Nur), as shown by the red long-dashed line in reffig:fn,t, , whichisalmostoverlappingwiththeoriginalOT "," We find that the local stellar radiation does not have a significant impact on the shape of $\fn$, as shown by the red long-dashed line in \\ref{fig:fn_rt}, which is almost overlapping with the original OTUV run without RT." +current’Ph bee ," This is because the stellar radiation can only increase the ionization fraction of gas near the ionization boundary where it makes a transition from neutral to highly ionized, and the high density neutral gas remains largely intact." +, We will report more details of the RT calculation results in a separate publication (H. Yajima et al. +," 2011, in preparation)." +"Using cosmological SPH simulations, we examined the effects of UVB on and clarified the reason why earlier simulations have f(Nur),underestimated this quantity compared to the observations."," Using cosmological SPH simulations, we examined the effects of UVB on $\fn$, and clarified the reason why earlier simulations have underestimated this quantity compared to the observations." +" We find that the radiation sinks into the halo gas too deeply under the optically thin approximation of UVB, and the gas with 19H3(aτιδα) and y==i,1/3(−↙∣↓−↓+(2-(d,3).+i) L7."," Putting these values of $r_1$ and $r_2$ into the equations $r_1^{2}=(x+\mu)^{2}+y^2$ and $r_2^{2}=(x+\mu-1)^{2}+y^2$ and then solvingwith the rejection of second and higher order terms of $\delta_1$ and $\delta_2$, we get $x=\frac{q_1^{2/3}}{2}-\mu+(q_1^{2/3} \delta_1-\delta_2)$ and $y=\pm q_1^{1/3}\left(1-\frac{q_1^{2/3}}{4}+(2-q_1^{2/3}) \delta_1+\delta_2\right){}^{1/2}$ ." +" We determine the values of 04 ancl 95 by pulling the values of e.y (alter neglecting the terms containing 041.09«& l). r4=qiwal+04) and ο=1+do into the equation (7)) and (8)) aud solving them with the rejection of second and higher order terms οἱ δι ancl 95. we get llence. the coordinates of triangular points are : where 6, and à» are given byequation (27)) and (23)) respectively."," We determine the values of $\delta_1$ and $\delta_2$ by putting the values of $x,y$ (after neglecting the terms containing $\delta_1,\delta_2\ll1$ ), $r_1=q_1^{1/3}(1+\delta_1)$ and $r_2=1+\delta_2$ into the equation \ref{eq:wx}) ) and \ref{eq:wy}) ) and solving them with the rejection of second and higher order terms of $\delta_1$ and $\delta_2$ , we get Hence, the coordinates of triangular points are : where $\delta_1$ and $\delta_2$ are given byequation \ref{eq:dl1}) ) and \ref{eq:dl2}) ) respectively." + Numerically (he co-ordinatesof triangular equilibrium points are L;=(0.366171. 0.641213). andLa=(0.366171.20.641213) which are obtained by using same parametric values as," Numerically the co-ordinatesof triangular equilibrium points are $L_4=(0.366171, 0.641213)$ , and$L_5=(0.366171, -0.641213)$ which are obtained by using same parametric values as" +istances to match those which would be computed by an observer assuming a ACDAL cosmology.,distances to match those which would be computed by an observer assuming a $\Lambda$ CDM cosmology. + The ensemble average of Eq., The ensemble average of Eq. + 1. for each subhalo pair in the INV (SUCGRA) simulation is plotted in Fig., \ref{sin2t} for each subhalo pair in the INV (SUGRA) simulation is plotted in Fig. + 10. as red circles (green triangles). with error bars.," \ref{assumelcdm} as red circles (green triangles), with error bars." + H£ we Lit for a at each redshift. we obtain the purple dot-dashed line in Fig.," If we fit for $\alpha$ at each redshift, we obtain the purple dot-dashed line in Fig." + 10 for the INV model., \ref{assumelcdm} for the INV model. + Although we have assumed. incorrectly a ACDAL cosmology we find that the AAP function agrees with the measured sample mean for the LNW model at cach redshift.," Although we have assumed, incorrectly a $\Lambda$ CDM cosmology we find that the AAP function agrees with the measured sample mean for the INV model at each redshift." + In Fig., In Fig. + 10. a similar analysis is presented. for the SUGRA model., \ref{assumelcdm} a similar analysis is presented for the SUGRA model. + The measured mean for this dark energy nmiocel. assuming a ACDAL cosmology to compute comoving distances. is shown as green triangles.," The measured mean for this dark energy model, assuming a $\Lambda$ CDM cosmology to compute comoving distances, is shown as green triangles." + The AAD function using the best fit value for a at cach redshift and a AC'DAL expansion history is shown as a grev dashed. line., The AAP function using the best fit value for $\alpha$ at each redshift and a $\Lambda$ CDM expansion history is shown as a grey dashed line. + Again. theory and observations agree when we would expect them not to às we have used the wrong cosmology in the AAP function and to compute distances.," Again, theory and observations agree when we would expect them not to as we have used the wrong cosmology in the AAP function and to compute distances." + Our results show that the AAD function. using either a fixed value of ας=0) ora best fit value at each redshift. is not an accurate model with which to test for dynamical dark energy models if the correct cosmological model is unknown and that further input from numerical simulations is needed to arrive at à viable test.," Our results show that the AAP function, using either a fixed value of $ \alpha(z=0)$ or a best fit value at each redshift, is not an accurate model with which to test for dynamical dark energy models if the correct cosmological model is unknown and that further input from numerical simulations is needed to arrive at a viable test." + From the previous section it is clear that the cosmological test proposed. by Alarinoni Buzzi relies heavily on measuring the parameter a accurately at cach redshift., From the previous section it is clear that the cosmological test proposed by Marinoni Buzzi relies heavily on measuring the parameter $\alpha$ accurately at each redshift. + The assumption that à does not vary with redshift is incorrect and. could falsely rule out ACDAL if this test is misapplied to pairs of galaxies in future surveys., The assumption that $\alpha$ does not vary with redshift is incorrect and could falsely rule out $\Lambda$ CDM if this test is misapplied to pairs of galaxies in future surveys. + The value of a also depends on the cosmological model., The value of $\alpha$ also depends on the cosmological model. + For example at z=0 the values for the ACDAL SUGIRA and INV cosmologies are a=5.56.a=6.32 and à=5.:22 respec‘tively. with a tvpical error of 0.1.," For example at $z=0$ the values for the $\Lambda$ CDM, SUGRA and INV cosmologies are $\alpha=5.56$, $\alpha=6.32$ and $\alpha=5.32$ respectively, with a typical error of 0.1." + Ehe dilliculty is not just a xoblem of measuring a accurately but stems from the fact that the cosmology assumed alfects both the data and the heoretical prediction in à wav which cannot be disentangled., The difficulty is not just a problem of measuring $\alpha$ accurately but stems from the fact that the cosmology assumed affects both the data and the theoretical prediction in a way which cannot be disentangled. + The accuracy and predictive power of the AAP function can be restored. if instead. of measuring à. from. observations. we employ. N-body simulations which contain à comparable number of subhalo pairs to the number of galaxy pairs in the survey uncler consideration.," The accuracy and predictive power of the AAP function can be restored if instead of measuring $\alpha$ from observations, we employ N-body simulations which contain a comparable number of subhalo pairs to the number of galaxy pairs in the survey under consideration." + I is clear that independent information about à is necessary and numerical simulations plav an important role in providing these predictions in a given cosmology., It is clear that independent information about $\alpha$ is necessary and numerical simulations play an important role in providing these predictions in a given cosmology. + We propose a new approach to measuring dark energv. where observational measurements of the mean of the anisotropic distribution of pairs ancl predictions of the AAP function from numerical simulations are combined.," We propose a new approach to measuring dark energy, where observational measurements of the mean of the anisotropic distribution of pairs and predictions of the AAP function from numerical simulations are combined." + The new method we propose to test a given cosmology is às follows:, The new method we propose to test a given cosmology is as follows: +We define triple induced mass transfer (TIMT) systems to be those binaries that are brought into MT via the the Kozai meachanism.,We define triple induced mass transfer (TIMT) systems to be those binaries that are brought into MT via the the Kozai meachanism. + We find that the fraction of TIMT systems ranges between 0.07 (for a=ISR...) and 0.01 (for most separations. ¢=4O0R ..).," We find that the fraction of TIMT systems ranges between 0.07 (for $a=15 R_\odot$ ) and 0.01 (for most separations, $a\ga 40 R_\odot$ )." + Combining it with the triple formation rate. we find that all BH-WD binaries with I5R..=ay=80R.. could make it to the MT through the triple formation mechanism.," Combining it with the triple formation rate, we find that all BH-WD binaries with $15 R_\odot \la a_1 \la 80 R_\odot$ could make it to the MT through the triple formation mechanism." +" At a conservative level. assuming even that all the binaries that have a binding energy 10 times more than the kinetic energy of an average object in the core are destroyed. we find that à BH-WD binary with a250R.. has a chance to become become a TIMT system within | Gyr for a,~80R.. and for a,~SOR..): this chance is for a,=35R..."," At a conservative level, assuming even that all the binaries that have a binding energy 10 times more than the kinetic energy of an average object in the core are destroyed, we find that a BH-WD binary with $a_1\ga 50 R_\odot$ has a chance to become become a TIMT system within 1 Gyr for $a_1\sim 80 R_\odot$ and for $a_1\sim 50 R_\odot$ ); this chance is for $a_1\la 35 R_\odot$." +" During several Gyr. all BH-WD binaries with a,=80R.. can become a TIMT system at least once."," During several Gyr, all BH-WD binaries with $a_1 \la 80 R_\odot$ can become a TIMT system at least once." +" This TIMT system formation will be successful only if the time between subsequent encounters is longer than the time necessary to achieve ej44,.", This TIMT system formation will be successful only if the time between subsequent encounters is longer than the time necessary to achieve $e_{\rm max}$. +" The period of the cycle to achieve Cmax"" IS1 (99se) where aj, and nz» are the companion mases of the inner binary. e; 1s the initial eccentricity of the inner binary. 72, is the mass of the outer star. ας is the initial semimajor axis for the outer orbit. and 5b,=a.(1-el lds the semiminor axis of the outer orbit."," The period of the cycle to achieve $e_{\rm max}$ is \citep{Innanen97_kozai,Miller02_kozai} + where $m_{i1}$ and $m_{i2}$ are the companion mases of the inner binary, $e_{\rm i}$ is the initial eccentricity of the inner binary, $m_o$ is the mass of the outer star, $a_{\rm o}$ is the initial semimajor axis for the outer orbit, and $b_{\rm o}= a_{\rm o}(1 - e_{\rm o}^2)^{1/2}$ is the semiminor axis of the outer orbit." + Roughly. ας will be of the order of magnitude of a».," Roughly, $a_{\rm o}$ will be of the order of magnitude of $a_2$." +" Considering the extreme case e»>>αι. for which τικ. would be maximum. we find: Here fp, 1s the binary fraction. 7gp=T3.(OppfofivY. and 735={ως has been evaluated at k=2."," Considering the extreme case $a_2\gg a_1$, for which $\tau_{\rm Koz}$ would be maximum, we find: Here $f_b$ is the binary fraction, $\tau_{\rm BB}=\Gamma_{\rm BB}^{-1}=(\sigma_{\rm BB}f_{\rm b}n_{\rm c}v_\infty)^{-1}$, and $\tau_{\rm BS}=1/\Gamma_{\rm BS}$ has been evaluated at $k=2$." + An average dynamically formed triple would have 0.9 ?.., An average dynamically formed triple would have $e_{\rm o}\approx 0.9 $ \cite{natatrip}. + For the purpose of the estimate. we adopt that a BH-WD binary would have its initial eccentricity distributed thermally. with an average e;2/3 and adopt ig=54 (this is the mean inclination of dynamically formed Kozai affected triples).," For the purpose of the estimate, we adopt that a BH-WD binary would have its initial eccentricity distributed thermally, with an average $e_{\rm i} \sim 2/3$ and adopt $i_0=54^o$ (this is the mean inclination of dynamically formed Kozai affected triples)." + From 16). we have then that triples with ISR...>a). can be roughly estimated as (e.g...2?) Assuming that all hardening happenedwith the maximum ó~ma£n,0.04. it can therefore be estimated that. the hardening of a 1000 R.. BH-WD binary to. e.g.. 35R.. should take about 100 encounters."," This change, for an eccentric binary with a large mass ratio of one star to a companion and an encountering $m_3$ star, if occurred at the distance $q$ $q\gg a$ ), can be roughly estimated as \citep[e.g., ][]{heggie75,2003CeMDA..87..411R} + Assuming that all hardening happenedwith the maximum $\delta\sim {m_3}/{m_{\rm bh}}\sim0.04$, it can therefore be estimated that, the hardening of a 1000 $R_\odot$ BH-WD binary to, e.g., $35 R_\odot$ should take about 100 encounters." + As the collision time for a 1000 R. BH-WD binary is only about 107 vr. and is still only about 10? yr fora 35 R.. BH-WD binary. it is plausible therefore that all 1000 R.. BH-WD binary can be hardened to 35R.. within a few Gyr.," As the collision time for a 1000 $R_\odot$ BH-WD binary is only about $10^7$ yr, and is still only about $10^8$ yr for a 35 $R_\odot$ BH-WD binary, it is plausible therefore that all 1000 $R_\odot$ BH-WD binary can be hardened to $35 R_\odot$ within a few Gyr." + We choose here 35R.. as the important separation at which triple formation starts to have efficiency in making this binary à MT BH-WD binary (see refkozaitrip))., We choose here $35 R_\odot$ as the important separation at which triple formation starts to have efficiency in making this binary a MT BH-WD binary (see \\ref{kozaitrip}) ). + However. this is an idealistic picture.," However, this is an idealistic picture." + There are plenty of encounters that this binary would have undergone in order to reach 35 R.. and certainly not all them will be simple fly-by hardening encounters.," There are plenty of encounters that this binary would have undergone in order to reach 35 $R_\odot$, and certainly not all them will be simple fly-by hardening encounters." + Some of the encounters would result in exchanges (where the lighter companion is often exchanged with a more massive incoming star. and the binary gets wider) mergers. or even binary ionizations. reducing therefore the chance for a binary to harden to the separation we are interested in.," Some of the encounters would result in exchanges (where the lighter companion is often exchanged with a more massive incoming star, and the binary gets wider), mergers, or even binary ionizations, reducing therefore the chance for a binary to harden to the separation we are interested in." + We set up a numerical experiment. by taking à BH-WD binary with the specific initial binary separation aj.," We set up a numerical experiment, by taking a BH-WD binary with the specific initial binary separation $a_{\rm i}$." + At the collision rate predicted by the current binary separation and the adoptedn.=10°pe“. we bombard the binary with single stars drawn from the simplified core’s population. randomizing impact parameters and usingly.," At the collision rate predicted by the current binary separation and the adopted$n_{\rm c}=10^5 \ {\rm pc^{-3}}$, we bombard the binary with single stars drawn from the simplified core's population, randomizing impact parameters and using." + Initial eccentricities of BH-WD binaries for this experiment is adopted to have a thermal distribution., Initial eccentricities of BH-WD binaries for this experiment is adopted to have a thermal distribution. + À simplified core population is taken from Monte Carlo runs (?) andhas only 4 different groups for the non-BH population: stars with masses 0.22.0.506.0.75.. and Τ.Μ. with according 33%.38%.25%. and 4% contributions to the non-BH population.," A simplified core population is taken from Monte Carlo runs \citep{ivanova08} andhas only 4 different groups for the non-BH population: stars with masses $0.22, 0.506, 0.75$, and $1.13 M_\odot$, with according $33\%, 38\%, 25\%$, and $4\%$ contributions to the non-BH population." +" Then we vary the BH component. starting from the highest possible. where the number of BHs ts of all other stars in the core (this is about of the initially formed BH population. see the discussion in $11. or fouo.= 10). (this corresponds to the case of fano, 1).0.004%... and no contribution at all (this correspond to the case when only one BH. which is in the considered BH-WD binary. is left)."," Then we vary the BH component, starting from the highest possible, where the number of BHs is of all other stars in the core (this is about of the initially formed BH population, see the discussion in 1, or $f_{\rm BH,0.1}=10$ ), (this corresponds to the case of $f_{\rm BH,0.1}=1$ ), and no contribution at all (this correspond to the case when only one BH, which is in the considered BH-WD binary, is left)." + Here. one BH corresponds to 0.001% of the core population.," Here, one BH corresponds to $0.001\%$ of the core population." + We consider the fraction of BH-WD binaries that would harden to 35R.. within 10 Gyr as well as the average time it will take them.," We consider the fraction of BH-WD binaries that would harden to $35 +R_\odot$ within 10 Gyr as well as the average time it will take them." + We also separately consider cases where we insisted that the origina? BH-WD binary would made it to 35R ... or simply binary containing initial BH would made it (allowing multiple exchanges).," We also separately consider cases where we insisted that the BH-WD binary would made it to $35 R_\odot$ , or simply binary containing initial BH would made it (allowing multiple exchanges)." + The latter case could correspond to the case when almost all the stellar non-BH, The latter case could correspond to the case when almost all the stellar non-BH +inclicating that they form deep in the atmosphere. where the LTE approximation should hold even in giants of low gravity.,"indicating that they form deep in the atmosphere, where the LTE approximation should hold even in giants of low gravity." + Moreover. one of the major mechanisms which can cause a deviation from LTE. namely over-ionization by UV radiation. is less efficient in cool giants. while photon suction can have some relevance.," Moreover, one of the major mechanisms which can cause a deviation from LTE, namely over-ionization by UV radiation, is less efficient in cool giants, while photon suction can have some relevance." + According to NLTE computations on Fe and Me lines(seee.g.Grattonοἱal.1999:Zhao&Gehren2000) deviations from LTE (at a level of 20.1 dex) are mainly observed in stars which are significantly hotter ancl more metal poor than those in our program.," According to NLTE computations on Fe and Mg lines\citep[see e.g.][]{gra99,zha00} deviations from LTE (at a level of $\ge$ 0.1 dex) are mainly observed in stars which are significantly hotter and more metal poor than those in our program." + The code is based on the molecular blanketed model abtmospheres of Johnson.Bernat&Ixrupp(1980) in the 3000-4000 Ix temperature range ancl ihe ATLASO models lor temperatures above 4000 Ix. Since in the near IR. the major source ofcontinuum opacity is with its minimum near 1.6 jin. the dependence of the results on the choice of reasonable model atmospheres should not be criGical.," The code is based on the molecular blanketed model atmospheres of \citet{jbk80} in the 3000-4000 K temperature range and the ATLAS9 models for temperatures above 4000 K. Since in the near IR the major source ofcontinuum opacity is $^-$ with its minimum near 1.6 $\mu$ m, the dependence of the results on the choice of reasonable model atmospheres should not be critical." + ILowever. as a check. we also computed synthetic spectra using the more updated NextGen model atmospheres by llauschildtetal.(1999). and we compare them with (hose obtained using Johnson.Bernat&hNrupp(1980) models. finding minor differences (Rich&Origlia2005).," However, as a check, we also computed synthetic spectra using the more updated NextGen model atmospheres by \citet{hau99} and we compare them with those obtained using \citet{jbk80} models, finding minor differences \citep{ro05}." +. Three main compilations of atomic oscillator strengths are used: the INurucz database (ef. ha," Three main compilations of atomic oscillator strengths are used: the Kurucz database (c.f. )," +rward.edu/amedala/ampdala/Iuwrucz23/sekur.html). Biemont&Grevesse(1973). and Meléndez&Barbuy(1999)., \citet{bg73} and \citet{mb99}. +. Reference solar abundances are [rom Grevesse&Sauval(1993)., Reference solar abundances are from \citet{gv98}. +". In the first iteration. we estimate stellar temperature from the (J—Ix), colors (see Table 2)) and the color-temperature transformation of Montegriffoetal.(1998). specifically calibrated on globular cluster giants."," In the first iteration, we estimate stellar temperature from the $\rm (J-K)_0$ colors (see Table \ref{tab2}) ) and the color-temperature transformation of \citet{MFFO98} specifically calibrated on globular cluster giants." + Gravity has been estimated [rom theoretical evolutionary. tracks. according to the location of the stars on the RGB (seeOrigliaetal.1997.andreferences{hereinforamoredetailed cliscussion)..," Gravity has been estimated from theoretical evolutionary tracks, according to the location of the stars on the RGB \citep[see][and references therein for a more detailed discussion]{ori97}." + For microturbulence velocity an average value £—2.0 kin/s has been adopted., For microturbulence velocity an average value $\xi$ =2.0 km/s has been adopted. + More stringent constraints on (he stellar parameters are obtained by (he simultaneous spectral fitting of the several CO and OIL molecular bands. which are very sensilive to (temperature. οταν and microturbulence variations (see Figs.," More stringent constraints on the stellar parameters are obtained by the simultaneous spectral fitting of the several CO and OH molecular bands, which are very sensitive to temperature, gravity and microturbulence variations (see Figs." + 6.7 of Castro (2002))).," 6,7 of \citet{orc02}) )." + The adopted values are listed in Table 2.., The adopted values are listed in Table \ref{tab2}. +" From our spectral analvsis we find all the 6 stus likely members of the cluster. showing an average heliocentric radial velocity (v,)=—5241Im/s."," From our spectral analysis we find all the 6 stars likely members of the cluster, showing an average heliocentric radial velocity $\rm \langle v_r \rangle = -52 \pm 1~Km/s$." + This value is in good agreement with previous estimates (Friel&Janes1993:Frieletal.2002).," This value is in good agreement with previous estimates \citep{fj93,friel02}." +. We derive abundances for Fe. C. OQ. Ca. Si. Me.Ti and Al.," We derive abundances for Fe, C, O, Ca, Si, Mg,Ti and Al." + The final values of our best-fit models together with random lo errors are listed in Table 2.., The final values of our best-fit models together with random $\sigma$ errors are listed in Table \ref{tab2}. . + We find an average Ρο)=+0.85£0.02 dex. roughly solar [n /Fe]. [C/Fe]=—0.35+0.03dex and low PC/MCz10-- 2.," We find an average $\rm [Fe/H]=+0.35 \pm 0.02~dex$ roughly solar $\alpha$ /Fe], $\rm [C/Fe]=-0.35 \pm 0.03~dex$ and low $\rm ^{12}C/^{13}C\approx10\pm2$ ." + We also explored the results using models with .N[N/II]= 40.2 dex. NT;= £200 Is," We also explored the results using models with $\rm \Delta [X/H]=\pm$ 0.2 dex, $\rm \Delta T_{eff}=\pm$ 200 K," + We also explored the results using models with .N[N/II]= 40.2 dex. NT;= £200 Is.," We also explored the results using models with $\rm \Delta [X/H]=\pm$ 0.2 dex, $\rm \Delta T_{eff}=\pm$ 200 K," +significant Ilux.,significant flux. + The total Dux tends to increase with the number of micro minima., The total flux tends to increase with the number of micro minima. + Interestingly. the micro saddles adjacent o the micro minima also tend to be non-trivial in terms of Lux.," Interestingly, the micro saddles adjacent to the micro minima also tend to be non-trivial in terms of flux." + In Figure 2. we show image configurations formed around. macro sacdcles., In Figure \ref{odd-fig} we show image configurations formed around macro saddles. + As before. the original macro-image would rave formed at the center of the Frame.," As before, the original macro-image would have formed at the center of the frame." + The upper left panel shows a typical configuration with no micro minima., The upper left panel shows a typical configuration with no micro minima. + Star-lenses adel numerous saddle-point loops enclosing micro maxima. ane adding micro saddles at contour intersections. but these are vpically faint.," Star-lenses add numerous saddle-point loops enclosing micro maxima, and adding micro saddles at contour intersections, but these are typically faint." + Phe sketch above it has two configurations: the one on the left is typical: the one on the right can replace the single point sacelle-point contour selt-intersection., The sketch above it has two configurations; the one on the left is typical; the one on the right can replace the single point saddle-point contour self-intersection. + Being symmetric. the configuration in the second sketch is not stable. and renee in practice only approximations to it are seen.," Being symmetric, the configuration in the second sketch is not stable, and hence in practice only approximations to it are seen." + A micro minimum can appear near à macro saddle. as shown in the upper right panel.," A micro minimum can appear near a macro saddle, as shown in the upper right panel." + Phat local well is possible to form because to the upper left and. lower left of it the macro-topology has existing “walls”. so just one or two stars to the right are needed to make a local well.," That local well is possible to form because to the upper left and lower left of it the macro-topology has existing “walls”, so just one or two stars to the right are needed to make a local well." + Phe sketeh above it also illustrates how a more symmetric version of a typical configuration can create two additional micro sactelles., The sketch above it also illustrates how a more symmetric version of a typical configuration can create two additional micro saddles. + The lower panels of the same Figuree are simple. but common modifications: the left panel shows that similar lemniscate loops can be added on either side of the macro saddle. and the right panel shows that multiple. nested lemniscates can be added on the same side.," The lower panels of the same Figure are simple, but common modifications; the left panel shows that similar lemniscate loops can be added on either side of the macro saddle, and the right panel shows that multiple, nested lemniscates can be added on the same side." + Again. we see that the micro minima are most important for the (ux. with the adjacent micro sacdcdles also contributing signilicantlv.," Again, we see that the micro minima are most important for the flux, with the adjacent micro saddles also contributing significantly." + We remark that the idealized versions of our lower left panel of Figure |. and the upper left panel of Figure 2. are equivalent to the examples of macro minima and macro saddles that 2? use to explain demagnification of sadcdles., We remark that the idealized versions of our lower left panel of Figure \ref{even-fig} and the upper left panel of Figure \ref{odd-fig} are equivalent to the examples of macro minima and macro saddles that \cite{2002ApJ...580..685S} use to explain demagnification of saddles. + The above ciscussion can be summarized as follows., The above discussion can be summarized as follows. + So far we have put all the mass into stars. which average to &.," So far we have put all the mass into stars, which average to $\bkappa$." +" However there is no loss of generality with respect to a smoothlv-distributed mass component &,. as the microlensing οσοι of the latter can be accounted for by the simple transformation (seee.g..Equation20in2).."," However there is no loss of generality with respect to a smoothly-distributed mass component $\kappa_c$, as the microlensing effect of the latter can be accounted for by the simple transformation \citep[see e.g., Equation 20 in][]{1986ApJ...301..503P}." + Such a transformation multiplies all magnifications bv the constant (1.ανY. and is in fact equivalent (ef2). to the well-known mass-sheet degencracy in macrolensing.," Such a transformation multiplies all magnifications by the constant $\left(1-\kappa_c\right)^2$, and is in fact equivalent \cite[cf.][]{2000AJ....120.1654S} to the well-known mass-sheet degeneracy in macrolensing." + Some applications of micro- ancl milli-Iensing call for extended: perturbers., Some applications of micro- and milli-lensing call for extended perturbers. + extended lenses can be mimicked to some extent by softening the point lenses. which leaves the basic picture intact. and only moves micro maxima out from under the stars.," Extended lenses can be mimicked to some extent by softening the point lenses, which leaves the basic picture intact, and only moves micro maxima out from under the stars." + But we do not attempt eencral extended lenses in this paper., But we do not attempt general extended lenses in this paper. + The most important observable is the macro magnification., The most important observable is the macro magnification. + As we saw in the previous section. the brightest images tend to be micro minima. which suggestsBS that the macro magnificationg will depend. primarily on the number of micro mimima.," As we saw in the previous section, the brightest images tend to be micro minima, which suggests that the macro magnification will depend primarily on the number of micro mimima." + The key role of micro minima has been noted in previous work (??) but the arrival-time arguments of this paper make it evident.," The key role of micro minima has been noted in previous work \citep{1992ApJ...386...30R,2002ApJ...580..685S} + but the arrival-time arguments of this paper make it evident." + Το quantify our results in terms of the magnification probability distribution we simulated 10 realizations of each of the macro minimum anc macro saddle cases. with Af=£5 and &=0.5 (vhich implies +=0.22 and 0.67. respectively).," To quantify our results in terms of the magnification probability distribution we simulated $10^4$ realizations of each of the macro minimum and macro saddle cases, with $\bar M=\pm5$ and $\bar\kappa=0.5$ (which implies $\bgamma=0.22$ and $0.67$ respectively)." + AMicro-images were searched. for within a square centred on the macro-image position ancl containing 300 stars randomly distributed., Micro-images were searched for within a square centred on the macro-image position and containing 300 stars randomly distributed. + In each realization. of order 300 micro sacdcles and up to 4 were minima were found.," In each realization, of order 300 micro saddles and up to 4 were minima were found." + The small number of minima suggested grouping the realizations according to the number of minima., The small number of minima suggested grouping the realizations according to the number of minima. + Figure 3. shows magnification distributions decomposed in this way. with the left and right panel showing macro minima and macro saccdles respectively.," Figure \ref{histog-fig} shows magnification distributions decomposed in this way, with the left and right panel showing macro minima and macro saddles respectively." + Similar decompositions appear in Figure 5 of ? and Figure 4 of ?..," Similar decompositions appear in Figure 5 of \cite{1992ApJ...386...30R} + and Figure 4 of \cite{2003ApJ...583..575G}." + Ht is interesting that all the sub-clistributions representing cases with at [east one micro minimum have similar shapes. with a steep dropolf on the left and a heavy tail on the right.," It is interesting that all the sub-distributions representing cases with at least one micro minimum have similar shapes, with a steep dropoff on the left and a heavy tail on the right." + Phe case of zero micro minima (thick red histogram in the right panel) is more svninictric., The case of zero micro minima (thick red histogram in the right panel) is more symmetric. + The sub-cistributions overlap. but not to the degree that the individual peaks smear out completely.," The sub-distributions overlap, but not to the degree that the individual peaks smear out completely." + Phe total distributions are shown as the solid histograms in Figure 4.., The total distributions are shown as the solid histograms in Figure \ref{histog-tot-fig}. + Xs a check we compare these to the magnification distributions obtained with rav-tracing. using a tree code.," As a check we compare these to the magnification distributions obtained with ray-tracing, using a tree code." + The rav-tracing algorithm does not find individual images. hence it does not separate out cases according to the number of micro minima.," The ray-tracing algorithm does not find individual images, hence it does not separate out cases according to the number of micro minima." + However. the random shear field. Equation 4.. is statistically approximated much better. because Large buller region of ravs and stars. with up to LO” stars outside the main microlensing frame is used. to," However, the random shear field, Equation \ref{microarriv}, is statistically approximated much better, because large buffer region of rays and stars, with up to $10^5$ stars outside the main microlensing frame is used, to" +in nimch more signal for the πω=Lb model (orauge dot-dashed curves). with a 36 detection. possibleeven at Ji&0.3.,"in much more signal for the ${x}_{\rm HeII} = 1$ model (orange dot-dashed curves), with a $3 \, \sigma$ detection possibleeven at $\sigma_{\rm inst} \approx 0.3$." + Even though this mask includes denser reeious than the mask with τοις>3. the expected SNR is a factor of 3 times huger at diyzcU.l iu the Πω=d onmeodel than in the model with 1016 15 The exact form of the aabsorptiou signal will never be known. aud instead we have some best guess 7jpj; for its foxiu from coeval Ίνα forest measurements.," Even though this mask includes denser regions than the mask with $\tau_{\rm HI, 1216} > 3$, the expected SNR is a factor of $3$ times larger at $\sigma_{\rm inst} \approx 0.1$ in the ${x}_{\rm HeII} = 1$ model than in the model with $\Gamma_{\rm HeII} = 10^{-16}~$ $^{-1}$ The exact form of the absorption signal will never be known, and instead we have some best guess $\Trans_{\rm HeI, i}^{\rm est}$ for its form from coeval $\alpha$ forest measurements." + In cases where the signal is uot perfectly known. the achievable SNR is decreased by the cross correlation cocficient k& (equ. 6)).," In cases where the signal is not perfectly known, the achievable SNR is decreased by the cross correlation coefficient $r$ (eqn. \ref{eqn:ston}) )." + The different amounts of thermal broadening between and aabsorption lines make r<1 even with a perfect measurement of Tyτοις.," The different amounts of thermal broadening between and absorption lines make $r < 1$ even with a perfect measurement of $\tau_{\rm HI, 1216}$." + This effect was inchided in all our calculations. but we find it has a uegligible effect on the SNR for detection of the cross correlation (= 10543.," This effect was included in all our calculations, but we find it has a negligible effect on the SNR for detection of the cross correlation $\lesssim 10\%$ )." + To the extent the IGM had a single temperature. the effect of thermal broadening is a convolution iu wavelength space with a single Gaussian filter.," To the extent the IGM had a single temperature, the effect of thermal broadening is a convolution in wavelength space with a single Gaussian filter." + In this sinele-temmperature limit. the filters divide out aud do not affect the value of + aud. therefore. the SNR ofdetection.," In this single-temperature limit, the filters divide out and do not affect the value of $r$ and, therefore, the SNR of detection." + Another complication arises because the measurement of τητοις Will never be perfect.," Another complication arises because the measurement of $\tau_{\rm HI, 1216}$ will never be perfect." + There will be noise in the estimate for this field that reduces + further., There will be noise in the estimate for this field that reduces $r$ further. + To test the iuportance of an imperfect reconstruction of 7431216. We iive added noise to τοις With the standard deviation iu the noise per pixel o σηςοπλίτηποιο).," To test the importance of an imperfect reconstruction of $\tau_{\rm HI, 1216}$, we have added noise to $\tau_{\rm HI, 1216}$ with the standard deviation in the noise per pixel of $\sigma^{\rm HI}_{\rm inst}/\exp(-\tau_{\rm HI, 1216})$." +" We find a ieelieible difference in the SNR of detection for cht, 3$ mask, which indicates that noise in the reconstruction of $\tau_{\rm HI, 1216}$ does not significantly degrade the The absorption signal can also differ from the estimate for this signal from $\tau_{\rm HI, 1216}$ because of the patchy structure of reionization." +" The signal iu the CLOSS correlation is coming from &—1eMpe. 1, whereas the structure iu the ffraction is thought to be modulated at scales of Fhyaaaae~30 cAlIpe. the size of the bbubbles around quasars (Furlanctto&Dixon2009:Mc-Quinnetal.2009)."," The signal in the cross correlation is coming from $k \sim 1~$ $^{-1}$, whereas the structure in the fraction is thought to be modulated at scales of $R_{\rm bubble} \sim 30$ cMpc, the size of the bubbles around quasars \citep{furlanetto09, mcquinn09}." +. The wavevectors affected by tle structure of rrejonizatiou À~Tus wil be more than an order of magnitude simaller than those that contribute to the SNR., The wavevectors affected by the structure of reionization $k \sim R_{\rm bubble}^{-1}$ will be more than an order of magnitude smaller than those that contribute to the SNR. + If Well roionizatiou is perfectly patchy such that the helium is either singly ionized or doubly ionized aud a skewoer of leugth Z9Fac Is measured. heu rvg2 at dcmFlu where Πω is the volumnce-averaged ffraction.," If HeII reionization is perfectly patchy such that the helium is either singly ionized or doubly ionized and a skewer of length $\gg R_{\rm bubble}$ is measured, then $r \approx \bar{x}_{\rm HeII}^{1/2}$ at $k \gg R_{\rm bubble}^{-1}$, where $\bar{x}_{\rm HeII}$ is the volume-averaged fraction." + Therefore. the total SNR of the CLOSS correlation is reduced on average by the factor μωῃ.," Therefore, the total SNR of the cross correlation is reduced on average by the factor $\bar{x}_{\rm HeII}$." + Also uote that in the contrasting tov case that ircionization was perfectly homogeneous. the SNR is also reduced by eye:," Also note that in the contrasting toy case that reionization was perfectly homogeneous, the SNR is also reduced by $\bar{x}_{\rm HeII}$." + A detection of aabsorption from low deusity gas would translate to a lo error ou «rg of OriyyySNR)/SNR. where (SNR) ds the expected yap for a given estimatedarty SNB. of detection in cross correlation witli exp(0.025τμ]πο1ο).," A detection of absorption from low density gas would translate to a $1 \, \sigma$ error on $\bar{x}_{\rm HeII}$ of $\delta x_{\rm HeII} \approx \bar{x}^e_{\rm HeII}({\rm {SNR}})/{\rm {SNR}}$, where $\bar{x}^e_{\rm HeII}({\rm SNR})$ is the expected $\bar{x}_{\rm HeII}$ for a given estimated SNR of detection in cross correlation with $\exp(-0.025\,\tau_{\rm HI, 1216})$." + Thus. a la detection from low deusitv eas would vield a 25% constraint (iguorine ΠΕ ," Thus, a $4\,\sigma$ detection from low density gas would yield a $25\%$ constraint (ignoring uncertainty in $\Gamma_{\rm HeI}$ )." +This coustraint assumes that the low density gas during welonization was composed of large-scale reeious in which the helium was either ooril.. which is expected theoretically ancl is what is seen in simulations (MeQuiunctal. 2009)..," This constraint assumes that the low density gas during reionization was composed of large-scale regions in which the helium was either or, which is expected theoretically and is what is seen in simulations \citep{mcquinn09}. ." + This paper discussed the usefulness of the Sala foresttostudy rreionizationatà Xlm1.5., This paper discussed the usefulness of the $584~$ forest to study reionization at $3 \lesssim z \lesssim 4.5$. + The optical depth of the Sala llincisproportionaltotheopticaldepthinll LLyo bw the factor 0.025ryPanTia Genoriug differcuces in the amount of thermal broadeniug between and 1)).," The optical depth of the $584~$ line is proportional to the optical depth in $\alpha$ by the factor $0.025 \, x_{\rm HeII} \, \Gamma_{\rm HI}/\Gamma_{\rm HeI}$ (ignoring differences in the amount of thermal broadening between and )." + The factor jit; should have been spatially variable. but the ratio ΕμΠω should have been esscutially spatially independent aud roughly equal to unity at relevant redshifts.," The factor $x_{\rm HeII}$ should have been spatially variable, but the ratio $\Gamma_{\rm HI}/\Gamma_{\rm HeI}$ should have been essentially spatially independent and roughly equal to unity at relevant redshifts." + Therefore. this absorption cau be used to study weionization through its dependence on (qal.," Therefore, this absorption can be used to study reionization through its dependence on $x_{\rm HeII}$." + Our best method at preseut to probe rreionization. Ίσα absorption. saturates at neutral fractions of a part in a thousand at the cosmic mean deusitv.," Our best method at present to probe reionization, $\alpha$ absorption, saturates at neutral fractions of a part in a thousand at the cosmic mean density." + Ta coutrast. Sala aabsorptionisunsaturatedinallevcceptthedensestregions CCN FOS] l.," In contrast, $584~$ absorption is unsaturated in all except the densest regions, even for $x_{\rm HeII} = 1$ ." + This absorption provides a complementary window iuto the ionization state of intergalactic lelimm at 2~3 that can clefinitively test whether an opaque region m the Liye forest was due to a large-scale ireegion., This absorption provides a complementary window into the ionization state of intergalactic helium at $z\sim 3$ that can definitively test whether an opaque region in the $\alpha$ forest was due to a large-scale region. + Even for realistic amounts of instriuuoeutal noise and foreground Liye absorption. weshowed that the coeval Ίσα forest absorption can be used to construct a matched filter that can detect the," Even for realistic amounts of instrumental noise and foreground $\alpha$ absorption, weshowed that the coeval $\alpha$ forest absorption can be used to construct a matched filter that can detect the" +Alorphological classification alone provides a limited approach for understanding the properties and. evolution of galaxies.,Morphological classification alone provides a limited approach for understanding the properties and evolution of galaxies. + Using just the phwsical properties may be more straightforward. but. these. schemes co not. address he origin or evolution of galaxy morphology., Using just the physical properties may be more straightforward but these schemes do not address the origin or evolution of galaxy morphology. + However. he multiwaveleneth nature of the recently developed QAIAL classification method provides an opportunity o connect morphological classification with underbing physical parameters.," However, the multiwavelength nature of the recently developed QMM classification method provides an opportunity to connect morphological classification with underlying physical parameters." + Phe colour information encoded in the multiwavelength images provides the kev. as galaxy colours are a consequence of the combination of stellar evolutionary oocesses and multiple stellar populations.," The colour information encoded in the multiwavelength images provides the key, as galaxy colours are a consequence of the combination of stellar evolutionary processes and multiple stellar populations." + This suggests here should be a direct connection between a quantitative morphology derived. from. multiwavelength images ancl the underlying properties of the stellar population within the galaxies., This suggests there should be a direct connection between a quantitative morphology derived from multiwavelength images and the underlying properties of the stellar population within the galaxies. + We have used Pixel-z and CAS as a way of quantifying several physical properties of galaxies so that they can be correlated with the QAIAL method. in order to identify how well QAIAL can represent. the distribution of physical properties in galaxies.," We have used Pixel-z and CAS as a way of quantifying several physical properties of galaxies so that they can be correlated with the QMM method, in order to identify how well QMM can represent the distribution of physical properties in galaxies." + In order to connect the two methods. we carry out a regression analysis by performing a multiple linear regression fit to identify the extent to which QMM correlates with spatial distributions of physical properties in galaxies represented through the CCAS method.," In order to connect the two methods, we carry out a regression analysis by performing a multiple linear regression fit to identify the extent to which QMM correlates with spatial distributions of physical properties in galaxies represented through the CAS method." + In an ideal case we would find strong correlations between he tested. parameters. but due to the large scatter. seen in the above [figures this is unlikely.," In an ideal case we would find strong correlations between the tested parameters, but due to the large scatter seen in the above figures this is unlikely." + For this reason we focus on the relative correlations between the CAS »wanmeters measured for the physical properties ancl the r-xuxd to Observe whether any physical properties consistentLy show correlation coellicients higher than the r-bancd CAS XUOelers., For this reason we focus on the relative correlations between the CAS parameters measured for the physical properties and the $r$ -band to observe whether any physical properties consistently show correlation coefficients higher than the $r$ -band CAS parameters. + ‘To do this we carry oul a regression analysis of the XX components for cach physical property against. the CAS analysis of the r-band and iband light. clistribution of the galaxy., To do this we carry out a regression analysis of the PCA components for each physical property against the CAS analysis of the $r$ -band and $u$ -band light distribution of the galaxy. + The results are shown in Table 1. for the ull sample ancl Table 2. for cach of the smaller. redshift, The results are shown in Table \ref{table:corr} for the full sample and Table \ref{table:bins} for each of the smaller redshift +the initial bispectrum Ly (neglecting two-loop contributions at the fourth order. in PT that depend. on the initial trispectrum).,the initial bispectrum $B_0$ (neglecting two-loop contributions at the fourth order in PT that depend on the initial trispectrum). + The amplitude of this correction for local non-Gaussian initial conditions was studied in. Taruvaetal.(2008)... who considered. also initial conditions of the equilateral kind.," The amplitude of this correction for local non-Gaussian initial conditions was studied in \citet{TaruyaKoyamaMatsubara2008}, who considered also initial conditions of the equilateral kind." + They found that the elect of a primordial non-Gaussian Component within the bounds. from CMD observations is tvpically below at mildly nonlinear scales. at the limit of detectability in future large-scale structure observations.," They found that the effect of a primordial non-Gaussian component within the bounds from CMB observations is typically below at mildly nonlinear scales, at the limit of detectability in future large-scale structure observations." + One-loop corrections to the matter. bispectrum Lor Gaussian initial conditions have been studied in Scoccimarro(19907):Scoccimarroetal.(1998). while the extension to generic non-Gaussian initial conditions is explored. in Sefusatti(2009).," One-loop corrections to the matter bispectrum for Gaussian initial conditions have been studied in \citet{Scoccimarro1997, ScoccimarroEtal1998} while the extension to generic non-Gaussian initial conditions is explored in \citet{Sefusatti2009}." +". For the bispectrum up to sixth-order in ITE and excluding two-loop corrections. we have the following expression 12 where By,=By is the initial bispectrum and Diis! — 2 is the other trec-levelDES: nube:contribution.Pie12 perm,while the I-Ioop Corrections are given by = 2 perm... Djis—4 ) perm... TER = quen perm... Jl perm. }..-- 6 qv..q)) )perm...Dii- 6 lU,κι) Loh)[DEN pk dq Pk0e qv) = PaaiibaiEdPiha: d perm... Bude Pig perm."," For the bispectrum up to sixth-order in PT and excluding two-loop corrections, we have the following expression B = + +, where $B_{111}\equiv B_0$ is the initial bispectrum and ^I = 2 _2) P_0(k_1) is the other tree-level contribution, while the 1-loop corrections are given by = ) ), = 2 = (k_2)+P_0(k_2) ]+ , = 4 ) ) |) |) , ^I = )P_0(q)+ , 3 |)+ , ^I 8 _2) |), 6 ) ) |), 6 P_0(k_1) P_0(k_2) _2) d^3q _1, ) = (k_2)+P_0(k_2) ]+ , ^I P_0(q)+ ." +".. Specifically. the one-Ioop contributions present. because of non-Gaussian initial conditions are D1H. which depends on the initialtrispeetrum Zi. and all the fifth-order terms DL. HH, Bi and Dll which dependonthe initial bispectrum Dy."," Specifically, the one-loop contributions present because of non-Gaussian initial conditions are $B_{112}^{II}$, which depends on the initialtrispectrum $T_0$ , and all the fifth-order terms $B_{122}^I$ , $B_{122}^{II}$ , $B_{113}^I$ and $B_{113}^{II}$ , which dependonthe initial bispectrum $B_0$ ." +of distant quasars.,of distant quasars. + One can think reionization as complete. when the mean free path to the ionizing radiation is fully determined by (relatively) slowly evolving nut svstenis (Miralda-Escudé 20032).," One can think reionization as complete, when the mean free path to the ionizing radiation is fully determined by (relatively) slowly evolving Lyman-limit systems (Miralda-Escudé 2003a)." +" It is. however. tempting to try to assign a value for the ""redslufi of relonization."," It is, however, tempting to try to assign a value for the “redshift of reionization”." + Such a value. in order nof to be completely arbitrary. must be roled to the plivsies of the reionization process.," Such a value, in order not to be completely arbitrary, must be related to the physics of the reionization process." +" For example. if secus to be natural to ideutifv the moment of reionization with the overlap stage. but even it takes place over a sizable redshift interval Az~1 (Cnedin 2000). so we would need a better definition if we are to assign a value to ""the redshift of reiouization"," For example, it seems to be natural to identify the moment of reionization with the overlap stage, but even it takes place over a sizable redshift interval $\Delta z\sim1$ (Gnedin 2000), so we would need a better definition if we are to assign a value to “the redshift of reionization”." + Fortunately. such a definition exists.," Fortunately, such a definition exists." + Figure 1 shows the mean free path to ionizing radiation aud its tie derivative as a function of redshift for the fiducial simulation (AL) with ery=1«1095.," Figure \ref{figMP} shows the mean free path to ionizing radiation and its time derivative as a function of redshift for the fiducial simulation (A4) with $\epsilon_{\rm + UV}=1\times10^{-6}$." +" The tine derivative of the mean free path has a well-defined peak iu the middle of the overlap stage. which is a natural momen to identify with ""the redshift of reionization impr."," The time derivative of the mean free path has a well-defined peak in the middle of the overlap stage, which is a natural moment to identify with “the redshift of reionization” $z_{\rm REI}$." + However. this definition is not eutirelv practical. suce the time derivative of the mean free path cannot be observed directly.," However, this definition is not entirely practical, since the time derivative of the mean free path cannot be observed directly." + Tustead. a more easily observable quantity is the mean ucutral fraction.," Instead, a more easily observable quantity is the mean neutral fraction." + Figure 2 shows the mean mass aud volume weighted neutral hydrogen fraction for the fiducial siauulation., Figure \ref{figXH} shows the mean mass and volume weighted neutral hydrogen fraction for the fiducial simulation. +" The moment of relonization closely corresponds to the time when the mean mass (volume) weighted neutral fraction reaches a value of 107 (107) respectively - oue can consider that moment as an alternative definition to ""the redshift of τουκαο).", The moment of reionization closely corresponds to the time when the mean mass (volume) weighted neutral fraction reaches a value of $10^{-2}$ $10^{-3}$ ) respectively - one can consider that moment as an alternative definition to “the redshift of reionization”. + The latter definition is more practical. but it is a subject to an important clause: while the volue weighted neutral fraction is reliably. computed iu he simulation. the mass weighted one depends ou the numerical resolution.," The latter definition is more practical, but it is a subject to an important clause: while the volume weighted neutral fraction is reliably computed in the simulation, the mass weighted one depends on the numerical resolution." + Iu particular. the sinulations prescuted in this paper do not resolve he damped Lxauan-alpha svsteuis. so the quote above value of for the mass weighted ucutral yaction does rot include the neutral σας locked in the damp Lyuiui-alphlia svsteiis.," In particular, the simulations presented in this paper do not resolve the damped Lyman-alpha systems, so the quoted above value of for the mass weighted neutral fraction does not include the neutral gas locked in the damped Lyman-alpha systems." +" In this respect. the volume weehtec nuuber is more robust aud should be used as a dnalu cefiuition of ""the redshitt of relonization."," In this respect, the volume weighted number is more robust and should be used as a main definition of “the redshift of reionization”." + Figure 2 shows the mean trausiüitted flux as a function of redshift for the three simulations with different values of the ery parameter from the set DI., Figure \ref{figTZ} shows the mean transmitted flux as a function of redshift for the three simulations with different values of the $\epsilon_{\rm UV}$ parameter from the set B4. + The observational data shows with open circles were obtained from White et (2003) hy averaging the mean transmitted flux at a eiven redshift interval., The observational data shows with open circles were obtained from White et (2003) by averaging the mean transmitted flux at a given redshift interval. + The vertical error-bars are errors of the mean (not mean errors!), The vertical error-bars are errors of the mean (not mean errors!). + The horizontal error-bars are simply the width of the redshift interval over which the mean transmitted flux is computed., The horizontal error-bars are simply the width of the redshift interval over which the mean transmitted flux is computed. + The last data poiut (without the vertical error-bar) is likely to be coutamunated * a foreground galaxy aud is not included iu us analysis., The last data point (without the vertical error-bar) is likely to be contaminated by a foreground galaxy and is not included in this analysis. + Filled squares show the data from Songaila (2001)., Filled squares show the data from Songaila (2004). + Iu the latter case I do not show je error-bars for clavity. but they are comparable o that of White et (02003).," In the latter case I do not show the error-bars for clarity, but they are comparable to that of White et (2003)." + Two grav lines are the solid black line simply VAητος horizontally., Two gray lines are the solid black line simply shifted horizontally. + As oue cau sec. the chauge iu le ep parameter simply translates into the slüft in redshift.," As one can see, the change in the $\epsilon_{\rm UV}$ parameter simply translates into the shift in redshift." + This is not surprising eiven that in the ACDAL anodel clustering proceeds Licrarchically.," This is not surprising given that in the $\Lambda$ CDM model clustering proceeds hierarchically," +some cynamic role.,some dynamic role. + In fact. our set of simulations wilh varied Q indicate that im=4 is the fastest growing mode [ον all Q between 1.15 aud 1.5 (Pickett&Durisen2007b).," In fact, our set of simulations with varied $Q$ indicate that $m = 4$ is the fastest growing mode for all $Q$ between 1.15 and 1.5 \citep{pickett07b}." +. The Qc=1.0 case has so many [ast growing modes will various is. inelucling m.=4. that we cannot determine which of them grows most rapidly.," The $Q = 1.0$ case has so many fast growing modes with various $m$ s, including $m = 4$, that we cannot determine which of them grows most rapidly." + Comparison of fragmentation criteria derived bv different. authors involves some discussion about how Q is evaluated., Comparison of fragmentation criteria derived by different authors involves some discussion about how $Q$ is evaluated. + For our disk models. we use (11) but with the acliabalic sound speed (Pickettοἱal.1998.2000.2003).," For our disk models, we use (11) but with the adiabatic sound speed \citep{pickett98, pickett00, pickett03}." +. One of the goals of our body of work has been to consider the same basic equilibrium disk models evolved under clilferent assumptions about the equation of state of perturbed fluid elements., One of the goals of our body of work has been to consider the same basic equilibrium disk models evolved under different assumptions about the equation of state of perturbed fluid elements. + Decause (he models are derived from isentropic equilibrium configurations. it makes sense to use (he adiabatic sound speed (o compute a common reference Q that uniquely designates individual disk models within a set of related models.," Because the models are derived from isentropic equilibrium configurations, it makes sense to use the adiabatic sound speed to compute a common reference $Q$ that uniquely designates individual disk models within a set of related models." + For the purposes of comparison with other work. however. we need to compute Q (he same wav other authors do. to the extent that we can.," For the purposes of comparison with other work, however, we need to compute $Q$ the same way other authors do, to the extent that we can." + Johnson&Gammie(2003) and Maveretal.(2004) use what we call here Qi., \citet{johnson03} and \citet{mayer04} use what we call here $Q_{\rm i}$. + &Ganunie(2003) report Iragmentation if and only if (Qj;< about 1.4: the Mayer paper suggests a somewhat larger value., \citet{johnson03} report fragmentation if and only if $Q_{\rm i} <$ about 1.4; the \citet{mayer04} paper suggests a somewhat larger value. + We find fragmentation setüng in for Q< L.7 or. equivalentlv. for Q;« about 1.32. which is in reasonable agreement with these other works. especially considering (hat the precise limit in global simulations probably depends somewhat on the detailed structure of the disk.," We find fragmentation setting in for $Q <$ 1.7 or, equivalently, for $Q_{\rm i} <$ about 1.32, which is in reasonable agreement with these other works, especially considering that the precise limit in global simulations probably depends somewhat on the detailed structure of the disk." + Dynanmically. it may seem obvious that the isothermal sound speed is (he appropriate one to use in (his case.," Dynamically, it may seem obvious that the isothermal sound speed is the appropriate one to use in this case." + However. the perturbations in our simulations arefocally isothermal. ie.. (he temperatures are fixed spatially throughout the grid.," However, the perturbations in our simulations are isothermal, i.e., the temperatures are fixed spatially throughout the grid." + Sound waves (raveling in the © direction are (ruly isothermal. but waves moving in the r or z directions are not.," Sound waves traveling in the $\phi$ direction are truly isothermal, but waves moving in the $r$ or $z$ directions are not." +of the AGN. such as black hole mass ancl multiwavelength emission. we can further refine our understanding of AGN fueling mechanisms.,"of the AGN, such as black hole mass and multiwavelength emission, we can further refine our understanding of AGN fueling mechanisms." + We are grateful to Lei Hao for providing us with eatalogs of AGN from DI»., We are grateful to Lei Hao for providing us with catalogs of AGN from DR5. + We thank Will Serber. Rvan Seranton. and Nikhil Padmanabhan for Πορ conversations.," We thank Will Serber, Ryan Scranton, and Nikhil Padmanabhan for helpful conversations." + We also thank (he referee for comments (hat have greatly improved the manuscript., We also thank the referee for comments that have greatly improved the manuscript. + We acknowledge support rom Microsoft Research. the University of Hlinois. and NASA through grants NNGOGGIIIS6 and NB 2006-02049.," We acknowledge support from Microsoft Research, the University of Illinois, and NASA through grants NNG06GH156 and NB 2006-02049." + The authors made extensive use of the storage and computing facilities al the National Center for Supercomputing Applications and thank the technical staff for their assistance in enabling this work., The authors made extensive use of the storage and computing facilities at the National Center for Supercomputing Applications and thank the technical staff for their assistance in enabling this work. + Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese Monbukagakusho.e and the Max Planck Society.," Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society." + The SDSS Web site is http:/if/www.sdss.org/.oj The SDSS is managed by the Astroplivsical Research Consortium (ARC) for (he Participating Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. + The Participating Institutions are The University of Chicago. Fermilab. the Institute for Advanced Study. the Japan Participation Group. The Johns Hopkins University. the Korean Scientist Group. Los Alamos National Laboratory. the Max-Planck-Institute for Astronomy (AIPIA). the Max-Planck-Institute for Astrophysies (AIPA). New Mexico State University. University of Pittsburgh. University of Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington." +"As explained earlier, we have used different rest-frame B-1 colour cuts to define red and blue galaxies in the model and in the observations.","As explained earlier, we have used different rest-frame $B-I$ colour cuts to define red and blue galaxies in the model and in the observations." +" One may argue that the higher clustering amplitude observed for SAM red galaxies could be due to the redder colour cut applied to select the two populations, redder galaxies being expected to be more strongly clustered."," One may argue that the higher clustering amplitude observed for SAM red galaxies could be due to the redder colour cut applied to select the two populations, redder galaxies being expected to be more strongly clustered." +" To test this possibility we measure the clustering strength of red galaxies in the VVDS-Deep using the same colour cut used in the SAM, i.e. (B—D)""=1.3."," To test this possibility we measure the clustering strength of red galaxies in the VVDS-Deep using the same colour cut used in the SAM, i.e. $(B-I)^{cut}=1.3$." +" In this way, we isolate in the VVDS-Deep sample red galaxies which have the same rest-frame B—I colour distribution than red model galaxies."," In this way, we isolate in the VVDS-Deep sample red galaxies which have the same rest-frame $B-I$ colour distribution than red model galaxies." +" As shown in Fig. 13,,"," As shown in Fig. \ref{rovsz_col}," + we find that these galaxies in the VVDS- show a higher clustering amplitude than those selected with B—7»0.95., we find that these galaxies in the VVDS-Deep show a higher clustering amplitude than those selected with $B-I>0.95$. +" However, the SAM clustering remains significantly stronger, demonstrating that red model galaxies are intrinsically more clustered than observed in the VVDS-Deep."," However, the SAM clustering remains significantly stronger, demonstrating that red model galaxies are intrinsically more clustered than observed in the VVDS-Deep." +" When studying the shape of the projected correlation functions in more detail, one finds that blue SAM galaxies are characterised by a shallower correlation function than VVDS-Deep galaxies, in particular on small scales."," When studying the shape of the projected correlation functions in more detail, one finds that blue SAM galaxies are characterised by a shallower correlation function than VVDS-Deep galaxies, in particular on small scales." +" Within the HOD framework, this implies a weaker 1-halo term that can be interpreted as a lack of blue satellite galaxies in the SAM."," Within the HOD framework, this implies a weaker 1-halo term that can be interpreted as a lack of blue satellite galaxies in the SAM." +" In contrast, red model galaxies exhibit a correlation function which is significantly steeper and higher than observed."," In contrast, red model galaxies exhibit a correlation function which is significantly steeper and higher than observed." +" Here, the very prominent l-halo term may be due to an overabundance of red satellite galaxies."," Here, the very prominent 1-halo term may be due to an overabundance of red satellite galaxies." +" Similarly, ? find an absence of “Finger of God"" (FoG,?) in the correlation function of blue model galaxies at z«1 at variance with red model galaxies, which have a very strong FoG. The FoG effect is associated with the infall of satellite galaxies inside haloes and its strength is related to the abundance of satellite galaxies ?).."," Similarly, \citet{coil08} find an absence of “Finger of God” \citep[FoG,][]{jackson72} in the correlation function of blue model galaxies at $z\simeq1$ at variance with red model galaxies, which have a very strong FoG. The FoG effect is associated with the infall of satellite galaxies inside haloes and its strength is related to the abundance of satellite galaxies \citep[e.g.][]{slosar06}." +" These results suggest that in the real Universe, (at least part of) the red satellites likely evolve less rapidly than in the model, and remain in the blue tail of the colour distribution for a longer time scale."," These results suggest that in the real Universe, (at least part of) the red satellites likely evolve less rapidly than in the model, and remain in the blue tail of the colour distribution for a longer time scale." +" This could adjust the different small-scale clustering behaviours of blue and red SAM and VVDS-Deep galaxies, but would not affect significantly the amplitude of the correlation functions."," This could adjust the different small-scale clustering behaviours of blue and red SAM and VVDS-Deep galaxies, but would not affect significantly the amplitude of the correlation functions." +contributes with to the bolometric flux. but rising to when only the A -band is considered.,"contributes with to the bolometric flux, but rising to when only the $K$ -band is considered." + is a widely used library of evolutionary. stellar population synthesis models., is a widely used library of evolutionary stellar population synthesis models. + It is computed with the isochrones synthesis code of Bruzual&Charlot(2003.alsoknownasBCO3) The spectral coverage of this library is from 91 uup toL605m.. with a resolution of 3 between 3200 and 9500À.. and a lower resolution elsewhere.," It is computed with the isochrones synthesis code of \citet[][also known as BC03]{bc03} The spectral coverage of this library is from 91 up to, with a resolution of 3 between 3200 and 9500, and a lower resolution elsewhere." + Ages range from 10° up to 2- yr. for a wide range of metallicities (-sa|=« . t," Ages range from $\rm 1 \times 10^5$ up to $\rm 2 \times 10^{10}$ yr, for a wide range of metallicities ${\rm \frac{1}{200}} \lesssim \frac{Z}{Z_{\odot}} \lesssim \rm 2.5$ )." +"aThese models use the SeL libraries (seeLejeuneet1997,1999:Westera as well as the STELIB/Pickles libraries 1998).."," These models use the STELIB/BaSeL libraries \citep[see][and references therein]{lejeune97,lejeune98,westera02} as well as the STELIB/Pickles libraries \citep{pickles98}. ." + allows the use of two IMFs (Chabrier(Schaller(Pickles2003:Salpeter1955) and 3 stellar evolution tracks: Geneva etal.1992). 994 (Alongietal.1993:Bressanetal.1993:Fagotto1994a.b:Girardi1996) and 000 (Girardietal.2000).," allows the use of two IMFs \citep{chabrier03,salpeter55} and 3 stellar evolution tracks: Geneva \citep{schaller92}, 94 \citep{alongi93,bressan93,fagotto94a,fagotto94b,girardi96} and 00 \citep{girardi00}." +.M These models do not include the TP-AGB phase., These models do not include the TP-AGB phase. + First. we investigate the dependence of the stellar population components on the normalisation point. from the NUV to the NIR.," First, we investigate the dependence of the stellar population components on the normalisation point, from the NUV to the NIR." + To do this. we select spectral regions free from emission/absorption MSNto be used as normalisation points.£\.," To do this, we select spectral regions free from emission/absorption lines to be used as normalisation points,." +. They are: mcitepbicaSS.mauroO8.mauroQ9.cidO4.fatimaQL.riffel08," They are: \\citep{bica88,mauro08,mauro09,cid04,fatima01,riffel08}." + In addition. we select SSPs with ages: 0.005. 0.025. 0.050. 0.1. 0.2. 0.3.0.4 0.5.0.6. 0.7. 0.8. 0.9. 1.0. 2.0. 5.0 and 13 Gyr as representative of the stellar populations observed in galaxies.," In addition, we select SSPs with ages: 0.005, 0.025, 0.050, 0.1, 0.2, 0.3,0.4 0.5,0.6, 0.7, 0.8, 0.9, 1.0, 2.0, 5.0 and 13 Gyr as representative of the stellar populations observed in galaxies." + As a first exercise we combine two components: 13GGry (the old population) and one of the other SSPs representing the “young” population.," As a first exercise we combine two components: Gry (the old population) and one of the other SSPs representing the “young"" population." +" The combination was made by summing up. along the whole spectral range (~3500A tto AM increasing fractions of the “young” component from | to1004c.. according to where f is the fractional flux. which we vary in steps of 0.01. [Vids the flux of spectrum of the ""young"" component. for each A between ~3500A tto2.5jm.. normalised to unity at Που the optical. or at Που the NIR. and η, is them flux of the 13GGyr spectrum also normalised at the same points."," The combination was made by summing up, along the whole spectral range $\sim$ to ), increasing fractions of the “young"" component from 1 to, according to where $f$ is the fractional flux, which we vary in steps of 0.01, $F_{\rm y}$ is the flux of spectrum of the “young"" component, for each $\lambda$ between $\sim$ to, normalised to unity at for the optical, or at for the NIR, and $F_{\rm o}$ is the flux of the Gyr spectrum also normalised at the same points." + Note that the normalisation of the spectra is done by dividing their fluxes by that of the normalisation point oor m3). after the computations are done.," Note that the normalisation of the spectra is done by dividing their fluxes by that of the normalisation point or ), after the computations are done." + In addition. by normalising the spectra we are dealing with light-fractions. which are directly related to the observations.," In addition, by normalising the spectra we are dealing with light-fractions, which are directly related to the observations." + I? is the resulting flux of the combined SSPs (young + old) at a specitic A., $\rm F$ is the resulting flux of the combined SSPs (young + old) at a specific $\lambda$. + The averaged stellar population componentsspread over all wwere derived by: Eq.2 represents the young and old light fractions for differentPN. this is what we call fraction at A.," The averaged stellar population componentsspread over all were derived by: \ref{eqfrac} represents the young and old light fractions for different, this is what we call fraction at $\lambda$." + The result of such process is summarised in Figs., The result of such process is summarised in Figs. + | and 2.., \ref{fractionsOPT} and \ref{fractionsNIR}. +" In these figures we show the sum of a ""young"" component with a GGyr SSP ¢the old component) in steps of10%."," In these figures we show the sum of a “young"" component with a Gyr SSP (the old component) in steps of." +. In practice we start with of the flux of the “young” SSP + of the flux of the GGyr SSP. and finishwith of the young + of the old component.," In practice we start with of the flux of the “young"" SSP + of the flux of the Gyr SSP, and finishwith of the young + of the old component." + This procedure is done over all As between the NUV and NIR., This procedure is done over all $\lambda$ s between the NUV and NIR. + It is worth mentioning that Figs., It is worth mentioning that Figs. + | and 2.. show MOS EPS models as reference (Sec. ὁ1)).," \ref{fractionsOPT} and \ref{fractionsNIR}, show M05 EPS models as reference (Sec. \ref{discussion}) )." + These figures suggest that one cannot directly compare the light fractions of the young component (/.= 400 Myrs) derived in the optical with those obtained in the NIR. and vice versa (.e. of the MMvyr population at represents only at Aum».," These figures suggest that one cannot directly compare the light fractions of the young component $t \lesssim$ 400 Myrs) derived in the optical with those obtained in the NIR, and vice versa (i.e. of the Myr population at represents only at )." +" However. the intermediate to ""ld components {κ cens.500 M""ThisMyrs) can be directly compared between different w"," However, the intermediate to old components $t \gtrsim$ 500 Myrs) can be directly compared between different wavelengths." + does not occur when dealing with mass fractions. since the age derived by the mass fraction is a more physical parameter. but has a much less direct relation with the observables. depending strongly on the A7/L ratio. which is not constant.," This does not occur when dealing with mass fractions, since the age derived by the mass fraction is a more physical parameter, but has a much less direct relation with the observables, depending strongly on the $M/L$ ratio, which is not constant." + Thus. the light fraction can be taken as an direct observable parameter and use Eqs.," Thus, the light fraction can be taken as an direct observable parameter and use Eqs." + | and 2.. to propagate the results over other spectral regions (see Appendix A).," \ref{eqfrac2} and \ref{eqfrac}, , to propagate the results over other spectral regions (see Appendix \ref{appen}) )." + However. the stellar population of galaxies is not so simple as two components.," However, the stellar population of galaxies is not so simple as two components." +" B we have divided our SSPs into 3 population vectors. .0,20.005 Ον .70;20.025... GGvr. and r,=l3GGyr."," Therefore, we have divided our SSPs into 3 population vectors $x_y$ Gyr; $x_i$ Gyr and $x_o$ Gyr." +" To invne "" effect of adding one more component to the above exercise. we combined three population vectors according to: where. . 0 and + are the fractional fluxes from to100€. which are varied in steps of166: PV. Pj and £5, are the normalised fluxes (at A=S870A oor A 3pm of the ary. ary and on, population vectors. respectively."," To investigate the effect of adding one more component to the above exercise, we combined three population vectors according to: where, $\gamma$, $\delta$ and $\eta$ are the fractional fluxes from to, which are varied in steps of; $F_{\rm y}$, $F_{\rm i} $ and $F_{\rm o}$ are the normalised fluxes (at $\lambda$ or $\lambda$ ) of the $x_{\rm y}$ , $x_{\rm i}$ and $x_{\rm o}$ population vectors, respectively." +I’ is the resulting flux of the combined SSPs (young + intermediate + old) at a specitic A.,$\rm F'$ is the resulting flux of the combined SSPs (young + intermediate + old) at a specific $\lambda$ . + The averaged stellar population components distributed over all As were derived similarly to Eq. 2::, The averaged stellar population components distributed over all $\lambda$s were derived similarly to Eq. \ref{eqfrac}: : +"as a challenge for current models (e.g.,?)..","as a challenge for current models \citep[e.g.,][]{2010ApJ...717..289S}." +" Exactly what these observations tell us about the cold mode has however been ambiguous, as we are only beginning to quantify how the predictions for the accretion dynamics should manifest themselves in observables."," Exactly what these observations tell us about the cold mode has however been ambiguous, as we are only beginning to quantify how the predictions for the accretion dynamics should manifest themselves in observables." +" The opportunity that is presented to us by this state of affairs can hardly be understated, as it is a unique case of a nearly physical prediction in galaxy formation that has yet to be tested, but for which observations are rapidly approaching truly discriminating power."," The opportunity that is presented to us by this state of affairs can hardly be understated, as it is a unique case of a nearly physical prediction in galaxy formation that has yet to be tested, but for which observations are rapidly approaching truly discriminating power." + It therefore behooves us to robustly quantify the predictions of our models., It therefore behooves us to robustly quantify the predictions of our models. +" In ?,, we made a step in this direction by calculating the Lya cooling emission from cold streams, showing that the treatment of self-shielded gas introduced orders-of-magnitude uncertainties in most previous work, and concluding that pure accretion cooling is unlikely to dominate the Lya emission of the bright Lya blobs now routinely imaged (e.g.,?),, although it could be important for some fainter sources (e.g.,?).."," In \cite{2010ApJ...725..633F}, we made a step in this direction by calculating the $\alpha$ cooling emission from cold streams, showing that the treatment of self-shielded gas introduced orders-of-magnitude uncertainties in most previous work, and concluding that pure accretion cooling is unlikely to dominate the $\alpha$ emission of the bright $\alpha$ blobs now routinely imaged \citep[e.g.,][]{2010arXiv1010.2877M}, although it could be important for some fainter sources \citep[e.g.,][]{2008ApJ...681..856R}." + In this we address absorption spectroscopy as a different observational probe of the cold streams., In this we address absorption spectroscopy as a different observational probe of the cold streams. +" Using high-resolution cosmological simulations of a Milky Way progenitor and of a typical LBG-mass halo, we quantify the covering factor of the cold streams in Lyman limit (LLSs) and damped systems (DLAs)."," Using high-resolution cosmological simulations of a Milky Way progenitor and of a typical LBG-mass halo, we quantify the covering factor of the cold streams in Lyman limit (LLSs) and damped systems (DLAs)." +" We show that the covering fraction of such dense gas decreases with time and that it is sufficiently small at z~2 that the presence of cold streams in the halos of Lyman break-selected galaxies is consistent with current observations, consisting principally of stacked spectra, that are dominated by outflow signatures."," We show that the covering fraction of such dense gas decreases with time and that it is sufficiently small at $z\sim2$ that the presence of cold streams in the halos of Lyman break-selected galaxies is consistent with current observations, consisting principally of stacked spectra, that are dominated by outflow signatures." + Our simulations use a modified version of the GADGET 2 cosmological code (?).., Our simulations use a modified version of the GADGET 2 cosmological code \citep[][]{2005MNRAS.364.1105S}. + The gas dynamics is calculated using an SPH algorithm that conserves both energy and entropy (?).., The gas dynamics is calculated using an SPH algorithm that conserves both energy and entropy \citep[][]{2002MNRAS.333..649S}. +" The modifications with respect to the public version of the code include the treatment of cooling, the effects an uniform ultra-violet background (UVB), and a multiphase star formation algorithm as in ?.."," The modifications with respect to the public version of the code include the treatment of cooling, the effects an uniform ultra-violet background (UVB), and a multiphase star formation algorithm as in \citet[][]{2003MNRAS.339..289S}." +" The thermal and ionization properties of the gas are calculated including all relevant processes in a plasma with primordial abundances of hydrogen and helium following ?,, using an update of the ? UV background including galaxies and quasars."," The thermal and ionization properties of the gas are calculated including all relevant processes in a plasma with primordial abundances of hydrogen and helium following \cite{1996ApJS..105...19K}, using an update of the \cite{1996ApJ...461...20H} UV background including galaxies and quasars." +" Self-shielding effects are modeled in processing, as described in the next section."," Self-shielding effects are modeled in post-processing, as described in the next section." +" To achieve ultra-high resolution, we ‘zoom in’ on individual halos within a (10/h comoving Mpc)? simulation box and follow the local gas dynamics at a resolution refined 64x in mass."," To achieve ultra-high resolution, we `zoom in' on individual halos within a $(10/h$ comoving $)^{3}$ simulation box and follow the local gas dynamics at a resolution refined $64\times$ in mass." +" Our main simulation of a Milky Way progenitor (labeled B1) is identical to the one analyzed by ?,, but with a mass resolution higher by a factor of 3.375 because we used 192? dark matter particles in the unrefined volume instead of 128?."," Our main simulation of a Milky Way progenitor (labeled B1) is identical to the one analyzed by \cite{2009ApJ...700L...1K}, but with a mass resolution higher by a factor of 3.375 because we used $192^{3}$ dark matter particles in the unrefined volume instead of $128^{3}$ ." +" The minimum achieved gas smoothing length is 27 proper pc at z—2, with a Plummer-equivalent gravitational force softening of 92[((1--z)/3] proper pc."," The minimum achieved gas smoothing length is 27 proper pc at $z=2$, with a Plummer-equivalent gravitational force softening of $92 [(1+z)/3]^{-1}$ proper pc." +" The halo mass £:3x1011 Mo at z=2 corresponds! to a low-mass LBG, and the simulation is among the highest-resolution cosmological SPH realizations of such a halo to date."," The halo mass $\approx3\times10^{11}$ $_{\odot}$ at $z=2$ corresponds to a low-mass LBG, and the simulation is among the highest-resolution cosmological SPH realizations of such a halo to date." +" The dark matter particle mass of this simulation is 2x10° Mo, and gas particle mass is 4x104 Mo."," The dark matter particle mass of this simulation is $2\times10^{5}$ $_{\odot}$, and gas particle mass is $4\times10^{4}$ $_{\odot}$ ." +" We also study a zoom-in simulation of a more typical LBG halo (labeled A1) of mass £:9x10!! Mo at this redshift, with a spatial resolution lower by a factor of 1.5."," We also study a zoom-in simulation of a more typical LBG halo (labeled A1) of mass $\approx9\times10^{11}$ $_{\odot}$ at this redshift, with a spatial resolution lower by a factor of 1.5." +" We assume a flat ACDM cosmology with Om=0.27, Qn=0.044, h=0.7, og=0.8, and ns=0.95, consistent with the latest analysis (7).."," We assume a flat $\Lambda$ CDM cosmology with $\Omega_{\rm m}=0.27$, $\Omega_{\rm b}=0.044$, $h=0.7$, $\sigma_{8}=0.8$, and $n_{\rm s}=0.95$, consistent with the latest analysis \citep[][]{2010arXiv1001.4538K}." +" Galactic winds are neglected in this work to isolate the accretion streams, but will be studied in future work."," Galactic winds are neglected in this work to isolate the accretion streams, but will be studied in future work." +" We define the virial radius, Rvir, as the radius enclosing a mean overdensity of 180 times the mean matter density."," We define the virial radius, $R_{\rm vir}$, as the radius enclosing a mean overdensity of 180 times the mean matter density." + The covering factor of thecold streams can only be meaningfully quantified forspecific boundary criteria., The covering factor of thecold streams can only be meaningfully quantified forspecific boundary criteria. + For absorption statistics a natural definition is tied to the column density of the material., For absorption statistics a natural definition is tied to the column density of the material. + We limit our attention here, We limit our attention here +"For comparison and interpretation of the results, we should mention that in the original radiation benchmark test (?) the different Monte-Carlo codes themselves differ in the radial temperature profile through the midplane of the circumstellar disk in the most optically thick case Τσσοπι=100 by in most of the region between 1.2 to 200 AU and up to towards the outer border of the computational domain in the radial direction.","For comparison and interpretation of the results, we should mention that in the original radiation benchmark test \citep{Pascucci:2004p39} + the different Monte-Carlo codes themselves differ in the radial temperature profile through the midplane of the circumstellar disk in the most optically thick case $\tau_{550\mathrm{nm}} = 100$ by in most of the region between 1.2 to 200 AU and up to towards the outer border of the computational domain in the radial direction." + This means that the deviations in the optically thin case (Fig. 3)), This means that the deviations in the optically thin case (Fig. \ref{Tau0001}) ) + as well as the frequency dependent ray-tracing part of the optically thick case (Fig. 4)), as well as the frequency dependent ray-tracing part of the optically thick case (Fig. \ref{Tau1000ab}) ) + stay beneath the discrepancy of the different Monte-Carlo solutions., stay beneath the discrepancy of the different Monte-Carlo solutions. +" As expected, the direct stellar irradiation is determined highly accurately, when considering the frequency dependence."," As expected, the direct stellar irradiation is determined highly accurately, when considering the frequency dependence." +" Therefore, the errors introduced by using the FLD approximation can be limited in the test throughout the irradiated regions."," Therefore, the errors introduced by using the FLD approximation can be limited in the test throughout the irradiated regions." +" The influence of the so-called photon noise in the Monte-Carlo method is illustrated in the highly optically thin regions (|6|>30° from the midplane) in Fig. 6,,"," The influence of the so-called photon noise in the Monte-Carlo method is illustrated in the highly optically thin regions $|\theta| > 30\degr$ from the midplane) in Fig. \ref{Tau1e+2_polar}," + where the temperature should actually be independent for large polar angles (as displayed by the solid line)., where the temperature should actually be independent for large polar angles (as displayed by the solid line). +" A special feature of the setup of the original benchmark test (2?) is the fact that even in the most optically thick case Ts5sdnm=100, which is defined for a wavelength of 550 nm, the pre-described disk is locally optically thin for the radiation from thermal dust emission."," A special feature of the setup of the original benchmark test \citep{Pascucci:2004p39} is the fact that even in the most optically thick case $\tau_{550\mathrm{nm}} = 100$, which is defined for a wavelength of $550$ nm, the pre-described disk is locally optically thin for the radiation from thermal dust emission." +" Integrating the corresponding local optical depth Tr(η)=kr(T)p(r)Ar from the outer edge of the disk through the midplane towards the center yields a final optical depth of rgz0.5, see Fig. 8.."," Integrating the corresponding local optical depth $\tau_\mathrm{R}\left(r\right) = \kappa_\mathrm{R}\left(T\right) ~ \rho\left(r\right) ~ \Delta r$ from the outer edge of the disk through the midplane towards the center yields a final optical depth of $\tau_\mathrm{R} \approx 0.5$, see Fig. \ref{OpticalDepth}." +" The plot shows clearly the low optical depth for the thermal component of the radiation field especially in the outer part of the disk, which results in an underestimation of the temperature in the transition region at roughly r« 200 AU due to the overestimation of the radiative flux in the outward direction by the FLD approximation."," The plot shows clearly the low optical depth for the thermal component of the radiation field especially in the outer part of the disk, which results in an underestimation of the temperature in the transition region at roughly $r \approx$ 200 AU due to the overestimation of the radiative flux in the outward direction by the FLD approximation." + The FLD approximation is known to be valid in the most optically thin (free-streaming limit) as well as in the most optically thick (diffusion limit) regions only., The FLD approximation is known to be valid in the most optically thin (free-streaming limit) as well as in the most optically thick (diffusion limit) regions only. + The apparent yet surprisingly good agreement between the Monte-Carlo based runs and the herein proposed radiation transport module also in the intermediate region of the flared disk atmosphere (see Fig. 6)), The apparent yet surprisingly good agreement between the Monte-Carlo based runs and the herein proposed radiation transport module also in the intermediate region of the flared disk atmosphere (see Fig. \ref{Tau1e+2_polar}) ) + is due to the newly implemented direct irradiation routine which yields the correct flux and depth of penetration for the different frequency bins of the stellar irradiation spectrum (see Sect. 3.3.2))., is due to the newly implemented direct irradiation routine which yields the correct flux and depth of penetration for the different frequency bins of the stellar irradiation spectrum (see Sect. \ref{sect:irradiation_thick}) ). + The slight underestimation of the temperature at r~200AU (see Fig. 5)), The slight underestimation of the temperature at $r \approx 200 \mbox{ AU}$ (see Fig. \ref{Tau1e+2_Irradiation+FLD_radial}) ) + in the disk midplane in the most optically thick case is most likely a result of an, in the disk midplane in the most optically thick case is most likely a result of an +"are formally allowed, but produce unnaturally high temperatures.)","are formally allowed, but produce unnaturally high temperatures.)" +" An excellent fit, with x?—69.5 for 70 degrees of freedom (DoF) was obtained for an absorbing column Ng=(1.6+0.3)x107? em~? and photon index T—1.04-0.2 confidence intervals are used throughout)."," An excellent fit, with $\chi^2=69.5$ for 70 degrees of freedom (DoF) was obtained for an absorbing column $N_{\rm H} = (1.6\pm0.3) \times +10^{22}$ $^{-2}$ and photon index $\Gamma = 1.0\pm0.2$ confidence intervals are used throughout)." +" The absorbed 2-10 keV source flux is [ρου=5.3x10715 erg cm? s~!, implying an isotropic luminosity of Lx—7.0x1035 erg s! at 10 kpc distance."," The absorbed 2–10 keV source flux is $F_{\rm PSR} = 5.3 \times +10^{-13}$ erg $^{-2}$ $^{-1}$, implying an isotropic luminosity of $L_{\rm X} = 7.0 \times 10^{33}$ erg $^{-1}$ at 10 kpc distance." +" As described in refsec:xtespec,, this sspectrum was also used in joint fits with ddata."," As described in \\ref{sec:xtespec}, this spectrum was also used in joint fits with data." +" 'To investigate the spectrum of the nebula, we used an elliptical extraction region (Figure 1)), with semi-major and -minor axes of length 873x5""1, centered on the pulsar, with the point-source region (r« 2""5) excluded."," To investigate the spectrum of the nebula, we used an elliptical extraction region (Figure \ref{fig:chandraimage}) ), with semi-major and -minor axes of length $8\farcs3 \times 5\farcs1$, centered on the pulsar, with the point-source region $r<2\farcs5$ ) excluded." +" For the local background, we extracted photons from a concentric annular region well outside the nebular extent (20"" 0.36) and expectedoverestimated (A,= 0.05)."," With fewer fields $\Nfields\le100$ ), the expected uncertainty in the measured bias is large $\sigmab/b\ge0.36$ ) and overestimated $\Deltab\gtrsim 0.05$ )." +" When Nga; is small, the measured dispersion σᾷ can be less than N, providing D?<0 in Equation 4.."," When $\Nfields$ is small, the measured dispersion $\sigmaN^{2}$ can be less than $\Nbar$ , providing $b^{2}<0$ in Equation \ref{eqn:bias_measure}." +" In these catastrophic failures (26% for Λρειας=30 and 9% for Nae,= 100, shown as the b=0 bin), an unusually smallPoisson scatter limitssensitivity to the cosmic variance in number counts."," In these catastrophic failures $26\%$ for $\Nfields=30$ and $9\%$ for $\Nfields=100$ , shown as the $b=0$ bin), an unusually smallPoisson scatter limitssensitivity to the cosmic variance in number counts." + Thesefailures decrease as the number of pointings increases(to 3% for Νρειας= 200)., Thesefailures decrease as the number of pointings increases(to $3\%$ for $\Nfields=200$ ). + The larger numbers of z~6 galaxies per ACS field compared with the number of z~7galaxies WFC3 field(see $3.2)) makes the z~6 ACS experiment permuch easier., The larger numbers of $z\sim6$ galaxies per ACS field compared with the number of $z\sim7$galaxies per WFC3 field(see \ref{subsection:uncorrelated_acs_fields}) ) makes the $z\sim6$ ACS experiment much easier. +Figures G through 10. show both the IIess diagrams of the CAIDs and the unbinned CAIDs of the foreground clusters with the fitted Ser isochrones overlaved.,Figures \ref{f:sgrbg1} through \ref{f:sgrbg5} show both the Hess diagrams of the CMDs and the unbinned CMDs of the foreground clusters with the fitted Sgr isochrones overlayed. + The parameters ol the fits are listed in Table 2. and include coordinates in the Ser svstem. the distances and reddenings to the foreground elusters. and the distances anc recldenings to the Ser CMD features.," The parameters of the fits are listed in Table \ref{t:bgtab} and include coordinates in the Sgr system, the distances and reddenings to the foreground clusters, and the distances and reddenings to the Sgr CMD features." + (D—V) values are caleulated from E(F606V—E814) using the coefficients of Paper I. We estimate. for each field. (hat the distance modulus uncertainty. is 0.05 magnitudes and the reddening uncertainty is 0.01 mag.," $E(B-V)$ values are calculated from $E(F606W-F814W)$ using the coefficients of Paper I. We estimate, for each field, that the distance modulus uncertainty is 0.05 magnitudes and the reddening uncertainty is 0.01 mag." + The absolute distance uncertainty is larger. depending on the absolute calibration of the isochrones.," The absolute distance uncertainty is larger, depending on the absolute calibration of the isochrones." + Table 2. also lists a value for Nga a crude measure of the strength of the Ser feature.," Table \ref{t:bgtab} also lists a value for $N_{\rm Sgr}$, a crude measure of the strength of the Sgr feature." + It is simply the number of stars in the magnitude range 211994).","the expression where and The parameter $b_{0}$ can also be represented as $b_{0}\approx 6\left( C/20% +\textrm{ MeVfm}^{-3}\right) \left( \gamma /18\textrm{ MeVfm}^{-1}\right) $\left[ +\sigma /\left( 75\textrm{ MeV}\right) ^{3}\right] ^{-2}$." + To find the value of the critieal radius for a non-negligible electrostatic energy of the bubble we use an iterative method. by. substituting in the right-hand side of Eq. (6))," To find the value of the critical radius for a non-negligible electrostatic energy of the bubble we use an iterative method, by substituting in the right-hand side of Eq. \ref{eqgen}) )" + r bv the zeroth order approximation given by Eq. (7))., $r$ by the zero'th order approximation given by Eq. \ref{rc0}) ). +" Then. in the first order. (he critical radius is given by where For values of C=20 MeVfm 7. 4=18 !. o in the range (75—100MeV)"". pq89—0.4e oE and negligible p, the critical radius is of the order of 2=— v Bn."," Then, in the first order, the critical radius is given by where For values of $C=20$ $^{-3}$ , $\gamma =18$ $^{-1}$, $\sigma $ in the range $\left( 75-100\textrm{ MeV}\right) ^{3}$, $\rho _{q}\approx -0.4e$ $^{-3}$ and negligible $\rho _{n}$ the critical radius is of the order of $% +R_{c}=2- 7 fm." + The Coulomb correction has the effect of increasing the critical radius., The Coulomb correction has the effect of increasing the critical radius. + The value r=FR. corresponds to the limit bevond which large quantities of the quark phase begin to be formel., The value $r=R_{c}$ corresponds to the limit beyond which large quantities of the quark phase begin to be formed. + In fact. it is more appropriate to refer not (o a limit point r=A. but (o a critical range of values of r near that point. with width or~(T/Axo)!.1930).," In fact, it is more appropriate to refer not to a limit point $r=R_{c}$, but to a critical range of values of $r$ near that point, with width $\delta r\sim \left( T/4\pi +\sigma \right) ^{1/2}$." +. The flictuational development of nuclei in Chis range can süll. with high probability. throw them back into the subcritical range. but iuclei bevond the critical range will inevitably develop into the new quark phase.," The fluctuational development of nuclei in this range can still, with high probability, throw them back into the subcritical range, but nuclei beyond the critical range will inevitably develop into the new quark phase." + The minimum critical work required (o form a stable quark bubbleis therelore given bv where we denoted, The minimum critical work required to form a stable quark bubbleis therefore given by where we denoted +"the GLIMPSE archives. we fitted its SED and thebest-fitting parameters are Ay=17. T, 222200 K. E34 xιο, Tp21100 K. RpzIOR.. and the reduced y is 6.6/6.","the GLIMPSE archives, we fitted its SED and thebest-fitting parameters are $\textrm{A}_\textrm{v}$ =17, $\textrm{T}_*$ =22200 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $3.74\times10^{-{10}}$, $\textrm{T}_{\rm D}$ =1100 K, $\textrm{R}_{\rm D}$ $\textrm{R}_\ast$, and the reduced $\chi^2$ is 6.6/6." +" The best-fitting parameters without the additional component are Avz17.9. T.218200 K. Ras x107, and the corresponding reduced y is 425/8."," The best-fitting parameters without the additional component are $\textrm{A}_\textrm{v}$ =17.9, $\textrm{T}_*$ =18200 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $5.1\times10^{-{10}}$, and the corresponding reduced $\chi^2$ is 425/8." + We then confirm that the MIR excess is likely due to the presence of warm dust around the system. as already suggested by ? and reported in ?..," We then confirm that the MIR excess is likely due to the presence of warm dust around the system, as already suggested by \citet*{2004Filliatre} and reported in \citet{2006Kaplan}. ." + IGR J16320-4751 was detected by on 2003 February (?) and corresponds to the ASCA source AX J1631.9-4752., IGR J16320-4751 was detected by on 2003 February \citep{2003Tomsick} and corresponds to the ASCA source AX J1631.9-4752. + ? report observations with XMM-Newton., \citet{2003Rodrigueza} report observations with . +.. They give an accurate localisation (37) and fitted its high-energy spectrum with an absorbed power law., They give an accurate localisation $\arcsec$ ) and fitted its high-energy spectrum with an absorbed power law. + They derive [~1.6 and Ny~2.1x10? em., They derive $\Gamma\sim1.6$ and $N_{\rm H}\sim2.1\times10^{23}$ $^{-2}$. + ? report the discovery of X-Ray pulsations (P.1309. 5). which proves the compact object is a neutron star.," \citet{2005Lutovinov} report the discovery of X-Ray pulsations $\sim1309$ s), which proves the compact object is a neutron star." + Moreover. ? obtained the light curve of IGR J16320-4751 between 2004 December 21 and 2005 September 17 with Swift and report the discovery of a 8.96 days orbital period.," Moreover, \citet{2004Corbet} obtained the light curve of IGR J16320-4751 between 2004 December 21 and 2005 September 17 with Swift and report the discovery of a 8.96 days orbital period." + IGR. 16320-4751 is then an X-ray binary whose compact object is a neutron star., IGR J16320-4751 is then an X-ray binary whose compact object is a neutron star. + ? searched for the NIR counterpart of the source in the 2MASS catalogue and found its position was consistent with 2MASS J16320215-4752289., \citet*{2007Negueruela} searched for the NIR counterpart of the source in the 2MASS catalogue and found its position was consistent with 2MASS J16320215-4752289. + They also concluded that. if it was an O/B supergiant. it had to be extremely absorbed.," They also concluded that, if it was an O/B supergiant, it had to be extremely absorbed." + The optical and NIR photometry and spectroscopy of this source were carried out at ESO/NTT. and results are reported in CHAOS.," The optical and NIR photometry and spectroscopy of this source were carried out at ESO/NTT, and results are reported in CHA08." + It is shown that its NIR spectrum is consistent with an O/B supergiant and that its intrinsic absorption ts very high. because it was not detected in any of the visible bands.," It is shown that its NIR spectrum is consistent with an O/B supergiant and that its intrinsic absorption is very high, because it was not detected in any of the visible bands." + We searched for the MIR counterpart of IGR J16320-4751 in the GLIMPSE archives and found it to be consistent with G336.3293+00.1689., We searched for the MIR counterpart of IGR J16320-4751 in the GLIMPSE archives and found it to be consistent with G336.3293+00.1689. + We observed IGR J16320-4751 with VISIR on 2005 June 20 in PAH! and PAH2. and the respective exposure times were 1800 s and 2400 s. Typical seeing and airmass were 07663 and 1.13.," We observed IGR J16320-4751 with VISIR on 2005 June 20 in PAH1 and PAH2, and the respective exposure times were 1800 s and 2400 s. Typical seeing and airmass were 63 and 1.13." + We detected it in both filters. and the respective fluxes are 12.1z1.7 mJy and 6.341.8 mJy.," We detected it in both filters, and the respective fluxes are $\pm$ 1.7 mJy and $\pm$ 1.8 mJy." +" Using the ESO/NTT NIR magnitudes given in CHAOS. as well as the GLIMPSE and the VISIR fluxes. we fitted its SED and the best-fitting parameters are Ay=35.4. T,=33000 K. K=138x 107. and the reduced y is 7.7/6."," Using the ESO/NTT NIR magnitudes given in CHA08, as well as the GLIMPSE and the VISIR fluxes, we fitted its SED and the best-fitting parameters are $\textrm{A}_\textrm{v}$ =35.4, $\textrm{T}_*$ =33000 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $1.38\times10^{-{10}}$ , and the reduced $\chi^2$ is 7.7/6." + This result is in good agreement with an extremely absorbed O/B supergiant as reported in CHAOS., This result is in good agreement with an extremely absorbed O/B supergiant as reported in CHA08. + The best fit with the additional component gives a larger reduced v of S/4 and Tp«200 K. We therefore think that IGR J16320-4751 1s an O/B supergiant whose enshrouding material marginally contributes to its MIR emission. even if its intrinsic absorption is extremely high.," The best fit with the additional component gives a larger reduced $\chi^2$ of 8/4 and $\textrm{T}_{\rm D}\,<\,200$ K. We therefore think that IGR J16320-4751 is an O/B supergiant whose enshrouding material marginally contributes to its MIR emission, even if its intrinsic absorption is extremely high." + IGR J16358-4726 was detected with on 2003 March 19 (?) and first observed with on 2003 March 24 (?).., IGR J16358-4726 was detected with on 2003 March 19 \citep{2003Revnivtsev} and first observed with on 2003 March 24 \citep{2004Patel}. + They give its position with 0766 accuracy and fitted its high-energy spectrum with an absorbed power law., They give its position with 6 accuracy and fitted its high-energy spectrum with an absorbed power law. +" They derive Γ~0.5 and Ny~3.3x107 em"".", They derive $\Gamma\sim0.5$ and $N_{\rm H}\sim3.3\times10^{23}$ $^{-2}$. + They also founc a 5880450 s modulation. which could be either a neutror star pulsation or an orbital modulation.," They also found a $\pm$ 50 s modulation, which could be either a neutron star pulsation or an orbital modulation." + Nevertheless. ? performed detailed spectral and timing analysis of this source using multi- archival observations and identified a 94 s spin up. \vhich points to a neutron star origin.," Nevertheless, \citet{2006Patel} + performed detailed spectral and timing analysis of this source using multi-satellite archival observations and identified a 94 s spin up, which points to a neutron star origin." + Assuming that this spi up was due to accretion. they estimate the source magnetic field is between 10 and 10% G. which could support a nagnetar nature for IGR J16358-4726.," Assuming that this spin up was due to accretion, they estimate the source magnetic field is between $10^{13}$ and $10^{15}$ G, which could support a magnetar nature for IGR J16358-4726." + ? propose 2MASS J16355369-4725398 as the possible NIR counterpart. and NIR spectroscopy and photometry of this counterpart was performed at ESO/NTT and ts reported in CHAOS.," \citet{2003Kouveliotou} propose 2MASS J16355369-4725398 as the possible NIR counterpart, and NIR spectroscopy and photometry of this counterpart was performed at ESO/NTT and is reported in CHA08." + They show that its spectrum is consistent with a B supergiant belonging to the same family as IGR JI16318-4848. the so-called Ble] supergiants.," They show that its spectrum is consistent with a B supergiant belonging to the same family as IGR J16318-4848, the so-called B[e] supergiants." + We also found its MIR counterpart in the GLIMPSE archives (6337.0994-00.0062)., We also found its MIR counterpart in the GLIMPSE archives (G337.0994-00.0062). + We observed IGR J16358-4726 with VISIR on 2006 June 29 but did not detect it in any filter., We observed IGR J16358-4726 with VISIR on 2006 June 29 but did not detect it in any filter. +" Using the NIR magnitudes given in CHAOS and the GLIMPSE fluxes. we fitted its SED and the best-fitting parameters are Ay=17.6. T,=24500 K. K=3.16x101. Tp=810 Κ. RpzIO.IR.. and the reduced C is 3.6/2."," Using the NIR magnitudes given in CHA08 and the GLIMPSE fluxes, we fitted its SED and the best-fitting parameters are $\textrm{A}_\textrm{v}$ =17.6, $\textrm{T}_*$ =24500 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $3.16\times10^{-{11}}$, $\textrm{T}_{\rm D}$ =810 K, $\textrm{R}_{\rm D}$ $\textrm{R}_\ast$, and the reduced $\chi^2$ is 3.6/2." +" The best-fitting parameters without the additional component are Ay=16.7. T, 29800 K. ο. x107""! and the corresponding reduced y is 8.8/4."," The best-fitting parameters without the additional component are $\textrm{A}_\textrm{v}$ =16.7, $\textrm{T}_*$ =9800 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $6.05\times10^{-{11}}$ and the corresponding reduced $\chi^2$ is 8.8/4." + The additional component is then necessary to correctly fit the SED. since this source exhibits à MIR excess (see Fig 4).," The additional component is then necessary to correctly fit the SED, since this source exhibits a MIR excess (see Fig 4)." + Even if we lack MIR data above 5.8 jm. we think this excess is real and stems from warm dust. as 1t is consistent with the source being a sgB[e]. as reported in CHAOS.," Even if we lack MIR data above 5.8 $\mu$ m, we think this excess is real and stems from warm dust, as it is consistent with the source being a sgB[e], as reported in CHA08." + IGR J16418-4532 was discovered with on 2003 February 1-5 (?).., IGR J16418-4532 was discovered with on 2003 February 1-5 \citep{2004Tomsick}. + Using observations. ? report an SEXT behaviour of this source and a peak-flux of ~ 80 mCrab (20-30 keV).," Using observations, \citet{2006Sguera} report an SFXT behaviour of this source and a peak-flux of $\sim\,$ 80 mCrab (20-30 keV)." + Moreover. using and observations. ? report a pulse period of 12464100 s and derive Nu-1053 emo.," Moreover, using and observations, \citet{2006Walter} report a pulse period of $\pm$ 100 s and derive $N_{\rm H}\sim10^{23}$ $^{-2}$." + They also proposed 2MASS J16415078- as its likely NIR counterpart., They also proposed 2MASS J16415078-4532253 as its likely NIR counterpart. + The NIR photometry of this counterpart was performed at ESO/NTT and is reported in CHAOS., The NIR photometry of this counterpart was performed at ESO/NTT and is reported in CHA08. + We also foundthe MIR counterpart in the GLIMPSE archives (6339.1889--004889)., We also foundthe MIR counterpart in the GLIMPSE archives (G339.1889+004889). + We observed IGR.J16418-4532. with VISIR on 2006 June 29 but did not detect it in any filter., We observed IGRJ16418-4532 with VISIR on 2006 June 29 but did not detect it in any filter. + Using The NIR magnitudes given in CHAOS. as well as the GLIMPSE fluxes. we fitted its SED. and thebest-fitting parameters are Ay=14.5. T.232800 K. E TI107! . and the reduced y is 1.4/4.," Using The NIR magnitudes given in CHA08, as well as the GLIMPSE fluxes, we fitted its SED, and thebest-fitting parameters are $\textrm{A}_\textrm{v}$ =14.5, $\textrm{T}_*$ =32800 K, $\frac{\textrm{R}_\ast}{\textrm{D}_{\ast}}$ $3.77\times10^{-{11}}$ , and the reduced $\chi^2$ is 1.4/4." + The, The +activities.,activities. +" It can also be appreciated that, at a given total stellar mass and irrespective of the morphological appearance of the interacting pairs, major interactions are those more efficient in forming new stars (up to a factor 2)."," It can also be appreciated that, at a given total stellar mass and irrespective of the morphological appearance of the interacting pairs, major interactions are those more efficient in forming new stars (up to a factor 2)." +" In a similar way, we performed an analysis computing the global index colors as a function of a total stellar mass."," In a similar way, we performed an analysis computing the global index colors as a function of a total stellar mass." + The results are displayed in Fig. 14.., The results are displayed in Fig. \ref{Col12M12}. +" It can be seen that galaxies in disturbed pairs (upper panel) show bluer colors than non-disturbed systems (lower panel), at a given total stellar mass; and we have also noted that major mergers show a significant bluer population."," It can be seen that galaxies in disturbed pairs (upper panel) show bluer colors than non-disturbed systems (lower panel), at a given total stellar mass; and we have also noted that major mergers show a significant bluer population." +" Also, galaxies in the control sample are redder than galaxies in different interaction classes (minor/major mergers, disturbed/non-disturbed pairs), indicating that the global efficiency of different stages/classes of interactions are associated with triggered star formation activity, reflected in the blue colors."," Also, galaxies in the control sample are redder than galaxies in different interaction classes (minor/major mergers, disturbed/non-disturbed pairs), indicating that the global efficiency of different stages/classes of interactions are associated with triggered star formation activity, reflected in the blue colors." + We have performed a statistical analysis of 1959 galaxy pairs (rp«25 kpc h-! and AV<350 km s!) within z«0.1 selected from SDSS-DR7 and we have carried out an eye-ball classification of images according to the evidence of interaction through distorted morphologies and tidal features., We have performed a statistical analysis of 1959 galaxy pairs $r_p < 25$ kpc $h^{-1}$ and $\Delta V < 350$ km $s^{-1}$ ) within $z<0.1$ selected from SDSS-DR7 and we have carried out an eye-ball classification of images according to the evidence of interaction through distorted morphologies and tidal features. + We can summarize the main results in the following conclusions., We can summarize the main results in the following conclusions. +this question since our earlier studies of voids in LORS and in LCDÀM-simulations (??) showed a dependence of the void size distribution on the brightness limit of the ealaxies uncer study and a characteristic void size scaling relation.,"this question since our earlier studies of voids in LCRS and in LCDM-simulations \citep{Mueller00, Arbabi02} showed a dependence of the void size distribution on the brightness limit of the galaxies under study and a characteristic void size scaling relation." + ?— confirmed. this scaling relation in simulated galaxy distributions. but the quantitative parameters were different.," \citet{Benson03} confirmed this scaling relation in simulated galaxy distributions, but the quantitative parameters were different." + They. suspected. dillerences in the void search algorithms as reason. but we suspect that the elfective 2-dimensional nature of the LOTO is the most likely cause.," They suspected differences in the void search algorithms as reason, but we suspect that the effective 2-dimensional nature of the LCRS is the most likely cause." + But their demand for using the same void search algorithm both in data and simulations seenis a prerequisite for trustworth results., But their demand for using the same void search algorithm both in data and simulations seems a prerequisite for trustworth results. + More recently. Colbere ct al. (," More recently, Colberg et al. (" +2007 in. preparation) compared cillerent void. search. algorithms and. found. that most proposed algorithm find comparable locations and sizes of Large voids.,2007 in preparation) compared different void search algorithms and found that most proposed algorithm find comparable locations and sizes of large voids. + This is very likely not the case for the large number of small voids that fill a significant part of space., This is very likely not the case for the large number of small voids that fill a significant part of space. + Therefore we shall present in this study an comparable analysis of voids both in simulations and in the data that explores the detailed void size distribution in dependence on the faint brightness limit of the galaxies definingο the voids., Therefore we shall present in this study an comparable analysis of voids both in simulations and in the data that explores the detailed void size distribution in dependence on the faint brightness limit of the galaxies defining the voids. + We shall use for our study the 24ος {7) thereby coming back to the property of the sel(-similaritv of the vold statistics., We shall use for our study the 2dFGRS \citep{Cole05} thereby coming back to the property of the self-similarity of the void statistics. + Ἡ tells that the void. size. clistribution depends on the mean galaxy. separation. in such a wax that brighter galaxies define larger voids than fainter ones.," It tells that the void size distribution depends on the mean galaxy separation, in such a way that brighter galaxies define larger voids than fainter ones." + Even if voids in the 2cdkORS were previously analyzed (??).. this concerned. mainly large voids and not the detailed vold statistics proposed by us previously.," Even if voids in the 2dFGRS were previously analyzed \citep{Hoyle04, +Patiri06a}, this concerned mainly large voids and not the detailed void statistics proposed by us previously." + ?7 provided a detailed: study of the void. probability: clistribution/— for the 2dECGIUS which is related. to the void. size. clistribution but it provides an clillercnt statistics., \citet{Croton04} provided a detailed study of the void probability distribution for the 2dFGRS which is related to the void size distribution but it provides an different statistics. + Essentially the void probability cistribution is a weighted sum over the void size distribution (?).., Essentially the void probability distribution is a weighted sum over the void size distribution \citep{Otto86}. + The 2dkGRS is a densely sampled. survey with a compact survey geometry., The 2dFGRS is a densely sampled survey with a compact survey geometry. + This is of advantage for the question of the dependence. of the void sizes on the galaxy magnitudes. defining voids., This is of advantage for the question of the dependence of the void sizes on the galaxy magnitudes defining voids. + We shall derive phenomenological fits to the void size distribution that will be compared with simulation results., We shall derive phenomenological fits to the void size distribution that will be compared with simulation results. + Furthermore. we shall take up the question of the faint galaxies within voids.," Furthermore, we shall take up the question of the faint galaxies within voids." + Thereby we cut both questions. the matter content inside large5 underdense regions5 in the universe. ancl the change5 of galaxy properties.," Thereby we cut both questions, the matter content inside large underdense regions in the universe, and the change of galaxy properties." + The color distribution of galaxies in the 2dGIU emplovs SuperCOSMOS data (2). for the Fi-band., The color distribution of galaxies in the 2dFGRS employs SuperCOSMOS data \citep{Hambly01} for the $R$ -band. + We will find a clear bimodality in the void. galaxies so [ar only studied in detail for the SDSS (??2) but not vet for the 34115.," We will find a clear bimodality in the void galaxies so far only studied in detail for the SDSS \citep{Rojas05, Patiri06b} but not yet for the 2dFGRS." + We shall evaluate our void analysis with mocel galaxy samples constructed. from the Millenium simulation of ? and from semianalvtical galaxy formation theory applied to the numerical merecr trees (27).., We shall evaluate our void analysis with model galaxy samples constructed from the Millenium simulation of \citet{Springel05} and from semianalytical galaxy formation theory applied to the numerical merger trees \citep{Croton06}. + We analvzed. specific galaxy properties within voids and found results that can be qualitatively described by the model samples., We analyzed specific galaxy properties within voids and found results that can be qualitatively described by the model samples. + X quantitative comparison of the galaxy color distribution and the star formation ellicieney hints at certain clifferences between observations and simulations., A quantitative comparison of the galaxy color distribution and the star formation efficiency hints at certain differences between observations and simulations. + Tentatively we connect it with specific environmental. properties of galaxy formation in underdense regions., Tentatively we connect it with specific environmental properties of galaxy formation in underdense regions. + In particular. major mergers. galaxy harassment. tidal ancl ram-pressure stripping will not be as elfective there as in more dense regions of the universe (22).," In particular, major mergers, galaxy harassment, tidal and ram-pressure stripping will not be as effective there as in more dense regions of the universe \citep{Avila05, +Maulbetsch06}." + The outline of the paper is as follows: First we describe the galaxy extraction from the 2dGIU. and in Section 3 we provide some details of the galaxy mock data.," The outline of the paper is as follows: First we describe the galaxy extraction from the 2dFGRS, and in Section 3 we provide some details of the galaxy mock data." + In Section Jj we describe our void search algorithm and in Section 5 we provide our results., In Section 4 we describe our void search algorithm and in Section 5 we provide our results. + Section 6 is devoted to a discussion and in thefinal Section we draw our conclusions., Section 6 is devoted to a discussion and in thefinal Section we draw our conclusions. + We analyze the δα Galaxy Bedshift Survey (20ECGIUS. ?)) with about 222.000 galaxies covering a sky area of 1500 deg?," We analyze the 2dF Galaxy Redshift Survey (2dFGRS, \citet{Colless01}) ) with about 222,000 galaxies covering a sky area of 1500 $^2$." + For the void. search ancl statistics. it has the advantage of covering a sullicient large area with an average completeness of 90 in redshift measurements. 2...," For the void search and statistics, it has the advantage of covering a sufficient large area with an average completeness of $90\%$ in redshift measurements, \citet{Colless01}." + We. shall. discuss he method for treating the varying completeness. below., We shall discuss the method for treating the varying completeness below. +" ""hotometric data in 5; stem from the APAL photographic dates (2) which represents the basis of the fiber placement or redshift measurements.", Photometric data in $b_{J}$ stem from the APM photographic plates \citep{Maddox90} which represents the basis of the fiber placement for redshift measurements. + 6; and r-band data are available hrough the SuperCOSMOS catalog (2). The 2dEGIS has been used for icdntifving large volcds w ? and bv ?.. and for an analysis of the void. probability unction by 2..," $b_J$ and $r$ -band data are available through the SuperCOSMOS catalog \cite{Hambly01}) ).The 2dFGRS has been used for identifying large voids by \citet{Hoyle04} and by \citet{Patiri06a}, and for an analysis of the void probability function by \cite{Croton04}." + Our aim is to touch both points., Our aim is to touch both points. + We extract a large catalogue of voids. both small and large ones.," We extract a large catalogue of voids, both small and large ones." + This catalogue can be used for statistical studies of the void size distribution. and for identifving subpopulations within voids.," This catalogue can be used for statistical studies of the void size distribution, and for identifying subpopulations within voids." + We do not claim that all our voids are statistically significant., We do not claim that all our voids are statistically significant. + Especially the position of the large number of small voids are inlluenced by random galaxy positions., Especially the position of the large number of small voids are influenced by random galaxy positions. + But a detailed look at the large voids in Figs., But a detailed look at the large voids in Figs. + 1. and 2) verilies that both in data and simulations we catch as voids the same regions as the eve selects in the galaxy distribution (note the projection ellects that influences a part of voids in this Figure)., \ref{voids2df} and \ref{voidsmill} verifies that both in data and simulations we catch as voids the same regions as the eye selects in the galaxy distribution (note the projection effects that influences a part of voids in this Figure). + We extracted volume Limited samples from the 20bCRS in using the 5; magnitudes since it is the color defining the spectroscopic survey., We extracted volume limited samples from the 2dFGRS in using the $b_J$ magnitudes since it is the color defining the spectroscopic survey. + Apparent magnitudes were converted to absolute magnitudes by using the extinction corrections as given in the 20(1 catalog for the APAL 5; magnitudes., Apparent magnitudes were converted to absolute magnitudes by using the extinction corrections as given in the 2dFGRS catalog for the APM $b_{J}$ magnitudes. + The SuperCOSMOS magnitudes were corrected. using the Schlegel extinction maps (7)..., The SuperCOSMOS magnitudes were corrected using the Schlegel extinction maps \citep{Schlegel98}. + As à proxy lor the specific star formation rate we take the 7 parameter as defined. by 7 performing a principal component analysis of the optical spectra., As a proxy for the specific star formation rate we take the $\eta$ parameter as defined by \cite{Madgwick02} performing a principal component analysis of the optical spectra. + This parameter also shows a strong correlation with the specific star formation rate obtained from the SDSS. ?..," This parameter also shows a strong correlation with the specific star formation rate obtained from the SDSS, \citet{SolAlonso06}." + The parameter i is correlated with the Hubble types (2): yeld means mainly to DE/S0-galaxies. while yoo—L4 corresponds mostly to [ate type ο galaxies.," The parameter $\eta$ is correlated with the Hubble types \citep{Norberg02}: $\eta < -1.4$ means mainly to E/S0-galaxies, while $ \eta > +-1.4$ corresponds mostly to late type S galaxies." + But the scatter is large and we shall interpret our results in terms of the morphological type with some care., But the scatter is large and we shall interpret our results in terms of the morphological type with some care. + All galaxies with a quality ῷ>3B were used in order to have accurate redshift determinations., All galaxies with a quality $Q \ge 3$ were used in order to have accurate redshift determinations. + For determining the c- and &-corrections we follow themethod described in ? [or those galaxies whose type could be determined. and that by ? for those which could not be determined and therefore was derived for a mix of galaxy tvpes.," For determining the $e$ - and $k$ -corrections we follow themethod described in \cite{Folkes99} for those galaxies whose type could be determined, and that by \cite{Norberg02} for those which could not be determined and therefore was derived for a mix of galaxy types." + For the SuperCOSMOS magnitudes we use the A-correction proposed by 2 for the r-band. magnitudes.," For the SuperCOSMOS magnitudes we use the $k$ -correction proposed by \citet{Cole05} + for the $r$ -band magnitudes." + Eight volume limited samples where constructed. both from coherent regions of the SGP and. NCD slices of the 2dFORS., Eight volume limited samples where constructed both from coherent regions of the SGP and NGP slices of the 2dFGRS. + The SGP sample was restricted to the right ascension; range 2]xa:3.al 40. and a declinationMN range 33.700xὃ 25.750: the NGP was selected through 1480. 4.700«d 1.700.," The SGP sample was restricted to the right ascension range $ -2.^{\rm h}10 \le \alpha \le 3.^{\rm h}40 $ , and a declination range $ -33.^{\circ}00 \le \delta \le -25.^{\circ}50 $ ; the NGP was selected through $ 10.^{\rm h}00 \le \alpha \le 14.^{\rm h}80 $ , $ +-4.^{\circ}00 \le \delta \le 1.^{\circ}00 $ ." +that new passive galaxies with sizes comparable to local counterparts are formed.,that new passive galaxies with sizes comparable to local counterparts are formed. + Tn the bottom panel of Fig., In the bottom panel of Fig. + & we show the fraction of compact aud ultra-compact ETCs as a function of the redshift aud cosimic time., \ref{fig8} we show the fraction of compact and ultra-compact ETGs as a function of the redshift and cosmic time. +" The fraction of compact ETCs decreases frou, at ΕΕ ο εξ, whilethefractionof compactdrops from at ο ο ΕΕ ΜΗ "," The fraction of compact ETGs decreases from at $=1.6$ to at $z=0$, while the fraction of ultra-compact drops from at $=1.6$ to zero at $z=0$." +fractioncanbeshd tino s," We stress that these fraction can be slightly overestimated at $1.21.6$." +déhscrkedat C sate dedto ft," Anyway, strong lower limits to these fractions (if we limit the sample to $1.2100737. and ΕΠ«10τσ 5.," We selected a homogeneous and robust sample of 563 passive galaxies using the multiband photometry available in the GOODS N+S fields, selecting galaxies with $M>10^{10}M_{\odot}$ and $SSFR<10^{-2}Gyr^{-1}$ ." + We studied the morphological properties of the sample in the optical rest-frame. using the ACS + bandobjects at Doc12 aud the WFEC2 ZF baud for galaxies forat 2>1.2. and we discarded galaxies with late-type morplologics.," We studied the morphological properties of the sample in the optical rest-frame, using the ACS $z-$ band for objects at $z<1.2$ and the WFC3 $H-$ band for galaxies at $z>1.2$, and we discarded galaxies with late-type morphologies." + We then riu GALFIT to measure the Sérrsic indices aud dhivsical sizes., We then run GALFIT to measure the Sérrsic indices and physical sizes. + We found that. at all redshifts. the morphology traced o the rest-frame UV Πο is. within the statistical nucertaitics. very close to that traced by the optical ight. at least when parameters such as the Sérrsic iudices aud effective radii are used.," We found that, at all redshifts, the morphology traced by the rest-frame UV light is, within the statistical uncertainties, very close to that traced by the optical light, at least when parameters such as the Sérrsic indices and effective radii are used." + In fact. the sizes and Sérrsie iudices mmcasured in the UV. aud optical rest-rane correlate quite well with each other. with the sizes ueasured iu the optical rest-frame being slightly snaller (bv ~20% and —104 at:2d and :X d. respectively) han those derived from the UV. vest-frame.," In fact, the sizes and Sérrsic indices measured in the UV and optical rest-frame correlate quite well with each other, with the sizes measured in the optical rest-frame being slightly smaller (by $\sim$ and $\sim$ at $z\gtrsim1$ and $z\lesssim1$ , respectively) than those derived from the UV rest-frame." + This shows hat. at least for galaxies that are not currently. forming stars. the morphological K-correction is weak. aud thus hat ACS/: baud observations. if deep enough. cau c judecd used to measure the size of passive galaxies at 2>dl.," This shows that, at least for galaxies that are not currently forming stars, the morphological K-correction is weak, and thus that $z-$ band observations, if deep enough, can be indeed used to measure the size of passive galaxies at $z>1$." + This is du good agreecnieut with previous results bv Trujillo et al. (, This is in good agreement with previous results by Trujillo et al. ( +2007) and Cassata et al. (,2007) and Cassata et al. ( +2010) and. at lower redshift. with C'assata et al. (,"2010) and, at lower redshift, with Cassata et al. (" +2005) aud Papovich et al. (,2005) and Papovich et al. ( +2003).,2003). + We showed that the mass-size relation of ETCs evolves significautly fom 71.6to z0: ~80% of ETCs at >=L.Ginoursanplearcsinallerthantlocalcounterpartso μμ” ," We showed that the mass-size relation of ETGs evolves significantly from 1.6 to $z\sim0$: $\sim 80\%$ of ETGs at $=1.6$ in our sample are smaller than local counterparts of the same mass, and at later epochs ETGs are increasingly larger." +With the a, We showed as well that the fractional increase of the average size is almost independent on the stellar mass. +im of understanding whether the evolution of the mass-size relation is driven by the size erowth of cach individual ealaxy or by the appearance of new lavee ETCGs. we have built the size distribution in four redshift bius. scaled to the umuber density of ETCs iu bh ," With the aim of understanding whether the evolution of the mass-size relation is driven by the size growth of each individual galaxy or by the appearance of new large ETGs, we have built the size distribution in four redshift bins, scaled to the number density of ETGs in each bin." +We htzp2 Hyomrpl on average 0.5 dex smaller than local counterparts ο the same mass. and we ideutified a rich population ofultra-compact ETCs that have no identified counterparts in ternis of size and density iu the local Universe.," We observed that ETGs at $1.2=L.Gtez~ 1. in agrecincut with Arnouts et al. (," More in details, we showed that the number and mass density of massive and passive early-types increase by a factor of $\sim 5$ within the $\sim +2$ Gyr between $=1.6$ to $z\sim1$, in agreement with Arnouts et al. (" +2007) aud Ibert ot al. (,2007) and Ilbert et al. ( +2010).,2010). + In the following | Cyr. from 2—1 to :~0.5. the nuniber density increases by at most another factor of 1.5. while iu the same interval the mass deusitv remains constant.," In the following 4 Gyr, from $z\sim1$ to $z\sim0.5$, the number density increases by at most another factor of $\sim 1.5$, while in the same interval the mass density remains constant." + This implies that. as expected in a “downsizing” scenario. the added galaxies that drive the umuber evolution have small iniasses aud do not contribute too much to the mass deusitv.," This implies that, as expected in a “downsizing” scenario, the added galaxies that drive the number evolution have small masses and do not contribute too much to the mass density." + These findings are in good agreecneut with Franceschini et al. (, These findings are in good agreement with Franceschini et al. ( +2006). Borch et al (,"2006), Borch et al. (" +2006) and Abraham ct al. (,2006) and Abraham et al. ( +2007). aud simular to the results by Ciimatti. Daddi Boeuzini (2006) and Searlata et al. (,"2007), and similar to the results by Cimatti, Daddi Renzini (2006) and Scarlata et al. (" +2007).,2007). + From :~1 to 2~0. we showed also that the uunboer (aud mass) density ofcompact carly-types decreases by a factor of 2. wlüle the umuber density of mormal-size ETCs increases inch faster. indicating once again that the overall increase of the average size at fixed mass is ouly partly due to a size increase of individual galaxies. whereas part of the effect is due to the appearance of new ETGs with large size.," From $z\sim1$ to $z\sim0$, we showed also that the number (and mass) density of early-types decreases by a factor of 2, while the number density of normal-size ETGs increases much faster, indicating once again that the overall increase of the average size at fixed mass is only partly due to a size increase of individual galaxies, whereas part of the effect is due to the appearance of new ETGs with large size." + We interpret these results as the evidence that the phases at 2 Land :o«1 are dominated by distinct and different physical miechanisumis., We interpret these results as the evidence that the phases at $z>1$ and $z<1$ are dominated by distinct and different physical mechanisms. + The scenario that comes out is the following: the epoch at 1<:x3 is when the bulk of the stellar mass in local carly-type galaxies is assembled., The scenario that comes out is the following: the epoch at $1T5004. wavelengths where there are strong emission lines.," The sky background is a serious problem for ground-based spectroscopy, especially at redder, $\lambda>7500\rm \AA$, wavelengths where there are strong emission lines." + Phe ‘nocd-and-shullle’ =node was designed to provide improved subtraction of the gakv background. even where this is subject to considerable Esxdial and time variation.," The `nod-and-shuffle' mode was designed to provide improved subtraction of the sky background, even where this is subject to considerable spatial and time variation." +" Essentially. the telescope is ""nodded (by. 1 aresec in this case) along the spectroscopic gait. observing at cach position alternately in à rapid one-minute evcle."," Essentially, the telescope is `nodded' (by 1 arcsec in this case) along the spectroscopic slit, observing at each position alternately in a rapid one-minute cycle." + In. position A the object will be towards one side of the slit and. the adjacent skv on the other. in position D the object will be on the other side.," In position A the object will be towards one side of the slit and the adjacent sky on the other, in position B the object will be on the other side." +" With each evele. the charges stored. on the CCD from the two positions are ""shullled (by 2 aresee) into adjacent strips on the CCD frame. where they are accumulated over the course of cach half-hour exposure."," With each cycle, the charges stored on the CCD from the two positions are `shuffled' (by 2 arcsec) into adjacent strips on the CCD frame, where they are accumulated over the course of each half-hour exposure." + In this way the sky is observed simultaneously with. and as close as possible in position to. cach individual target. galaxy.," In this way the sky is observed simultaneously with, and as close as possible in position to, each individual target galaxy." + CGMOS data reduction was carried out using routines. including some specifically written for this instrument.," GMOS data reduction was carried out using routines, including some specifically written for this instrument." + Firstly. bias frames were subtracted from the target galaxy. are-lamp and standard star exposures.," Firstly, bias frames were subtracted from the target galaxy, arc-lamp and standard star exposures." + The next step was sky subtraction. performed. individually for each of the 170 exposures.," The next step was sky subtraction, performed individually for each of the 70 exposures." + The nod-and-shullle mode produces a CCD rame showing two adjacent strips for each spectrograph slit. corresponding to the two nod positions.," The nod-and-shuffle mode produces a CCD frame showing two adjacent strips for each spectrograph slit, corresponding to the two nod positions." + To sky subtract. the rame is shifted by the shullle step and subtracted it from itself (using the cgnsskvsub! task).," To sky subtract, the frame is shifted by the shuffle step and subtracted it from itself (using the `gnsskysub' task)." + This produces a »ositive and a negative skv-subtracted: spectrum for cach arget galaxy., This produces a positive and a negative sky-subtracted spectrum for each target galaxy. + Small dithers in the spectral ancl spatial clirections tween the TO exposures (introduced intentionally for the removal of charge traps: Abraham et al., Small dithers in the spectral and spatial directions between the 70 exposures (introduced intentionally for the removal of charge traps; Abraham et al. + 2004) were removed w registering the 70 exposures in both axes., 2004) were removed by registering the 70 exposures in both axes. +" The 10 skv-subtracted frames. could. then be combined. using ""àmcombine with a sigclip' rejection to remove most of the cosmic ravs. into a single 35.5 hour image. from which we extract the spectra."," The 70 sky-subtracted frames could then be combined, using `imcombine' with a `sigclip' rejection to remove most of the cosmic rays, into a single 35.5 hour image, from which we extract the spectra." + tasks (c.g. αρα} were then emploved to extract, tasks (e.g. `apall') were then employed to extract +a PN.,a PN. + WII J2128+44: A face-on spiral galaxy., WHI J2128+44: A face-on spiral galaxy. + WII J2133+31: Galactic nebulositv. which appears (though under condiGons which were anvthing bul photometric) to be fainter in V than in H. WII J2159+18: One end of a large. faint nebulosity.," WHI J2133+31: Galactic nebulosity, which appears (though under conditions which were anything but photometric) to be fainter in V than in R. WHI J2159+18: One end of a large, faint nebulosity." + WII J22014+71: Large and ill-defined nebulositv: no meaningful dimensions ean be given., WHI J2201+71: Large and ill-defined nebulosity; no meaningful dimensions can be given. + WIL J2205--43: An enormous skein of Galactic nebulositv. extending off the frame to the east. west. and north.," WHI J2205+43: An enormous skein of Galactic nebulosity, extending off the frame to the east, west, and north." + IXIXR99-239.2: A barred multiarmec spiral., KKR99-289.2: A barred multiarmed spiral. + Lumpy., Lumpy. + Catalogued by Karachentsey (1000): given a radial velocity of 1145 km/s by IIuchtmeierοἱal. (2000a)., Catalogued by \citet{KKR99}; given a radial velocity of 1145 km/s by \citet{HKK00}. . +. From the Πα image most of (he Iumps are II] regions. though not all.," From the $\alpha$ image most of the lumps are HII regions, though not all." + WII J2219+20: Galactic nebulositv., WHI J2219+20: Galactic nebulosity. + The size and position given correspond to a slightly brighter section. but. there is more throughout almost the whole field.," The size and position given correspond to a slightly brighter section, but there is more throughout almost the whole field." + No Ila. emission detected., No $\alpha$ emission detected. + Sharpless 141: Brightish emission nebula., Sharpless 141: Brightish emission nebula. + It is very difficult to get the surface brightness of the nebula alone. since (he star density is so high.," It is very difficult to get the surface brightness of the nebula alone, since the star density is so high." + Catalogued by Sharpless(1959) as an IU] region. though this reference was apparently too old to have been entered into Simbad when we checked.," Catalogued by \citet{S59} as an HII region, though this reference was apparently too old to have been entered into Simbad when we checked." + WIII J22344-20: Large. faint Galactic nebulosity: no apparent Ila.," WHI J2234+20: Large, faint Galactic nebulosity; no apparent $\alpha$." + WII J2259+58: Large Galactic nebula. probably emission. (hough we didn't get an Ia nage.," WHI J2259+58: Large Galactic nebula, probably emission, though we didn't get an $\alpha$ image." + WII J223094-4H4: Turbulent Galactic nebulositv., WHI J2309+44: Turbulent Galactic nebulosity. + WII J23124-25: Arrow-shaped bit of Galactic nebulositv., WHI J2312+25: Arrow-shaped bit of Galactic nebulosity. + WII J2319243: Galactic nebulosity., WHI J2319+43: Galactic nebulosity. + WIL J23534-10: LSB spiral., WHI J2353+70: LSB spiral. + Five objects were not included in Whiting.Hau.&Irwin(2002) because our analvsis of follow-up images did not appear to show anvthing at (hose positions., Five objects were not included in \citet{WHI02} because our analysis of follow-up images did not appear to show anything at those positions. + However. reprocessing ol the original data and remeasuring allow us to list them: WII J0551-39:A laree ring. possibly a very old PN.," However, reprocessing of the original data and remeasuring allow us to list them: WHI J0551-39:A large ring, possibly a very old PN." +The heat stored in the intracluster plasma is conducted down any temperature gradient present in the gas in a way that can be described through the following equations (Spitzer 1956. Sarazin 1988): where q is the heat flux. 7) is the electron temperature. and w is the thermal conductivity that can be expressed in term of the density. Πο. the electron mass. nz... and the electron mean free path. Av. as (Cowie and McKee 1977) In a fully ionized gas of (mostly) hydrogen. the electron mean free path is function of the gas temperature. density and impact parameters of the Coulomb collisions. A: where we have adopted the following dimensionless quantities: Using this expression and the adopted typical values for cluster plasma. we can then write If the mean electron free path is comparable to the scale length or of the temperature gradient. the heat flux tends to saturate to the limiting value which may be carried by the electrons (Cowie and McKee 1977): where the factor 0.42 comes from the reduction effect on the heat conducted by the electrons and that is produced from the secondary electric tield that maintain the total electric current along the temperature gradient at zero (Spitzer 1956).,"The heat stored in the intracluster plasma is conducted down any temperature gradient present in the gas in a way that can be described through the following equations (Spitzer 1956, Sarazin 1988): where $q$ is the heat flux, $T_{\rm e}$ is the electron temperature, and $\kappa$ is the thermal conductivity that can be expressed in term of the density, $n_{\rm e}$ , the electron mass, $m_{\rm e}$, and the electron mean free path, $\lambda_{\rm e}$, as (Cowie and McKee 1977) In a fully ionized gas of (mostly) hydrogen, the electron mean free path is function of the gas temperature, density and impact parameters of the Coulomb collisions, $\Lambda$: where we have adopted the following dimensionless quantities: Using this expression and the adopted typical values for cluster plasma, we can then write If the mean electron free path is comparable to the scale length $\delta r$ of the temperature gradient, the heat flux tends to saturate to the limiting value which may be carried by the electrons (Cowie and McKee 1977): where the factor 0.42 comes from the reduction effect on the heat conducted by the electrons and that is produced from the secondary electric field that maintain the total electric current along the temperature gradient at zero (Spitzer 1956)." + In this Letter. we apply these equations to estimate the efficiency of thermal conductivity in the intracluster medium of A2|42. a cluster of galaxies observed by the X-ray telescope during its calibration phase in August 1999.," In this Letter, we apply these equations to estimate the efficiency of thermal conductivity in the intracluster medium of A2142, a cluster of galaxies observed by the X-ray telescope during its calibration phase in August 1999." + Tarkeviteh et al. (, Markevitch et al. ( +2000) have analyzed the observation of the merging cluster of galaxies A2142 and made an important discovery.,2000) have analyzed the observation of the merging cluster of galaxies A2142 and made an important discovery. + The X-ray image reveals of sharp edges to the surface brightness of the central elliptical-shaped region., The X-ray image reveals of sharp edges to the surface brightness of the central elliptical-shaped region. + The edges are ocated about 3 arcmin to the northwest and | arcmin to the south with respect to the X-ray centre., The edges are located about 3 arcmin to the northwest and 1 arcmin to the south with respect to the X–ray centre. + Markevitch et al (2000) show hat the bright and fainter regions either side of an edge are in oressure equilibrium with each other. but with a dramatic electron emperature decrease on the inside.," Markevitch et al (2000) show that the bright and fainter regions either side of an edge are in pressure equilibrium with each other, but with a dramatic electron temperature decrease on the inside." + Considering the values of the intracluster gas properties in A2]|4? from their Figure +. together with the equations presented in our Introduction. we can estimate whether thermal conductivity is efficient in erasing the observed temperature gradient.," Considering the values of the intracluster gas properties in A2142 from their Figure 4, together with the equations presented in our Introduction, we can estimate whether thermal conductivity is efficient in erasing the observed temperature gradient." + The electron temperature (panel ὁ in their Fig., The electron temperature (panel $b$ in their Fig. + 4) varies from 5.8 to 10.6 keV on either side of the boundary of the southern edge of the central bright patch in A2142. and from 7.5 to13.8 keV at the," 4) varies from 5.8 to 10.6 keV on either side of the boundary of the southern edge of the central bright patch in A2142, and from 7.5 to13.8 keV at the" +"groups known as ""fossil groups” and found significant differences in their intergalactic hot gas properties in comparison to other galaxy groups.",groups known as “fossil groups” and found significant differences in their intergalactic hot gas properties in comparison to other galaxy groups. + By estimating the space density of fossil groups. they showed that fossils are as numerous as galaxy clusters.," By estimating the space density of fossil groups, they showed that fossils are as numerous as galaxy clusters." + Fossil groups are particularly important systems to study. in the context of scaling relations. as they are not subject to recent major group mergers. and should represent archetypal old undisturbed systems.," Fossil groups are particularly important systems to study, in the context of scaling relations, as they are not subject to recent major group mergers, and should represent archetypal old undisturbed systems." + Recent studies of fossil groups show interesting features which distinguish them from normal galaxy groups., Recent studies of fossil groups show interesting features which distinguish them from normal galaxy groups. + observations of the nearest fossil galaxy group. NGC 6482. showed avery high gravitational mass concentration and the absence of a cool core (Khosroshahietal.2004)... despite the short central cooling time.," observations of the nearest fossil galaxy group, NGC 6482, showed a very high gravitational mass concentration and the absence of a cool core \citep{kjp04}, despite the short central cooling time." + The and study of the fossil cluster.. RX 1141642315 showed similar features (Khosroshahietal. 2006).," The and study of the fossil cluster,, RX J1416.4+2315 showed similar features \citep{kmpj06}." + There has been only one statistical study of fossil groups (Jonesetal.2003).. based on ROSAT pointed observations. which demonstrated some of the differences in fossils compared to normal galaxy groups and clusters.," There has been only one statistical study of fossil groups \citep{jones03}, based on ROSAT pointed observations, which demonstrated some of the differences in fossils compared to normal galaxy groups and clusters." + The present study uses high resolution. short to moderate exposure. observations of fossil groups drawn from this flux-limited sample combined with previously studied fossils.," The present study uses high resolution, short to moderate exposure, observations of fossil groups drawn from this flux-limited sample combined with previously studied fossils." + Together. this provides the largest sample of fossil galaxy groups studied using the high resolution of..," Together, this provides the largest sample of fossil galaxy groups studied using the high resolution of." + Section 2 briefly reviews fossil groups and describes the observations., Section 2 briefly reviews fossil groups and describes the observations. + The results from imaging and spectral X-ray analysis and comments of individual systems are presented in Section 3., The results from imaging and spectral X-ray analysis and comments of individual systems are presented in Section 3. + The scaling relations involving X-ray and optical properties of fossils are presented in Section 4., The scaling relations involving X-ray and optical properties of fossils are presented in Section 4. + Section 5 studies the mass distribution. AJ7' relation and mass-to-light ratio.," Section 5 studies the mass distribution, $M-T$ relation and mass-to-light ratio." + A discussion and concluding remarks can be found in section 6., A discussion and concluding remarks can be found in section 6. +" We adopt a cosmology with //;=70 kms + + and Q,,=0.3 with cosmological constant O4=0.7 throughout this paper.", We adopt a cosmology with $H_0=70$ km $^{-1}$ $^{-1}$ and $\Omega_m=0.3$ with cosmological constant $\Omega_\Lambda=0.7$ throughout this paper. + Fossil galaxy groups are identified as galaxy groups dominated. optically. by a single giant elliptical galaxy surrounded by an extended X-ray emission with X-ray luminosity of 107h.7 ere +.," Fossil galaxy groups are identified as galaxy groups dominated, optically, by a single giant elliptical galaxy surrounded by an extended X-ray emission with X-ray luminosity of $L_{X,bol} \geq +10^{42} h^{-2}_{50}$ erg $^{-1}$." + There is at least a 2 magnitude difference between the luminosity of the first and the second ranked galaxies. measured in the R-band. within the half virial radius.," There is at least a 2 magnitude difference between the luminosity of the first and the second ranked galaxies, measured in the R-band, within the half virial radius." + Jonesetal.(2003) give the rationale for the above choices., \citet{jones03} give the rationale for the above choices. + The lower limit to Lx guarantees the existence of a collapsed galaxy system. while the optical criterion ensures that the M» galaxies have merged into a single luminous galaxy as a result of dynamical friction (Binney&Tremaine 1987).," The lower limit to $L_X$ guarantees the existence of a collapsed galaxy system, while the optical criterion ensures that the $\star$ galaxies have merged into a single luminous galaxy as a result of dynamical friction \citep{binney87}." +. No upper limit is placed on the X-ray luminosity or temperature. but as dynamical friction is the main player in the formation of fossil groups. the mass and physical size of the system cannot be arbitrarily large as the time scale for dynamical friction to lead to orbital decay. and hence to galaxy merging. should not exceed the age of the universe (Khosroshahietal.2006:Milosal. 2006).," No upper limit is placed on the X-ray luminosity or temperature, but as dynamical friction is the main player in the formation of fossil groups, the mass and physical size of the system cannot be arbitrarily large as the time scale for dynamical friction to lead to orbital decay, and hence to galaxy merging, should not exceed the age of the universe \citep{kmpj06,milos06}." +. The central galaxy in fossils can be as luminous as the brightest cluster galaxies (BCGs)., The central galaxy in fossils can be as luminous as the brightest cluster galaxies (BCGs). + However. despite apparent similarities. the isophotes of the central galaxy in fossil groups are found to be non-boxy in contrast to the isophotes of BCGs which are predominantly boxy (Khosroshahi.Ponman&Jones 2006)..," However, despite apparent similarities, the isophotes of the central galaxy in fossil groups are found to be non-boxy in contrast to the isophotes of BCGs which are predominantly boxy \citep{kpj06}. ." +of barvons (for details. see D).,"of baryons (for details, see )." + Note. however. that. as we show inL. the statistical ancl systematic uncertainties inf(a.) are subdominant in the analysis.," Note, however, that, as we show in, the statistical and systematic uncertainties in$f(\sigma,z)$ are subdominant in the analysis." + We have verified that 2 is essentially uncorrelated with ., We have verified that $\varepsilon$ is essentially uncorrelated with $\gamma$. + To compare the NLP data with the theoretical predictions of the mass function. we need to relate mass. M. to our observables: the M-rav luminosity. £. and average temperature. 2. of the clusters.," To compare the XLF data with the theoretical predictions of the mass function, we need to relate mass, $M$, to our observables: the X-ray luminosity, $L$, and average temperature, $T$, of the clusters." + In.LL. we describe the follow-up. X-ray. observations used. to determine these relations.," In, we describe the follow-up X-ray observations used to determine these relations." + As discussed inL. we simultaneously: and seli-consistentIv constrain both cosmological (sce Section 2)) and scaling relation parameters.," As discussed in, we simultaneously and self-consistently constrain both cosmological (see Section \ref{sec:cosmo}) ) and scaling relation parameters." +" Following the notation ofLb. we model the evolution of the Iuminositv-mass scaling relation as with a log-normal. and possibly evolving. intrinsic scatter of the luminosity at à given mass lere. 6=logsπου).l/10 ergs|] and mo=log,ECο1017AZ. ]. where the subseript 500 refers to quantities measured within radius roo. at which the mean. enclosed. density is 500 timesthe critical density of the Universe at. redshift 2."," Following the notation of, we model the evolution of the luminosity-mass scaling relation as with a log-normal, and possibly evolving, intrinsic scatter of the luminosity at a given mass Here, $\ell +\equiv\logTen[L_{500}E(z)^{-1}/10^{44}\erg\second^{-1}]$ and $m\equiv\logTen[E(z)M_{500}/10^{15}\Msun]$ , where the subscript $500$ refers to quantities measured within radius $r_{500}$, at which the mean, enclosed density is 500 timesthe critical density of the Universe at redshift $z$." + Phe factors of (2) are required to account lor the background: evolution. of the critical density., The factors of $E(z)$ are required to account for the background evolution of the critical density. +" Fixing 257=0. one has sel(-similar"" evolution of the scaling relation(?2).. determined. entirely by. the ££(z) factors."," Fixing $\beta_2^{\ell m}=0$, one has “self-similar” evolution of the scaling relation, determined entirely by the $E(z)$ factors." +"⋅ FixingVs σι,'= 0. one has constant scatter."," Fixing $\sigma_{\ell m}'=0$ , one has constant scatter." + In.LL. we show that departures from self-similar evolution and evolution in σεν) are not required by current data.," In, we show that departures from self-similar evolution and evolution in $\sigma_{\ell m}(z)$ are not required by current data." +" In this paper we present results both Lor pure selt- and constant scatter 3Hr=0. σι,∕= 0). and also allowing for additional evolution in the luninosity-mass relation and its scatter. through 1""; and σ;ian "," In this paper we present results both for pure self-similarity and constant scatter $\beta_2^{\ell m}=0$, $\sigma_{\ell m}'=0$ ), and also allowing for additional evolution in the luminosity-mass relation and its scatter, through $\beta_2^{\ell m}$ and $\sigma_{\ell m}'$." +As we shall show. our improved analysis method (of 1) and the inclusion. of high quality follow-up. data for a significant fraction of clusters allows us to address even general questions of this tvpe.," As we shall show, our improved analysis method (of ) and the inclusion of high quality follow-up data for a significant fraction of clusters allows us to address even general questions of this type." + We emphasize that for such analysis it is essential tosmeullancousti; model the mass function. scaling relations. growth history and the impact of systematic uncertainties fully. else spurious constraints mav be obtained.," We emphasize that for such analysis it is essential to model the mass function, scaling relations, growth history and the impact of systematic uncertainties fully, else spurious constraints may be obtained." + The data ancl analysis of and. LL also include measured temperatures. ο simultaneously constrain the tempoerature-mass relation., The data and analysis of and II also include measured temperatures to simultaneously constrain the temperature-mass relation. +" In.Lk. we show that a simple power law where -ο(E500/keV). without additional evolution parameters. such as PIE73"" and o5, (which are defined equivalently to the corresponding parameters in the luminositv-mass⋠⋠ relation.⋠ 5""∕ and ∕ σεν). is. sullicientD. to describe the data."," In, we show that a simple power law where $t\equiv \logTen\left(\mysub{kT}{500}/\keV\right)$, without additional evolution parameters, such as $\beta_2^{tm}$ and $\sigma_{tm}'$ (which are defined equivalently to the corresponding parameters in the luminosity-mass relation, $\beta_2^{\ell m}$ and $\sigma_{\ell m}'$ ), is sufficient to describe the data." +" Note also that. for clusters with 3keV. such as those used. here. the Εικ within the 0.124keV band is nearly independent of the temperature. and therefore⋅ 35""∕nn and. oj, are essentially. uncorrelated with. Thus. we do not further consider these parameters. and assume that the temperature-mass relation evolves similarly. with a constant log-normalscatter’."," Note also that, for clusters with $kT>3\keV$ , such as those used here, the flux within the $0.1-2.4\keV{}$ band is nearly independent of the temperature, and therefore $\beta_2^{tm}$ and $\sigma_{tm}'$ are essentially uncorrelated with $\gamma$ Thus, we do not further consider these parameters, and assume that the temperature-mass relation evolves self-similarly, with a constant log-normal." + Our analysis also accounts for the small. but non-negligible additional constraining power on > that is available from measurements from the ISW. etfect.," Our analysis also accounts for the small, but non-negligible additional constraining power on $\gamma$ that is available from measurements from the ISW effect." + The low multipoles of the CAIB are sensitive to the growth of structure through this cHeet., The low multipoles of the CMB are sensitive to the growth of structure through this effect. + Phe time-varving gravitational potentials of large scale structures contribute a net elfect on the energy of the photons crossing them., The time-varying gravitational potentials of large scale structures contribute a net effect on the energy of the photons crossing them. + For these photons. we calculate their contribution to the temperature anisotropy power spectrum as where / is the conformal time. 7 the optical depth to reionization. ζω) the spherical Bessel function. for the multipole /. and ó' the conformal time variation of the gravitational potential.," For these photons, we calculate their contribution to the temperature anisotropy power spectrum as where $t$ is the conformal time, $\tau$ the optical depth to reionization, $j_{l}(x)$ the spherical Bessel function for the multipole $l$, and $\phi'$ the conformal time variation of the gravitational potential." + The latter can be caleulated in terms o5 using the Poisson equation. (πό= ἀπέαOpis. as (2)) where # is the conformal Llubble parameter.," The latter can be calculated in terms of $\gamma$ using the Poisson equation, $k^2\phi=-4 \pi G +a^2\,\delta\rho_{\rm m}$, as ) where $\mathcal{H}$ is the conformal Hubble parameter." + Since we are performing a consistency test of GR. we assume that. as in GR. the contributions of the anisotropic stress and energy μις are negligible(7).," Since we are performing a consistency test of GR, we assume that, as in GR, the contributions of the anisotropic stress and energy flux are negligible." +.. As an initial condition. at 2= we match the ABNUK) to that of Gh. using Equation 19 to evolve the model to z=0.," As an initial condition, at $z=2$ we match the $\Delta_{l}^{\rm ISW}(k)$ to that of GR, using Equation \ref{eq:isw} + to evolve the model to $z=0$." + Unless stated. for results including CAIB data. we include the constraints on ~ available from the LISW οσοι.," Unless stated, for results including CMB data, we include the constraints on $\gamma$ available from the ISW effect." +" ‘To constrain the cosmic growth rate we use three wicle-area cluster samples drawn from the all-sky survey: BCS (2€«0.3: northern skv: £X(0.12dkeV)jo£7?Crestom 7). REPLEX ἐς< 0.3: southern sky: fx> 7). and Bright MACS(0.3<2 0.5: ~55 per cent skvcoverage: £x72101?oreslem >),"," To constrain the cosmic growth rate we use three wide-area cluster samples drawn from the all-sky survey: BCS $z<0.3$; northern sky; $F_{\rm X}(0.1-2.4\keV{})>4.4\times 10^{-12} \erg \second^{-1} +\cm^{-2}$ ), REFLEX $z<0.3$ ; southern sky; $F_{\rm X}>3.0\times +10^{-12} \erg\second^{-1} \cm^{-2}$ ), and Bright MACS$0.32\times 10^{-12} \erg +\second^{-1} \cm^{-2}$ )." + In order to keep systematic uncertainties to a minimum. for all three surveys. we impose à lower Luminosity cut of 2.50HALTergs (0.1.2.4 keV).," In order to keep systematic uncertainties to a minimum, for all three surveys, we impose a lower luminosity cut of $2.5\E{44} h_{70}^{-2}\erg\second^{-1}$ $0.1-2.4\keV{}$ )." + For the BCS. this gives a total of 78 clusters: for REFLEX. 126 clusters: ancl for Bright ALACS. 34 clusters.," For the BCS, this gives a total of 78 clusters; for REFLEX, 126 clusters; and for Bright MACS, 34 clusters." + In total we have 238 clusters., In total we have 238 clusters. +Fiber collision incompleteness is reduced by the SDSS tiling method. which overlaps the spectroscopic plates to achieve continuous sky coverage.,"Fiber collision incompleteness is reduced by the SDSS tiling method, which overlaps the spectroscopic plates to achieve continuous sky coverage." + However. this still results in ~7% of tarected galaxies without measured redshifts.," However, this still results in $\sim 7 \%$ of targeted galaxies without measured redshifts." + Naturally. this incompleteness affects galaxy clustering nmieasuremients most severely at very small scales.," Naturally, this incompleteness affects galaxy clustering measurements most severely at very small scales." + To get around this problem. MOG cross-correlated the spectroscopic LRG. sample with the cutive sample of LRG targets in the SDSS imagine.," To get around this problem, M06 cross-correlated the spectroscopic LRG sample with the entire sample of LRG targets in the SDSS imaging." + For every LRG from the spectroscopic sample. nearbv LRG tarects Gvhether or not they have an observed spectrum) were considered to be at the same redshift as the spectroscopically observed LRG.," For every LRG from the spectroscopic sample, nearby LRG targets (whether or not they have an observed spectrum) were considered to be at the same redshift as the spectroscopically observed LRG." + This allowed MOG. to assien absolute magnitudes to the LRG tarects aud thus decide if they made it into the volume-limited siuuple., This allowed M06 to assign absolute magnitudes to the LRG targets and thus decide if they made it into the volume-limited sample. + MOG then statistically removed the contribution of galaxies that were not at the same redshift. but were considered to be by the algorithm. by coustructing randoni samples with the same redshift distribution as the spectroscopic sample. auc cross-correlating them with the LRG imaging sample.," M06 then statistically removed the contribution of galaxies that were not at the same redshift, but were considered to be by the algorithm, by constructing random samples with the same redshift distribution as the spectroscopic sample, and cross-correlating them with the LRG imaging sample." + AL06 tested this procedure onu niock galaxy catalogs aud found that it successfully recovers the LRG auto-correlation function., M06 tested this procedure on mock galaxy catalogs and found that it successfully recovers the LRG auto-correlation function. + The SDSS photometry of LRC galaxies is biased in cases where pais of LRGs are separated by tens of spe or less., The SDSS photometry of LRG galaxies is biased in cases where pairs of LRGs are separated by tens of kpc or less. + These galaxies have a regiou of overlap. and the light contained in this region ueeds to be xopoerlv distributed between the LRG pair.," These galaxies have a region of overlap, and the light contained in this region needs to be properly distributed between the LRG pair." + This process is called deblending., This process is called deblending. +" Since the LRC sample is defined by uninosty cuts (23.210ergss7!.," The lifetime of the persistent mass transfer (MT) at the Eddington level $\sim 4\times 10^{39}\ {\rm ergs\ s^{-1}}$ ) from a WD to such a BH, once started, is $\tau_{\rm X}\approx 2\times 10^5$ yr and is about 3 times longer for ULX luminosities $L_{X}\ga 10^{39}\ {\rm ergs\ s^{-1}}$." + If all but one BH ts evaporated. the formation rate of BH-WD binaries must be extremely high — up to one X-ray binary formation per BH per Gyr.," If all but one BH is evaporated, the formation rate of BH-WD binaries must be extremely high – up to one X-ray binary formation per BH per Gyr." + The minimum required formation rate. when a good fraction of BHs is retained which also do not form a BH subcluster. is about 4«107 per BH per Gyr (and more likely 1077 per BH per Gyr. if many clusters are metal-rich and have lower escape velocity than 50 km/s).," The minimum required formation rate, when a good fraction of BHs is retained which also do not form a BH subcluster, is about $4\times 10^{-3}$ per BH per Gyr (and more likely $10^{-2}$ per BH per Gyr, if many clusters are metal-rich and have lower escape velocity than 50 km/s)." + We therefore explore which dynamical formation channel would be able to provide the formation of BH-WD X-ray binaries at rates of 4«107 to 1 per BH per Gyr in an average dense massive cluster., We therefore explore which dynamical formation channel would be able to provide the formation of BH-WD X-ray binaries at rates of $4\times 10^{-3}$ to 1 per BH per Gyr in an average dense massive cluster. +" We can also define this as 4«107/fana, per BH per Gyr. where fguo=O.Lfgnaa is the fraction of BHs that is retained in the cluster and not detached in the BH subcluster. and is normalized to of all initially formed massive BHs (210M ..)."," We can also define this as $4\times 10^{-3}/f_{\rm BH,0.1}$ per BH per Gyr, where $f_{\rm BH,0.1}=0.1 f_{\rm BH,tot}$ is the fraction of BHs that is retained in the cluster and not detached in the BH subcluster, and is normalized to of all initially formed massive BHs $\ga 10 M_\odot$ )." + A smaller rate is possible only if essentially all globular clusters have experienced significant tidal stripping and the number of remaining BHs per present stellar mass unit Is significantly higher than | BH per 150 M..., A smaller rate is possible only if essentially all globular clusters have experienced significant tidal stripping and the number of remaining BHs per present stellar mass unit is significantly higher than 1 BH per 150 $M_\odot$. + To analyze the dynamical formation. we will proceed in reverse order: first. we will consider which BH-WD binaries. once formed. can become X-ray binaries. and then we will consider at what rates these BH-WD binaries can be formed via different dynamical channels.," To analyze the dynamical formation, we will proceed in reverse order: first, we will consider which BH-WD binaries, once formed, can become X-ray binaries, and then we will consider at what rates these BH-WD binaries can be formed via different dynamical channels." + In a dense stellar system. once a BH-WD binary is formed through a dynamical encounter. its further binary evolution could be affected by subsequent encounters with other stars.," In a dense stellar system, once a BH-WD binary is formed through a dynamical encounter, its further binary evolution could be affected by subsequent encounters with other stars." + The cross section for an encounter between two objects of total mass zn with a distance of closest approach less than Άμαν IS computed as where the second term accounts for gravitational focusing. with =(οrg and v4. the relative velocity at infinity.," The cross section for an encounter between two objects of total mass $m_{\rm tot}$ with a distance of closest approach less than $r_{\rm max}$ is computed as where the second term accounts for gravitational focusing, with $v_{\rm p}^2=2Gm_{\rm tot}/r_{\rm max}$ and $v_\infty$ the relative velocity at infinity." +" For strong"" interactions. ‘ya, is usually on the order of the binary semimajor axis: ra,=Ka. where & is of order unity (2).."," For strong interactions, $r_{\rm max}$ is usually on the order of the binary semimajor axis: $r_{\rm max}=k a$, where $k$ is of order unity \citep{hutbah83}." +" In the limit of strong gravitational focusing. ""»a and In our case. the first object is the BH-WD binary of mass MBHWD=tgpwp while the second object is a core star of mass 7..."," In the limit of strong gravitational focusing, $v_{\rm p}^2 \gg +v_{\infty}^2$ and In our case, the first object is the BH-WD binary of mass $m_{\rm BHWD}=m_{\rm BH}+m_{\rm WD}$ while the second object is a core star of mass $m_\star$." +" In globular clusters. the close approaches that we are interested 1n have >vL. and the BH mass is significantly more massive than""s both its WD companion and a typical core star."," In globular clusters, the close approaches that we are interested in have $v_{\rm p}^2 \gg v_{\infty}^2$, and the BH mass is significantly more massive than both its WD companion and a typical core star." + Thus. the rate at which à BH-WD binary undergoes a strong (binary-single) encounter is The final equal sign in equation (3)) defines the dimensionless parameter K.," Thus, the rate at which a BH-WD binary undergoes a strong (binary-single) encounter is The final equal sign in equation \ref{binsin}) ) defines the dimensionless parameter $K$." + The time-scale for a BH-WD binary to experience a strong encounter can be calculated as Tgs=1/Tys10.6K!R../et Gyr: see Figure |..," The time-scale for a BH-WD binary to experience a strong encounter can be calculated as $\tau_{\rm BS} = 1 / \Gamma_{\rm BS} = +10.6\,K^{-1} R_\odot/a$ Gyr: see Figure \ref{tau}." + Throughout this paper. we consider clusters with core number densities 71. near 10° pe. velocity dispersions of ~10 km s7!. and black hole masses of ~15M.: consequently. K is of order unity.," Throughout this paper, we consider clusters with core number densities $n_c$ near $10^5$ $^{-3}$, velocity dispersions of $\sim 10$ km $^{-1}$, and black hole masses of $\sim15M_\odot$: consequently, $K$ is of order unity." + Once formed. the orbit of a BH-WD binary starts to shrink due to gravitational radiation.," Once formed, the orbit of a BH-WD binary starts to shrink due to gravitational radiation." + The time των for the orbit to decay enough for mass transfer to commence depends on the initial post-encounter binary separation à and eccentricity e., The time $\tau_{\rm gw}$ for the orbit to decay enough for mass transfer to commence depends on the initial post-encounter binary separation $a$ and eccentricity $e$. + Applying ?. equations. we can find the maximum semimajor axis a. as a function of post-encounter eccentricity ο. for which à system will start MT within any specified time. e.g.. | Gyr and 10 Gyr (see the dotted curves in Fig.1)).," Applying \cite{peters64} equations, we can find the maximum semimajor axis $a$ , as a function of post-encounter eccentricity $e$, for which a system will start MT within any specified time, e.g., 1 Gyr and 10 Gyr (see the dotted curves in \ref{tau}) )." + In Figure l.. we also show the semimajor axis e(e) such that gs=Ce). assuming A=1.," In Figure \ref{tau}, we also show the semimajor axis $a_{\rm sep}(e)$ such that $\tau_{\rm BS} = \tau_{\rm gw}(e)$, assuming $K=1$." + BH-WD binaries with encounter 74semimajor axes a(e)eje) will have one or more strong encounters before they shrink to the point of merger due to gravitational waves radiation., BH-WD binaries with post-encounter semimajor axes $a(e)>a_{\rm sep}(e)$ will have one or more strong encounters before they shrink to the point of merger due to gravitational waves radiation. + In the next subsection. we consider the possible outcomes of such encounters.," In the next subsection, we consider the possible outcomes of such encounters." + Here we consider the outcomes and their frequencies for encounters between a BH-WD and a single star., Here we consider the outcomes and their frequencies for encounters between a BH-WD and a single star. + An encounter between a soft binary and a third star can leadto ionization if, An encounter between a soft binary and a third star can leadto ionization if +Until recently. (he vast majority of our knowledge regarding exoplanets has come from raclial-velocity studies.,"Until recently, the vast majority of our knowledge regarding exoplanets has come from radial-velocity studies." + Now with ground and space-based dedicated: instruments. transit studies are discovering and characterizing (he atmospheres of hot. jupiters/neptunes al a rapid pace.," Now with ground and space-based dedicated instruments, transit studies are discovering and characterizing the atmospheres of hot jupiters/neptunes at a rapid pace." + The frontier for exoplanet studies is the direct detection aud characterization of exoplanets. using high-contrast imagers/spectrographs.," The frontier for exoplanet studies is the direct detection and characterization of exoplanets, using high-contrast imagers/spectrographs." + The emphasis in the direct detection field. (hus far. has been on the discovery of planets.," The emphasis in the direct detection field, thus far, has been on the discovery of planets." + Now with a host of directlv-detected planetary mass objects and candidates. we can proceed wilh mulü-wavelength characterizations of their atinospheres. (he primary purpose of which. at least initially. is to determine the relationships between (heir masses. ages. radii. and spectra.," Now with a host of directly-detected planetary mass objects and candidates, we can proceed with multi-wavelength characterizations of their atmospheres, the primary purpose of which, at least initially, is to determine the relationships between their masses, ages, radii, and spectra." +" In this paper we concentrate on one object. 2AIASS 1207 b. the first clireetly detected. planetary-mass companion. which was found by ? 0.78"" [rom the brown cwarl 2MASSWJ 1207334-393254 (hereafter 2\IASS 1207 A)."," In this paper we concentrate on one object, 2MASS 1207 b, the first directly detected, planetary-mass companion, which was found by \citet{2004AA...425L..29C} 0.78"" from the brown dwarf 2MASSWJ 1207334-393254 (hereafter 2MASS 1207 A)." + 2MAÀSS 1207 A and ils companion. 2\IASS 1207 b. were verified to be co-moving bv ? and ?..," 2MASS 1207 A and its companion, 2MASS 1207 b, were verified to be co-moving by \citet{2005AA...438L..25C} and \citet{2006ApJ...652..724S}." + Since 2MASS 1207 A is known to be a member of the voung TW Ilva group (2).. ?. assign 2MASS 1207 A and b an age of 844 Myr.," Since 2MASS 1207 A is known to be a member of the young TW Hya group \citep{2002ApJ...575..484G}, \citet{2004AA...425L..29C} assign 2MASS 1207 A and b an age of $8\pm^{4}_{3}$ Myr." + Based on their measured. JIIINSL/ fluxes. ?.. estimate 2MASS 1207 b's mass to be 5x2 αμ with an effective temperature of 12504200 Ix. assuming a distance of 10 pe.," Based on their measured JHKsL' fluxes, \citet{2004AA...425L..29C}, estimate 2MASS 1207 b's mass to be $\pm$ 2 $M_{\rm jup}$ with an effective temperature of $\pm$ 200 K, assuming a distance of 70 pc." + Several groups have relined the clistance of 2AIASS 1207 with the moving cluster method (?7) and with (rigonometric parallax measurements (???)..," Several groups have refined the distance of 2MASS 1207 with the moving cluster method \citep{2005ApJ...634.1385M,2007ApJ...668L.175M} and with trigonometric parallax measurements \citep{2007ApJ...669L..41B,2007ApJ...669L..45G,2008AA...477L...1D}." + For (he remainder of this paper. we adopt the weighted average of the parallax measurements (52.841.0 pc) as the distance," For the remainder of this paper, we adopt the weighted average of the parallax measurements $\pm$ 1.0 pc) as the distance" +cascade develops.,cascade develops. + In these models multi-TeV emisstor can be easily produced. but the observed short variability timescale places extreme constraints on the magnetic. fielc strength. because the proton gyroradius has to be much smaller than the system itself. and on the Doppler factor. because the intrinsic timescale for switching off the cascade ts linkec to the observed soft photon flux via the energy loss rate for photomeson production.," In these models multi-TeV emission can be easily produced, but the observed short variability timescale places extreme constraints on the magnetic field strength, because the proton gyroradius has to be much smaller than the system itself, and on the Doppler factor, because the intrinsic timescale for switching off the cascade is linked to the observed soft photon flux via the energy loss rate for photomeson production." + For the most rapid outburst of Mrk 421 (Gaidos et al. 1996)), For the most rapid outburst of Mrk 421 (Gaidos et al. \cite{gai96}) ) + this leads to B710CG anc D100., this leads to $B\gg 10\ {\rm G}$ and $D\gg 100$. + Another class of models features hadronic collisions of a collimated proton jet with BLR clouds entering the jet (e.g. Dar Laor 1997:; Beall Bednarek 1999))., Another class of models features hadronic collisions of a collimated proton jet with BLR clouds entering the jet (e.g. Dar Laor \cite{dl97}; Beall Bednarek \cite{bb99}) ). + These models have two theoretical difficulties: the proton beam is weak compared with the background plasma and therefore quickly stopped by a two-stream instability., These models have two theoretical difficulties: the proton beam is weak compared with the background plasma and therefore quickly stopped by a two-stream instability. + Also the BLR clouds are usually optically thick and thus the efficiency of the system is drastically reduced., Also the BLR clouds are usually optically thick and thus the efficiency of the system is drastically reduced. + In this paper we consider a strong electron-proton beam that sweeps up ambient matter and thus becomes energized., In this paper we consider a strong electron-proton beam that sweeps up ambient matter and thus becomes energized. + The basic scenario is similar to the blast wave model for 7-ray bursts (GRBs) which successfuly explains the time dependence of the X-ray. optical and radio afterglows (e.g. Wijers et al. 1997..," The basic scenario is similar to the blast wave model for $\gamma $ -ray bursts (GRBs) which successfuly explains the time dependence of the X-ray, optical and radio afterglows (e.g. Wijers et al. \cite{wmr97}," + Vietri. 19973... Waxman 1997a)).," Vietri \cite{vie97a}, , Waxman \cite{wax97a}) )." + There the apparent release of ~1077Es» erg of energy in a small volume leads to the formation of a relativistically expanding pair fireball that transforms most of the explosion energy into Kinetic energy of baryons in a relativistic blast wave., There the apparent release of $\simeq 10^{52}E_{52}$ erg of energy in a small volume leads to the formation of a relativistically expanding pair fireball that transforms most of the explosion energy into kinetic energy of baryons in a relativistic blast wave. + We assume that a similar generation process also powers the relativistic outflows in active galactic nuclei (AGN). but that the outflow is not spherically symmetric and highly channelled along magnetic flux tubes into a small fraction of the full solid angle due to the structure of the medium surrounding the potnt of energy release.," We assume that a similar generation process also powers the relativistic outflows in active galactic nuclei (AGN), but that the outflow is not spherically symmetric and highly channelled along magnetic flux tubes into a small fraction of the full solid angle due to the structure of the medium surrounding the point of energy release." + We shall address the important issue how the kinetic energy of such channelled relativistic blast waves is converted into radiation., We shall address the important issue how the kinetic energy of such channelled relativistic blast waves is converted into radiation. + Existing radiation modelling of GRBs and AGNs (see e.g. Vietri 1997b:;: Waxman 1997b:; Bótttcher Dermer 1998)) are very unspecific on this crucial point., Existing radiation modelling of GRBs and AGNs (see e.g. Vietri \cite{vie97b}; Waxman \cite{wax97b}; Bötttcher Dermer \cite{bd98}) ) are very unspecific on this crucial point. + Typically it is assumed that a fraction & of the energy in nonthermal baryons in the blast wave region at position .r is transformed into a power-law distribution of ultrarelativistic cosmic ray protons with Lorentz factors Por)<τοuas In the fluid frame comoving with a small element of the blast wave region that travels with the bulk Lorentz factor Por}=PoCe/ary)? after the deceleration radius ry=2.6+101CESs/injP$ay)t? em through the surrounding medium of density #7).," Typically it is assumed that a fraction $\xi $ of the energy in nonthermal baryons in the blast wave region at position $x$ is transformed into a power-law distribution of ultrarelativistic cosmic ray protons with Lorentz factors $\Gamma (x)\le \gamma _{\rm CR}\le \gamma _{\rm max}$ in the fluid frame comoving with a small element of the blast wave region that travels with the bulk Lorentz factor $\Gamma (x)=\Gamma _0(x/x_0)^{-g}$ after the deceleration radius $x_0=2.6\cdot 10^{16}(E_{52}/n_0\Gamma _{0,300}^2)^{1/3}$ cm through the surrounding medium of density $n_0$." + For electrons it is argued (Katz Piran 1997.. Panaitescu Mésszárros 1998)) that their minimum Lorentz factor is vcauiuGny/m)E since they are in energy equilibrium with the protons.," For electrons it is argued (Katz Piran \cite{kp97}, Panaitescu Mésszárros \cite{pm98}) ) that their minimum Lorentz factor is $\gamma _{\rm e,min}=(m_{\rm p}/m_{\rm e})\Gamma $ since they are in energy equilibrium with the protons." + Here we investigate this transfer mechanism from the channelled blast wave to relativistic protons and electrons in more detail., Here we investigate this transfer mechanism from the channelled blast wave to relativistic protons and electrons in more detail. + In Sect., In Sect. +" 2 we consider the penetration of a blast wave consisting of cold protons and electrons with density #7), with the surrounding “interstellar” medium consisting also of cold protons and electrons on the basis of a two-stream instability."," 2 we consider the penetration of a blast wave consisting of cold protons and electrons with density $n_{\rm b}$ with the surrounding ""interstellar"" medium consisting also of cold protons and electrons on the basis of a two-stream instability." + Viewed from the coordinate system comoving with the blast wave. the interstellar protons and electrons represent a proton-electron beam propagating with the relativistic speed V(0)e(lD20r))*? antiparallel to the .c-axis.," Viewed from the coordinate system comoving with the blast wave, the interstellar protons and electrons represent a proton-electron beam propagating with the relativistic speed $V(x)=-c(1-\Gamma ^{-2}(x))^{1/2}$ antiparallel to the $x$ -axis." + We examine the stability of this beam assumingπα that the background magnetic field is uniform and directed along the x-axis., We examine the stability of this beam assuming that the background magnetic field is uniform and directed along the x-axis. + We demonstrate that very quickly the beam excites low-frequency magnetohydrodynamic plasma waves. mainly Alfvénn-ion-cyclotron and Alfvénn-Whistler waves.," We demonstrate that very quickly the beam excites low-frequency magnetohydrodynamic plasma waves, mainly Alfvénn-ion-cyclotron and Alfvénn-Whistler waves." + These plasma waves quasi-linearly isotropise the ΠΠΟΟΠΊΗΠα» interstellar protons and electrons in the blast wave plasma., These plasma waves quasi-linearly isotropise the incoming interstellar protons and electrons in the blast wave plasma. + In Sect., In Sect. + 3 we investigate the interaction. processes of these isotropised protons and electrons (hereafter referred to as primary protons and electrons). which have the relativistic Lorentz factor L'(.c). with the blast wave protons and electrons.," 3 we investigate the interaction processes of these isotropised protons and electrons (hereafter referred to as primary protons and electrons), which have the relativistic Lorentz factor $\Gamma (x)$, with the blast wave protons and electrons." + Since the primary protons carry much more mome!tum than the primary electrons. inelastic collisions betweer primary protons and the blast wave protons generate neutral and charged pions which decay into gamma rays. secondary electrons. positrons and neutrinos.," Since the primary protons carry much more momentum than the primary electrons, inelastic collisions between primary protons and the blast wave protons generate neutral and charged pions which decay into gamma rays, secondary electrons, positrons and neutrinos." + Both. the radiation products from these interactions. and the resulting cooling of the primary particles in the blast wave plasma. are calculated.," Both, the radiation products from these interactions, and the resulting cooling of the primary particles in the blast wave plasma, are calculated." + By transforming to the laboratory frame we calculate the time evolution of the emitted multiwavelength spectrun for an outside observer under different viewing angles., By transforming to the laboratory frame we calculate the time evolution of the emitted multiwavelength spectrum for an outside observer under different viewing angles. + Momentum conservation leads to a deceleration of the blast wave that ts taken into account self-consistently., Momentum conservation leads to a deceleration of the blast wave that is taken into account self-consistently. + Since we do not consider any re-acceleratior of particles in the blast wave. the evolution of particles and the blast wave is conpletely determined by the initial conditions.," Since we do not consider any re-acceleration of particles in the blast wave, the evolution of particles and the blast wave is completely determined by the initial conditions." + As sketched in Fig., As sketched in Fig. +" | we consider in the laboratory frame (all physical quantities inthis system are indexed with x) the cold blast wave electron-proton plasma of density »//, and thickness εἰ Π we-direetion running into the cold interstellar medium of density Πρ. consisting also of electrons and protons. parallel to the uniform magnetic field of strength 5."," 1 we consider in the laboratory frame (all physical quantities inthis system are indexed with $*$ ) the cold blast wave electron-proton plasma of density $n^*_{\rm b}$ and thickness $d^*$ in $x$ -direction running into the cold interstellar medium of density $n^*_0$, consisting also of electrons and protons, parallel to the uniform magnetic field of strength $B$." + In the comoving frame the total phase space distribution function of the plasma in theblast wave region at the start thus is where The Lorentz transformations (e.g. Hagedorn 1963.. p.41) to the blast wave rest frame with momentum and energy variables (pp.ppE) are," In the comoving frame the total phase space distribution function of the plasma in theblast wave region at the start thus is where The Lorentz transformations (e.g. Hagedorn \cite{hag73}, , p.41) to the blast wave rest frame with momentum and energy variables $(p_{\perp }, p_{\parallel }, +E)$ are" +(1994) but less steep Chan Chat found by them for early-(vpe galaxies.,(1994) but less steep than that found by them for early-type galaxies. + Llowever. thev found a weak dependence of the slope on the satellite luminosity. with fainter galaxies having a flatter slope.," However, they found a weak dependence of the slope on the satellite luminosity, with fainter galaxies having a flatter slope." + Extrapolating their results to the magnitude Imits reached in this study. (here is good agreement wilh the value presented here.," Extrapolating their results to the magnitude limits reached in this study, there is good agreement with the value presented here." + They did not find such a luminosity dependence of the slope lor late-twpe galaxies., They did not find such a luminosity dependence of the slope for late-type galaxies. + There are. in total. an average of 45+15 dwarls within 500 kpe of each primary down to the limiting magnitude of 14.6 and 1946 with —1606-07 i," A study of the local environment around them shows an excess of faint galaxies, presumably satellites, out to a projected distance of at least 500 kpc and with a projected density varying as $r^{-0.6\pm 0.2}$." +"""The numbers of these cdwarls suggests a steep faint end of the luminosity function. in contradiction to that founcl for the field but in good agreement with that found lor the outer regions of clusters."," The numbers of these dwarfs suggests a steep faint end of the luminosity function, in contradiction to that found for the field but in good agreement with that found for the outer regions of clusters." + A considerable number of questions remain which can only be answered (through a more detailed study of theseobjects and their environment., A considerable number of questions remain which can only be answered through a more detailed study of theseobjects and their environment. +voung stars before the circumstellar disk associated wilh star formation is clissipated.,young stars before the circumstellar disk associated with star formation is dissipated. + Currently. (he most favored model is (he accretion/clilfision model but new observational data has raised «questions about it.," Currently, the most favored model is the accretion/diffusion model but new observational data has raised questions about it." + Leiteretal.(2002). have shown that the composition of sslars might not be as consistent wilh cireumstellar gas has thought previously., \citet{Heiteretal02} have shown that the composition of stars might not be as consistent with circumstellar gas has thought previously. + They. have also raised (he question as to why some stars which have circumstellar disks with ongoing accretion and are similar to sstars do not have peculiar compositions., They have also raised the question as to why some stars which have circumstellar disks with ongoing accretion and are similar to stars do not have peculiar compositions. + This paper concentrates on if ancl how new insight in (he depth of mixing in slowly rolating F and A type stars (Richeretal.2000:Richard2001) might alfect the accretion model.," This paper concentrates on if and how new insight in the depth of mixing in slowly rotating F and A type stars \citep{RMT00,RMR01} might affect the accretion model." + Those models. which will be discussed further in Section ??.. have shown that the mixing in slowly rotating stars extends substantially deeper than the base of the II-IIe convection zone in A and D stus.," Those models, which will be discussed further in Section \ref{sec:accdiff}, have shown that the mixing in slowly rotating stars extends substantially deeper than the base of the H-He convection zone in A and B stars." + The depth of mixing is of crucial importance in determining the timescales for the formation and persistence of superficial abundance peculiarities in stars such as theBootis., The depth of mixing is of crucial importance in determining the timescales for the formation and persistence of superficial abundance peculiarities in stars such as the. +. Therelore. as a first step in the computation of more complete models for sslars including as much of the physics of chemical evolution in stars as possible. the possible effect of deep mixing on (imescales and accretion rates in models of accreting sstars will be cliscussed here.," Therefore, as a first step in the computation of more complete models for stars including as much of the physics of chemical evolution in stars as possible, the possible effect of deep mixing on timescales and accretion rates in models of accreting stars will be discussed here." + A brief overview of the aceretion/cdilfusion model in the context of deeper müxing will be presented first., A brief overview of the accretion/diffusion model in the context of deeper mixing will be presented first. + Simple models will then be used (o estimate timescales lor chemical evolution., Simple models will then be used to estimate timescales for chemical evolution. + The model which has met the most success in reproducing most observed properties of sslars is based on the idea of accretion of dust-depleted matter first suggested by (1990)., The model which has met the most success in reproducing most observed properties of stars is based on the idea of accretion of dust-depleted matter first suggested by \citet{VL90}. +.. A model featuring accretion and diffusion was developed by (hereafter C91) and a full numerical simulation in 1 and 2-D in a static moclel was perlormed by TurcotteandCharbonneau(1993) (hereafter TC93)., A model featuring accretion and diffusion was developed by \citet{C91} (hereafter C91) and a full numerical simulation in 1 and 2-D in a static model was performed by \citet{TC93} (hereafter TC93). + αι (his scenario. circumstellar matter would be depleted of most heavy elements as the result of cust formation.," In this scenario, circumstellar matter would be depleted of most heavy elements as the result of dust formation." + The gas would therealter fall back on the star whereas the dust. would be pushed out. presumably by radiation pressure.," The gas would thereafter fall back on the star whereas the dust would be pushed out, presumably by radiation pressure." + While there exists no complete model of the accretion process itself including (he dust-gas separation needed by the accretion scenario.," While there exists no complete model of the accretion process itself including the dust-gas separation needed by the accretion scenario," +The catalogue of pulsars maintained by the (2?) was used to obtain the observed P?P values.,The catalogue of pulsars maintained by the \citep{mhth05} was used to obtain the observed $P-\dot{P}$ values. + Because the interpulses of milli-seconcd pulsars are not considered. in this paper. all pulsars with an estimated surface magnetic field strength below 101. Gauss or a period faster than the Crab were excluded.," Because the interpulses of milli-second pulsars are not considered in this paper, all pulsars with an estimated surface magnetic field strength below $10^{11}$ Gauss or a period faster than the Crab were excluded." + PSR 1505.1726. witha magnetic Πο strength of 5.4.1017 Gauss. is excluded from the interpulse statisties for consistency.," PSR J1808–1726, with a magnetic field strength of $5.4\times10^{10}$ Gauss, is excluded from the interpulse statistics for consistency." + The globular cluster pulsars have unreliable P values and are therefore also not considered., The globular cluster pulsars have unreliable $\dot{P}$ values and are therefore also not considered. + Finally. all the pulsars with Pz4 seconds were removed to exclude the catalogued soft eamnma-ray repeaters and the anomalous X-ray. pulsars.," Finally, all the pulsars with $P>4$ seconds were removed to exclude the catalogued soft gamma-ray repeaters and the anomalous X-ray pulsars." + The first step is to draw random 2—P pairs Lrom the total population of observed: pulsars as described. in Sect 4.1., The first step is to draw random $P-\dot{P}$ pairs from the total population of observed pulsars as described in Sect 4.1. + Secondly. random values are generated for à and 3.," Secondly, random values are generated for $\alpha$ and $\beta$." + The magnetic pole and the line of sight are taken to be a random points on a sphere., The magnetic pole and the line of sight are taken to be a random points on a sphere. + This implies that the distribution of à and €=a|J are sinusoidal., This implies that the distribution of $\alpha$ and $\zeta=\alpha+\beta$ are sinusoidal. + Phe magnetic axis is allowed to align on a timescale Taina (7)) where ay is the random à. value at birth and / is the age of the pulsar. which is taken to be the characteristic age.," The magnetic axis is allowed to align on a timescale $\tau_\mathrm{align}$ \citealt{jon76}) ) where $\alpha_0$ is the random $\alpha$ value at birth and $t$ is the age of the pulsar, which is taken to be the characteristic age." + The final step is to determine if one or both beams of the pulsar intersect the line of sight given by the randomly generate geometry. which depends on the assumed. beam shape.," The final step is to determine if one or both beams of the pulsar intersect the line of sight given by the randomly generated geometry, which depends on the assumed beam shape." + As pointed out in the introduction. different shapes of the polar cap have been proposed.," As pointed out in the introduction, different shapes of the polar cap have been proposed." + Here we consider only the shape of a polar cap which is bounded: by the last open magnetic dipole field lines in order to get a feeling for the effect. of non-circular beam shapes., Here we consider only the shape of a polar cap which is bounded by the last open magnetic dipole field lines in order to get a feeling for the effect of non-circular beam shapes. + Such a beam is compressed. in the plain containing the magnetic and the rotation axis anc is roughly elliptic., Such a beam is compressed in the plain containing the magnetic and the rotation axis and is roughly elliptic. + The axial ratio &(a) of the ellipse is given by (2)) where (0) follows from numerically solving The axial ratio £(0) varies from 1 (for an aligned beam) to ~0.62 (for an orthogonal beam)., The axial ratio $\cal{E}(\alpha)$ of the ellipse is given by \citealt{mck93}) ) where $\delta(\alpha)$ follows from numerically solving The axial ratio $\cal{E}(\alpha)$ varies from 1 (for an aligned beam) to $\sim0.62$ (for an orthogonal beam). + Circular beams can be assumed in the model by forcing €=1 for all a., Circular beams can be assumed in the model by forcing $\cal{E}=\mathrm{1}$ for all $\alpha$. + Apart [rom the beam shape. a beam size has also to be assumed.," Apart from the beam shape, a beam size has also to be assumed." + For the half opening angle of the beam we use the relation measured by ? is consistent with the relation reported by various other authors (e.g. 22223).," For the half opening angle of the beam we use the relation measured by \cite{gou94} + which is consistent with the relation reported by various other authors (e.g. \citealt{ran90,ran93,kwj+94,gks93}) )." + For non-circular beams. p of Eq.," For non-circular beams, $\rho$ of Eq." + 6 is taken to be the half opening angle in the longit ucinaldirection., \ref{Eqrho} is taken to be the half opening angle in the longitudinal direction. + “Phe conditions for the two pulsar. beams to intersect the line of sight are and fanclom values of a and 3 are generated. until at least one of these conditions are met., The conditions for the two pulsar beams to intersect the line of sight are and Random values of $\alpha$ and $\beta$ are generated until at least one of these conditions are met. + The width of the pulse profile can then be calculated with Eq., The width of the pulse profile can then be calculated with Eq. + 2 for circular beams., \ref{EqW} for circular beams. + As noted in section 2. the list of interpulses is iot complete for two reasons.," As noted in section 2, the list of interpulses is not complete for two reasons." + The first reason is that some interpulses might have been nmüssed because the llux in the interpulse is too weak to be detected., The first reason is that some interpulses might have been missed because the flux in the interpulse is too weak to be detected. + Extremely weak interpulses could indicate that the pulsar beam just. grazes the line of sight., Extremely weak interpulses could indicate that the pulsar beam just grazes the line of sight. + Because the observed. p eq. 6)), Because the observed $\rho$ (Eq. \ref{Eqrho}) ) + has been derived considering the pulse widths. beams which just eraze the line of sight are not counted as detections in the model (eqs.," has been derived considering the pulse widths, beams which just graze the line of sight are not counted as detections in the model (Eqs." + 7 and SJ)., \ref{condition1} and \ref{condition2}) ). + This means that extremely weak interpulses are not accounted for in the model. as well as possibly in the observations.," This means that extremely weak interpulses are not accounted for in the model, as well as possibly in the observations." + However. some of the observed interpulses will be wide beams of aligned rotators.," However, some of the observed interpulses will be wide beams of aligned rotators." + Fherefore the observed interpulse fraction should be considered as an upper limit., Therefore the observed interpulse fraction should be considered as an upper limit. + Let us start with considering the simplest model. ie. a random o. distribution without alignment (za=o) ane circular. beams (£(0)= 1).," Let us start with considering the simplest model, i.e. a random $\alpha$ distribution without alignment $\tau_\mathrm{align}=\infty$ ) and circular beams $\cal{E}(\alpha)=\mathrm{1}$ )." + In this scenario our mode predicts that of the pulsars should have an interpulse. a factor of at least two higher than the observed. fraction.," In this scenario our model predicts that of the pulsars should have an interpulse, a factor of at least two higher than the observed fraction." + This model also clearly fails to explain the observed. perioc distribution of the pulsars with interpulses as the dottec curve of Fig., This model also clearly fails to explain the observed period distribution of the pulsars with interpulses as the dotted curve of Fig. + 1. Dies below the observed. distribution., \ref{Fig_ip_period} lies below the observed distribution. + This means that there are more short. period. pulsars with interpulses then predicted., This means that there are more short period pulsars with interpulses then predicted. + Short period pulsars are expectec to have a larger probability to show an interpulse because their beams are wider (Eq. 6)).," Short period pulsars are expected to have a larger probability to show an interpulse because their beams are wider (Eq. \ref{Eqrho}) )," + which is the reason why the precictect distribution of pulsars with interpulses (clottec line) lies above the distribution of all pulsars (lowest thick curve)., which is the reason why the predicted distribution of pulsars with interpulses (dotted line) lies above the distribution of all pulsars (lowest thick curve). + Nevertheless this effect is not enough to explain the observed. period distribution of the pulsars with interpulses., Nevertheless this effect is not enough to explain the observed period distribution of the pulsars with interpulses. + The predicted. pulse width for this model is correlated. with PP very close to the what ds expected from Eq. 6..," The predicted pulse width for this model is correlated with $P^{-0.51}$, very close to the what is expected from Eq. \ref{Eqrho}." + This model therefore fails to explain the three observational properties outlined in section 4., This model therefore fails to explain the three observational properties outlined in section 4. + 1n order to make the model more accurately rellect the data it is necessary to produce. fewer pulsars with interpulses. which can be done by relaxing the condition that forces the beams to be circular.," In order to make the model more accurately reflect the data it is necessary to produce fewer pulsars with interpulses, which can be done by relaxing the condition that forces the beams to be circular." + Because the minor axis of non-circular beams is in the plane containing the magnetic and rotation axis. it is less likely that the beams of both magnetic poles intersect the line of sight.," Because the minor axis of non-circular beams is in the plane containing the magnetic and rotation axis, it is less likely that the beams of both magnetic poles intersect the line of sight." + This in contrast to elongated beams. which will increase the fraction of pulsars with interpulses and are therefore not considered urther here.," This in contrast to elongated beams, which will increase the fraction of pulsars with interpulses and are therefore not considered further here." + Indeed. when applying Eq. 4..," Indeed, when applying Eq. \ref{Eqepsilon}," + the predicted raction of interpulses is decreased to‘a., the predicted fraction of interpulses is decreased to. +.. This is still a jit too high. especially as the observed fraction is an upper imit.," This is still a bit too high, especially as the observed fraction is an upper limit." + Because the ellipticity of the beam is independent of Pit follows that the predicted. pulse period distribution of oulsars. with interpulses and the pulse width distribution are identical to the model with circular beams., Because the ellipticity of the beam is independent of $P$ it follows that the predicted pulse period distribution of pulsars with interpulses and the pulse width distribution are identical to the model with circular beams. + Therefore he model with non-circular beams also fils to explain the observations., Therefore the model with non-circular beams also fails to explain the observations. + We next consider the elfect of alignment of the pulsar um., We next consider the effect of alignment of the pulsar beam. + By setting Των=Y010! vears (assuming circular, By setting $\tau_\mathrm{align}=7\times10^7$ years (assuming circular +in the previous expression e=SP. uo—PSRL aud gy=sii?ilsin?e(lcos?jj].,"in the previous expression $v=S-P$ , $u=PS-RL$ and $g=\sin^2i[1-\sin^2\alpha(1+\cos^2\beta)]$." + Squaring eq. (15)), Squaring eq. \ref{disp}) ) + gives a fourth order polynomial equation iu 57 which can be solved analytically., gives a fourth order polynomial equation in $n^2$ which can be solved analytically. +" Clearly ouly two out of four solutions satisfy tle original dispersion relation aud represeut the refractive imdices for the two propagation modes in the magnetized plasma. Ni, a=1.2."," Clearly only two out of four solutions satisfy the original dispersion relation and represent the refractive indices for the two propagation modes in the magnetized plasma, $n_m$, $m=1 \, ,2$." + As noted by B80. the ouly practical way of finding the two mecanineful roots is to substitute them back iuto eq. (15))," As noted by B80, the only practical way of finding the two meaningful roots is to substitute them back into eq. \ref{disp}) )" + aud. check mmuerically the residual., and check numerically the residual. + This. however. turned out to be troublesome for some values of the paramctors. as we discuss later on.," This, however, turned out to be troublesome for some values of the parameters, as we discuss later on." + For ;/—0. a=0 or 7/2.) =7/2 or 32/2. the right haud side of eq. (15))," For $i=0$, $\alpha =0$ or $\pi/2$, $\beta=\pi/2$ or $3\pi/2$, the right hand side of eq. \ref{disp}) )" + vanishes and the dispersion relation reduces to a quadratic equation in a? which is them solved instead of the quartic., vanishes and the dispersion relation reduces to a quadratic equation in $n^2$ which is then solved instead of the quartic. +" Once the refractive indices are known. we can solve the wave equation for the two refracted modes ο...0. where £5, ave the cartesian components of E. obtaining the two ratios £5,,/E5,. aud E5,,/E,,.."," Once the refractive indices are known, we can solve the wave equation for the two refracted modes $\lambda_{ij}(n_m)E'_{m,j}=0$, where $E'_{m,j}$ are the cartesian components of ${\bf E}'_m$, obtaining the two ratios $E'_{m,x}/E'_{m,z}$ and $E'_{m,y}/E'_{m,z}$." +" We performed the calculation (double-checked with the aid of an algebraic manipulator). obtaimius While the previous expression for b,, aerees with that eiven im D80. our result for αμ is different and we were unable to recover his expression."," We performed the calculation (double-checked with the aid of an algebraic manipulator), obtaining While the previous expression for $b_m$ agrees with that given in B80, our result for $a_m$ is different and we were unable to recover his expression." + The ratios in eq. (16)), The ratios in eq. \ref{aandb}) ) + are then inserted iuto the Fresnel equations which fix the boundary conditions at the interface between the two media (see JacksonL975 aud eqs. |, are then inserted into the Fresnel equations which fix the boundary conditions at the interface between the two media (see \citealt{ja75} and eqs. [ +17]-|15] iu Bs).,17]-[18] in B80). + This allows the derivation of the components of the electric Seld of the reflected wave parallel aud perpendicular to the plane of incidence (E and E) iu terms of the same compoucuts of the incident wave (7| aud £1)., This allows the derivation of the components of the electric field of the reflected wave parallel and perpendicular to the plane of incidence $E''_\parallel$ and $E''_\perp$ ) in terms of the same components of the incident wave $E_\parallel$ and $E_\perp$ ). +" We re-derived the expressions given in 50 and found n sinifcos.jAy=basin> P d,008J.jBu:=bucos d;|ousiuP:audD—A,Wn Bj."," We re-derived the expressions given in B80 and found where $w_m=\sqrt{n_m^2 - \sin^2 i}/\cos i$ , $\ac_m = b_m\sin\beta-a_m\cos\beta$, $\bc_m = b_m\cos\beta+a_m\sin\beta$ and $\dc = A_+-B_+$." + =Theseexpressions \ ye were double-checked with the aid of au algebraic manipulator aud differ again from those in D80: we also note that our definition of B+ is different from that of BAO., These expressions were double-checked with the aid of an algebraic manipulator and differ again from those in B80; we also note that our definition of $B_{\pm}$ is different from that of B80. + The reflection cocficicnt for uupolarized radiation cau be expressed as the combination of the reflectivity of parallel and perpendicularly polarized incident waves. ρω=(piusuc|ppuj/2.," The reflection coefficient for unpolarized radiation can be expressed as the combination of the reflectivity of parallel and perpendicularly polarized incident waves, $\rho_\omega = +(\rho_{\parallel,\omega} + \rho_{\perp,\omega})/2$." + Since the reflectivity is defined as the ratio of the reflected to the incideut wave amplitudes. is the sun of the square moduli of the coefficients of Ly in eqs. (07]].," Since the reflectivity is defined as the ratio of the reflected to the incident wave amplitudes, $\rho_{\parallel,\omega}$ is the sum of the square moduli of the coefficients of $E_\parallel$ in eqs. \ref{erefl}) )." +" Similarly. py. is obtained by adding together pi,the square moduli of the cocfiicicuts of E."," Similarly, $\rho_{\perp,\omega}$ is obtained by adding together the square moduli of the coefficients of $E_\perp$." + The absorption cocficicut a.=1py has been computed umucrically in the relevant angular ranges following the procedure outlined above aud the results have been used to evaluate the iuteeral in eq. (93)., The absorption coefficient $\alpha_\omega=1-\rho_\omega$ has been computed numerically in the relevant angular ranges following the procedure outlined above and the results have been used to evaluate the integral in eq. \ref{df}) ). + Although the uuuerical scheme is ratherstraightforward. care should be used since the refractive index becomes resonant where the coefficieut of the higher order tezii in eq. (15))," Although the numerical scheme is ratherstraightforward, care should be used since the refractive index becomes resonant where the coefficient of the higher order term in eq. \ref{disp}) )" + vanishes (B8O: seealso Melrose 19561)., vanishes (B80; seealso \citealt{mel86}) ). + This happens at P?esia= 0.that is to say at the two frequencies," This happens at $P+v\sin^2\alpha=0$ ,that is to say at the two frequencies" +"is located at Gann)ο and doy=—2452/172"". it has an orbital period 0.43502143 davs auc shows eclipses lor ~20%. of it (5. Déeein et al.","is located at $\alpha_{2000}=18^{\rm h} 24^{\rm m} 31.61^{\rm s}$ and $\delta_{2000}=-24^\circ 52' 17.2\arcsec$, it has an orbital period $P=0.43502743$ days and shows eclipses for $\sim 20\%$ of it (S. Béggin et al." + 2010. in preparation).," 2010, in preparation)." + There is also an associated X-rav source. possibly variable at the binary period and with a hard spectrum (Dogdanov et al.," There is also an associated X-ray source, possibly variable at the binary period and with a hard spectrum (Bogdanov et al." + 2010)., 2010). + Such N-ray. emission is likely due to the shock between (he MSP magnetospheric radiation aud the matter released by (he companion. like that detected in the case of MSP-W in 47 Tuc (Bogdanov οἱ al.," Such X-ray emission is likely due to the shock between the MSP magnetospheric radiation and the matter released by the companion, like that detected in the case of MSP-W in 47 Tuc (Bogdanov et al." + 2005)., 2005). + This further suggests that the companion star to M281I is a non-degenerate star., This further suggests that the companion star to M28H is a non-degenerate star. + In (his letter we present ils optical identification. based on high-quality. phase-resolved photometry obtained. with the new Wide Field Camera 3 (WEC3) on board the Hubble Space Telescope (LIST).," In this letter we present its optical identification, based on high-quality, phase-resolved photometry obtained with the new Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope (HST)." + The photometric data-set used for this work consists of HST high-resolution images obtained with the ultraviolet-visible (UVIS) channel of the WFC3., The photometric data-set used for this work consists of HST high-resolution images obtained with the ultraviolet-visible (UVIS) channel of the WFC3. + A set of supplementary LIST Wide Field Planetary Camera 2 (WEDPC?2) images. and erounc-based wide-field images obtained at the European Southern Observatory (ESO) have been retrieved from the Science Archive and usec for variability and astrometric purposes.," A set of supplementary HST Wide Field Planetary Camera 2 (WFPC2) images, and ground-based wide-field images obtained at the European Southern Observatory (ESO) have been retrieved from the Science Archive and used for variability and astrometric purposes." +" The WFC3 UVIS CCD consists of two twin detectors with a pixel-scale of ~0.04""/pixel and a global field of view (FOV) of ~162""x162""."," The WFC3 UVIS CCD consists of two twin detectors with a pixel-scale of $\sim 0.04\arcsec$ /pixel and a global field of view (FOV) of $\sim +162\arcsec\times 162\arcsec$." + The WFCS images have been obtained on 2009 August 3 (Prop., The WFC3 images have been obtained on 2009 August 8 (Prop. + 11615. P.I. Ferraro) in four different bands.," 11615, P.I. Ferraro) in four different bands." +" The data-set consists of: 6 images obtained through the F390W filter (+ ©) with an exposure (me of Jax),=800—350 sec each: T images in F606W (~ V) with fox,=200 sec: 7 images in FESIAW (~7) with log=200 sec: and 7 images in F656N (a narrow filter corresponding to Ha) with exposure lime ranging [rom foxy=935 sec. up {ο lexy=1100 sec."," The data-set consists of: 6 images obtained through the F390W filter $\sim U$ ) with an exposure time of $t_{\rm exp}=800-850$ sec each; 7 images in F606W $\sim V$ ) with $t_{\rm exp}=200$ sec; 7 images in F814W $\sim I$ ) with $t_{\rm exp}=200$ sec; and 7 images in F656N (a narrow filter corresponding to $\alpha$ ) with exposure time ranging from $t_{\rm exp}=935$ sec, up to $t_{\rm exp}=1100$ sec." + All the images are aligned and the Cluster is almost centered in CHIP1., All the images are aligned and the cluster is almost centered in CHIP1. + Additional public WEPC? images have been retrieved from the archive., Additional public WFPC2 images have been retrieved from the archive. + The first (hereafter. WEPC2-A) was obtained in 1997 (Prop., The first data-set (hereafter WFPC2-A) was obtained in 1997 (Prop. +" 6625) and consists of 8 images in F555W (~ V) with fog,=140 sec and 9 images in FES14W ο=160 sec and 3x/.4=180 sec)."," 6625) and consists of 8 images in F555W $\sim V$ ) with $t_{\rm + exp}=140$ sec and 9 images in F814W $6\times t_{\rm exp}=160$ sec and $3\times t_{\rm exp}=180$ sec)." + The second sample (herealter WEPC2-B) consists of 13 images in F675W ( HR). with lop=LOO sec each. secured in 2008 (Prop.," The second sample (hereafter WFPC2-B) consists of 13 images in F675W $\sim R$ ), with $t_{\rm + exp}=100$ sec each, secured in 2008 (Prop." + 11340)., 11340). + Finally. the wide-field data-set consists of 6 images in the V. and 7 filters. obtained in August 2000 with the Wide Field Imager (WFEI) at the ESO-MPI 2.2 m telescope (La Silla. Chile).," Finally, the wide-field data-set consists of 6 images in the $V$ and $I$ filters, obtained in August 2000 with the Wide Field Imager (WFI) at the ESO-MPI 2.2 m telescope (La Silla, Chile)." + The WFI consists of a mosaic of eight chips. for a global FOV of 34x34.," The WFI consists of a mosaic of eight chips, for a global FOV of $34'\times34'$." + The data reduction procedure (all the details will be discussed in a Forthcoming paper: E. Dalessandro οἱ al., The data reduction procedure (all the details will be discussed in a forthcoming paper; E. Dalessandro et al. + 2010. in preparation) has been performed on the WECS “flat fielded” C10)," 2010, in preparation) has been performed on the WFC3 “flat fielded"" (flt)" +been noted that the instability is essentially the same as the viscous overstability of axisvmmoetrie mocles discovered bv dxato. (1978),been noted that the instability is essentially the same as the viscous overstability of axisymmetric modes discovered by Kato (1978). + The instability can be. suppressed. by introducing a sullicient effective. bulk viscosity. although the values required. may not be realistic;," The instability can be suppressed by introducing a sufficient effective bulk viscosity, although the values required may not be realistic." + More. plausibly. the instability can be suppressed. by allowing for the non-zero relaxation time of the turbulence. even if the bulk viscosity is zero.," More plausibly, the instability can be suppressed by allowing for the non-zero relaxation time of the turbulence, even if the bulk viscosity is zero." + Lt has then been shown that an initially. uniformly eccentric dise does not retain its cecentricity over many viscous time-scales. as had been suggested. by Sver Clarke (1992. 1993) and Lyubarskij et al. (," It has then been shown that an initially uniformly eccentric disc does not retain its eccentricity over many viscous time-scales, as had been suggested by Syer Clarke (1992, 1993) and Lyubarskij et al. (" +1994).,1994). + These earlier. works neglected the dillerential. precession cause ον slightly non-Ixeplerian rotation resulting from the raclia oessure gradient., These earlier works neglected the differential precession caused by slightly non-Keplerian rotation resulting from the radial pressure gradient. + This leads to twisting of the disc. followec ov viscous decay of the eccentricitv.," This leads to twisting of the disc, followed by viscous decay of the eccentricity." + The theory presented: here goes. considerably: bevon o)evious analvtical treatments of eccentric. cises., The theory presented here goes considerably beyond previous analytical treatments of eccentric discs. + Lt also oovides a practical numerical scheme that involves. only one-dimensional equations and from which the fast orbita ime-scale has been eliminated., It also provides a practical numerical scheme that involves only one-dimensional equations and from which the fast orbital time-scale has been eliminated. + This scheme is to. be oeferred. in many circumstances to a direct numerica simulation of the [luid-dynamical equations., This scheme is to be preferred in many circumstances to a direct numerical simulation of the fluid-dynamical equations. + Almost al irect simulations to date attempt to represent the Navier-Stokes equation (vith or without. explicit. viscosity) in wo dimensions., Almost all direct simulations to date attempt to represent the Navier-Stokes equation (with or without explicit viscosity) in two dimensions. + Phe present analysis shows that a two-imensional treatment of eccentric disces may capture many of the correct. qualitative features but cannot. be trusted in detail., The present analysis shows that a two-dimensional treatment of eccentric discs may capture many of the correct qualitative features but cannot be trusted in detail. + Vertical motion is always present in eccentric disces and radiative damping can influence the evolution of eccentricitv., Vertical motion is always present in eccentric discs and radiative damping can influence the evolution of eccentricity. + Furthermore. the Navier-Stokes equation does not take into account 16 relaxation time of the turbulence. which can be of great importance in this context.," Furthermore, the Navier-Stokes equation does not take into account the relaxation time of the turbulence, which can be of great importance in this context." + Nevertheless. it would be valuable to make detaile comparisons between the present theory and direc simulations (preferably three-dimensional).," Nevertheless, it would be valuable to make detailed comparisons between the present theory and direct simulations (preferably three-dimensional)." + “The presen theory cannot be applied: reliably to thick dises. nor to situations in which the eecentricity varies rapidly in space (ic. on a length-seale comparable. to. the thickness of the disc) or in time (i.e. on a time-scale comparable to the orbital period).," The present theory cannot be applied reliably to thick discs, nor to situations in which the eccentricity varies rapidly in space (i.e. on a length-scale comparable to the thickness of the disc) or in time (i.e. on a time-scale comparable to the orbital period)." + Mean-motion resonances are therefore excluded from the analysis. which is secular in the sense of celestial mechanics.," Mean-motion resonances are therefore excluded from the analysis, which is secular in the sense of celestial mechanics." + Nevertheless. the cllect of mean-motion resonances could be included in the evolutionary equations by adding appropriate localized. source terms for angular momentum and eccentricitv.," Nevertheless, the effect of mean-motion resonances could be included in the evolutionary equations by adding appropriate localized source terms for angular momentum and eccentricity." + The theory developed. in. this paper has much in common with the theory of warped aceretion disces (e.g. Pringle 1992: Ogilvie 1999. 2000).," The theory developed in this paper has much in common with the theory of warped accretion discs (e.g. Pringle 1992; Ogilvie 1999, 2000)." + One distinction. noted above. is that the equations for an eccentric disc are not all in conservative form.," One distinction, noted above, is that the equations for an eccentric disc are not all in conservative form." + Another dillerence is that the theory of warped. dises is complicated by a resonance caused. by the coincidence of the orbital and epicyclic frequencies in a Ixeplerian disc., Another difference is that the theory of warped discs is complicated by a resonance caused by the coincidence of the orbital and epicyclic frequencies in a Keplerian disc. + As a result. the behaviour is qualitatively different depending on the relative magnitudes of à and f/f (Papaloizou Lin 1995).," As a result, the behaviour is qualitatively different depending on the relative magnitudes of $\alpha$ and $H/R$ (Papaloizou Lin 1995)." + Fortunately. no such complication arises in the case of eccentric disces.," Fortunately, no such complication arises in the case of eccentric discs." + A consistent. asvinptotic expansion of the IDuid-dynamical equations is possible for any value of a. and the fractional error in the asvimptotie approximation. OCTR)7). is very small in most applications.," A consistent asymptotic expansion of the fluid-dynamical equations is possible for any value of $\alpha$ , and the fractional error in the asymptotic approximation, $O((H/R)^2)$, is very small in most applications." + The evolutionary. equations should be useful in many applications. including understanding the eccentric planet-disc interaction and testing theories. of quasi-periodic oscillations in X-ray binaries.," The evolutionary equations should be useful in many applications, including understanding the eccentric planet-disc interaction and testing theories of quasi-periodic oscillations in X-ray binaries." + In future work the rate of change of the complex eccentricity caused. by external forcing should be evaluated explicitly in the non-linear case [or tidal forcing by à companion object on a circular or eccentric orbit. and also for Einstein precession near a black hole.," In future work the rate of change of the complex eccentricity caused by external forcing should be evaluated explicitly in the non-linear case for tidal forcing by a companion object on a circular or eccentric orbit, and also for Einstein precession near a black hole." + ] acknowledge valuable discussions with Steve Lubow and with Jim Pringle., I acknowledge valuable discussions with Steve Lubow and with Jim Pringle. + The idea of applying viscoelastic mocdels to aceretion disces originated from. discussions. with Jin Pringle some vears ago., The idea of applying viscoelastic models to accretion discs originated from discussions with Jim Pringle some years ago. + | thank Scott Tremaine for helpful comments., I thank Scott Tremaine for helpful comments. + L acknowledge the support of Clare College. Cambridge through a research fellowship. andthe Roval Society through a University Research Fellowship.," I acknowledge the support of Clare College, Cambridge through a research fellowship, andthe Royal Society through a University Research Fellowship." +»ofiles. suggest higher metallicities for these galaxies. above he range of metallicities for galaxies with strongerLL.,"profiles, suggest higher metallicities for these galaxies, above the range of metallicities for galaxies with stronger." + These results suggest. that. the existence of. two populations of LBC galaxies. defined by the presence. or absence of broad emission as discussed in Section 4.1.. may be explained » intrinsic galaxy properties dillerentiated: primarily bv he overall metallicity mass fraction of the voungest stellar population (which dominates the UV. emission. ancl hence he two stellar features under consideration here).," These results suggest that the existence of two populations of LBG galaxies, defined by the presence or absence of broad emission as discussed in Section \ref{sec:comp_spect_obs}, may be explained by intrinsic galaxy properties differentiated primarily by the overall metallicity mass fraction of the youngest stellar population (which dominates the UV emission and hence the two stellar features under consideration here)." + ΙΓ the metallicity mass fraction is low then OLLI is possible in jnaries ancl produces more long lived OF and. WIR stars. which contribute to the broad line.," If the metallicity mass fraction is low then QHE is possible in binaries and produces more long lived Of and WR stars, which contribute to the broad line." + By contrast. when he metallicity is high OLI is no longer possible because stellar wind mass-loss breaks the rotation of stars rapiclhy o prevent this unusual evolution. ancl emission. is comparatively weak.," By contrast, when the metallicity is high QHE is no longer possible because stellar wind mass-loss breaks the rotation of stars rapidly to prevent this unusual evolution, and emission is comparatively weak." + Importantly. in both sets of galaxies we see evidence for a sub-Solar carbon to oxygen ratio in he weaker than expected P-Cveni profiles.," Importantly, in both sets of galaxies we see evidence for a sub-Solar carbon to oxygen ratio in the weaker than expected P-Cygni profiles." + In this paper we provide evidence that our new svnthetic stellar population models can explain the observed. stellar emission lines in the UV. spectra of LBGs. with best. fit models as summarised. in. Table 2...," In this paper we provide evidence that our new synthetic stellar population models can explain the observed stellar emission lines in the UV spectra of LBGs, with best fit models as summarised in Table \ref{lbgsinfo}." + We see evidence. for two main tvpes of LBG UV. spectra. differentiated by 10 presence or absence of broad. line emission. and explained as the result of varving metallicity in the voungest gaellar population.," We see evidence for two main types of LBG UV spectra, differentiated by the presence or absence of broad line emission, and explained as the result of varying metallicity in the youngest stellar population." + This leads to the absence/presence of an extreme rotational effect. (uasi-homosgeneous evolution) in the stellar binaries incorporated in our synthesis models., This leads to the absence/presence of an extreme rotational effect (quasi-homogeneous evolution) in the stellar binaries incorporated in our synthesis models. + We find three details that must be included to model the spectra accurately: massive binary stars. OLLI from the spin-up of the secondary stars in binaries in the event of mass-transter events. and a reduced carbon-to-oxvecn abundance ratio.," We find three details that must be included to model the spectra accurately: massive binary stars, QHE from the spin-up of the secondary stars in binaries in the event of mass-transfer events, and a reduced carbon-to-oxygen abundance ratio." + Our models support the inference that the sub-Solar C/O] ratio derived. from nebula abuncanees in the ς=23 galaxy studied in detail by Erbetal.(20100). may be wide-spread in this population. and that its inclusion in svnthesis models is important when fitting individual spectral features.," Our models support the inference that the sub-Solar [C/O] ratio derived from nebula abundances in the $z=2.3$ galaxy studied in detail by \citet{erb} may be wide-spread in this population, and that its inclusion in synthesis models is important when fitting individual spectral features." + Depletion bv. a factor of approximately four is consistent with the entirety of the sample discussed here., Depletion by a factor of approximately four is consistent with the entirety of the sample discussed here. + In adclition. we confirm our earlier work which suggests that binary evolution has significant effects on the spectra of unresolved stellar populations.," In addition, we confirm our earlier work which suggests that binary evolution has significant effects on the spectra of unresolved stellar populations." + Phe main effect. of this is increased mass loss in binary stars. and therefore an increase in the overall number of WR stars.," The main effect of this is increased mass loss in binary stars, and therefore an increase in the overall number of WR stars." + Furthermore the effects of rotation (OLI) within a binary system can also lead to dramatic ancl hither-to unexpected. results in the derived model stellar spectra., Furthermore the effects of rotation (QHE) within a binary system can also lead to dramatic and hither-to unexpected results in the derived model stellar spectra. + Given the near-ubiquity of sub-Solar carbon-to-oxvgen ratios in this sample. and the increasing iniport. of QUE elfects at low metallicity. it is interesting to consider the possible implications for analysis of Lyman-break galaxies ab still higher. redshift.," Given the near-ubiquity of sub-Solar carbon-to-oxygen ratios in this sample, and the increasing import of QHE effects at low metallicity, it is interesting to consider the possible implications for analysis of Lyman-break galaxies at still higher redshift." + This analysis has focused on galaxies a 3., This analysis has focused on galaxies at $z\la3$. + However similar sources. selected for high rest-UV [lux (and hence recent star formation) have now been identified to =S and bevond.," However similar sources, selected for high rest-UV flux (and hence recent star formation) have now been identified to $z=8$ and beyond." + The detailed spectroscopic analysis of these sources is still more cillicult than that at 2=3 due to a combination of increased skv background at long wavelengths. decreased detector sensitivity and increasing luminosity distance. and is not considered further here.," The detailed spectroscopic analysis of these sources is still more difficult than that at $z=3$ due to a combination of increased sky background at long wavelengths, decreased detector sensitivity and increasing luminosity distance, and is not considered further here." + However. forthcoming facilities such as the COM) ancl the WALOS spectrograph may make analysis of the line ancl other. longer wavelength spectral signatures relatively straightforward at 2=+ and above.," However, forthcoming facilities such as the (JCMT) and the KMOS spectrograph may make analysis of the line and other, longer wavelength spectral signatures relatively straightforward at $z=4$ and above." + At the low. but non-zero. metallicities inferred at 2=4.8 (e.g.Ancoetal.2004:Douglasct2010).. the effects of depleted carbon abundance and OLI may have a significant elfect on observed spectral features and improved modelling in these areas will be essential for accurate interpretation of spectra obtained.," At the low, but non-zero, metallicities inferred at $z=4-8$ \citep[e.g.][]{2004ApJ...610..635A,2010MNRAS.409.1155D}, the effects of depleted carbon abundance and QHE may have a significant effect on observed spectral features and improved modelling in these areas will be essential for accurate interpretation of spectra obtained." + As the case of the S oclock arc makes clear. it is possible that the voungest star formation is atypical of the galaxy as whole. which has implications for our understanding of the processes of galaxy formation.," As the case of the 8 o'clock arc makes clear, it is possible that the youngest star formation is atypical of the galaxy as a whole, which has implications for our understanding of the processes of galaxy formation." + If cold-mode accretion is incleed increasingly common at high redshifts as has been suggested (e.g.Crescitetal.2010:Dekel2009). then stellar emission and absorption features may be an accessible indicator of this.," If cold-mode accretion is indeed increasingly common at high redshifts as has been suggested \citep[e.g.][]{cresci,2009Natur.457..451D} then stellar emission and absorption features may be an accessible indicator of this." + While the limited. sample discussed. here is. of course. dillieult to interpret. the use of IKMOS and the JCNIT to build a sample of high redshift sources with high quality rest-UV. spectra may allow the identification of galaxies for which the voungest stellar populations are anomalously low in metallicity.," While the limited sample discussed here is, of course, difficult to interpret, the use of KMOS and the JCMT to build a sample of high redshift sources with high quality rest-UV spectra may allow the identification of galaxies for which the youngest stellar populations are anomalously low in metallicity." + Such sources may well prove interesting targets to study as possible examples of the still hotly-clebatecl cold-mocde accretion scenario., Such sources may well prove interesting targets to study as possible examples of the still hotly-debated cold-mode accretion scenario. + The authors would like to thank those who kindly provided their spectra anc mace this paper possible. Miroslava Dessauge. Dawn Erb. Anna Quider ancl Max. Pettini.," The authors would like to thank those who kindly provided their spectra and made this paper possible, Miroslava Dessauge, Dawn Erb, Anna Quider and Max Pettini." + ‘Phe authors would also like to thank the anonymous referee for bringing the peculiar. nature of the S οclock are to their attention., The authors would also like to thank the anonymous referee for bringing the peculiar nature of the 8 o'clock arc to their attention. + The authors would like to thank Malcolm Memer. Max Pettini. Paul Crowther. Stephen Smartt. Nate Bastian and Norbert Langer for useful discussions.," The authors would like to thank Malcolm Bremer, Max Pettini, Paul Crowther, Stephen Smartt, Nate Bastian and Norbert Langer for useful discussions." +" ERS acknowledges: postdoctoral research. support. from the Ulx Science and ""Technology. Facilities Council (S'TEC) for part of this work.", ERS acknowledges postdoctoral research support from the UK Science and Technology Facilities Council (STFC) for part of this work. + JJI5 acknowledges support from the Ul Science and Technology. Facilities Council (8TEC) under the rolling theory grant for the Institute of Astronomy., JJE acknowledges support from the UK Science and Technology Facilities Council (STFC) under the rolling theory grant for the Institute of Astronomy. + The frequency of binary stars and multiple stellar systems around solar-like stars in the solar neighborhood has been extensively studied in the past., The frequency of binary stars and multiple stellar systems around solar-like stars in the solar neighborhood has been extensively studied in the past. + Duquennoy Mayor (1991). from a sample of 164 primary G-dwarf stars analyzed during almost 13 yr with the CORAVEL spectrograph. obtained that the ratios of single:double:triple:quadruple systems are 51:40:7:2 respectively.," Duquennoy Mayor (1991), from a sample of 164 primary G-dwarf stars analyzed during almost 13 yr with the CORAVEL spectrograph, obtained that the ratios of single:double:triple:quadruple systems are 51:40:7:2 respectively." + This fraction of binaries should be present also in a sample of planet host stars 1f planets do form in any kind of binary systems and there are no selection biases applied to define the sample of stars where the planets are searched for., This fraction of binaries should be present also in a sample of planet host stars if planets do form in any kind of binary systems and there are no selection biases applied to define the sample of stars where the planets are searched for. + From a theoretical point of view the problem of the formation of giant planets in close binary systems is still largely debated., From a theoretical point of view the problem of the formation of giant planets in close binary systems is still largely debated. + Truncation and heating of circumstellar protoplanetary disks are expected to occur in close binary systems (Artymowics Lubow 1994: Nelson 2000)., Truncation and heating of circumstellar protoplanetary disks are expected to occur in close binary systems (Artymowics Lubow 1994; Nelson 2000). + However there Is no general consensus on which consequences these processes have on planet formation., However there is no general consensus on which consequences these processes have on planet formation. + elson (2000) showed that the formation of giant planets ts unlikely in equal mass binaries with semi-major axis ~50 AU. both by means of the disk instability (Boss 1997) and the core aceretion mechanisms (Pollack et al.," Nelson (2000) showed that the formation of giant planets is unlikely in equal mass binaries with semi-major axis $\sim50$ AU, both by means of the disk instability (Boss 1997) and the core accretion mechanisms (Pollack et al." + 1996)., 1996). + On the contrary Boss (2006). showed that in the context of the disk instability scenario. the presence of a close-by stellar companion may in fact trigger clumps formation leading to giant planets.," On the contrary Boss (2006), showed that in the context of the disk instability scenario, the presence of a close-by stellar companion may in fact trigger clumps formation leading to giant planets." + Along the same lines Duchénne (2010) suggested that in tight binaries (ας100 AU) massive planets are formed by disk instability at the same rate as less massive planets in wider binaries and single stars., Along the same lines Duchênne (2010) suggested that in tight binaries $a<100$ AU) massive planets are formed by disk instability at the same rate as less massive planets in wider binaries and single stars. + According to Marzart et al. (, According to Marzari et al. ( +2005). independently from the planet formation mechanism. tidal perturbations of the companion star influence both the onset of instability and the following chaotic evolution of protoplanetary disks.,"2005), independently from the planet formation mechanism, tidal perturbations of the companion star influence both the onset of instability and the following chaotic evolution of protoplanetary disks." + In particular several studies have pointed out that the gravitational influence of stellar companions on the dynamics of planetary systems becomes significant at separations <100 AU (e.g. Pfhal Muterspaugh 2006: Desidera Barbieri 2007; Duchénne 2010)., In particular several studies have pointed out that the gravitational influence of stellar companions on the dynamics of planetary systems becomes significant at separations $\le100$ AU (e.g. Pfhal Muterspaugh 2006; Desidera Barbieri 2007; Duchênne 2010). + Despite that. four planetary systems have been discovered in binaries with separations around 20 AU: Gamma Cephet (Hatzes et al.," Despite that, four planetary systems have been discovered in binaries with separations around $20$ AU: Gamma Cephei (Hatzes et al." + 2003). Gliese 86 (Queloz et al.," 2003), Gliese 86 (Queloz et al." + 2000: Els et al., 2000; Els et al. + 2001). HD 41004 (Santos et al.," 2001), HD 41004 (Santos et al." + 2002). and HD196885 (Correia et al.," 2002), and HD196885 (Correia et al." + 2008)., 2008). + These observational results are clearly challenging our current knowledge of planet formation and evolution in binary systems., These observational results are clearly challenging our current knowledge of planet formation and evolution in binary systems. + Several imaging surveys have successfully identified stellar companions to planet-host stars (e.g. Patience et al., Several imaging surveys have successfully identified stellar companions to planet-host stars (e.g. Patience et al. + 2002; Luhman Jayawardhana 2002: Chauvin et al., 2002; Luhman Jayawardhana 2002; Chauvin et al. + 2006: Mugrauer et al., 2006; Mugrauer et al. + 2007: Eggenberger et al., 2007; Eggenberger et al. + 2007; Eggenberger Udry 2007)., 2007; Eggenberger Udry 2007). + At present. giant planets around wide binary systems appear as frequent as planets around single stars (Bonavita Desidera 2007). suggesting that wide binaries are not significantly. altering. planet. formation processes.," At present, giant planets around wide binary systems appear as frequent as planets around single stars (Bonavita Desidera 2007), suggesting that wide binaries are not significantly altering planet formation processes." + However. there is a marginal statistical. evidence that binaries with separations smaller than 100 AU may have a lower frequency of planetary systems than around single stars.," However, there is a marginal statistical evidence that binaries with separations smaller than 100 AU may have a lower frequency of planetary systems than around single stars." + Eggenberger et al. (, Eggenberger et al. ( +2008) estimated a difference in the binary. frequency between carefully selected samples of non planet-host and planet-host stars ranging betwee! 8.2%+5.0% and 12.5%+ 5.9%. considering binaries with semi-major axis between 35 AU and 250 AU. further pointing out that this difference seems mostly evident for binaries with a=«100. AU.,"2008) estimated a difference in the binary frequency between carefully selected samples of non planet-host and planet-host stars ranging between $8.2\%\,\pm\,5.0\%$ and $12.5\%\,\pm\,5.9\%$ , considering binaries with semi-major axis between 35 AU and 250 AU, further pointing out that this difference seems mostly evident for binaries with $a<100$ AU." +" These results are obtained using samples of stars hosting radial velocity discovered planets. for the obvious reason that Doppler spectroscopy has been so far the most successful planet detection method. providing then the largest sample of planets from which statistical conclusions can be drawn,"," These results are obtained using samples of stars hosting radial velocity discovered planets, for the obvious reason that Doppler spectroscopy has been so far the most successful planet detection method, providing then the largest sample of planets from which statistical conclusions can be drawn." + Nevertheless. planets discovered with this technique are known to be adversely selected against close binaries.," Nevertheless, planets discovered with this technique are known to be adversely selected against close binaries." + Doppler spectroscopy ts complicated by light contamination of stellar companions. and blending of spectral lines.," Doppler spectroscopy is complicated by light contamination of stellar companions, and blending of spectral lines." + This implies that radial velocity surveys typically exclude known moderately and close binaries from their target lists., This implies that radial velocity surveys typically exclude known moderately and close binaries from their target lists. + As a consequence the occurrence of planetary systems in binaries. and in particular at critical separations (<100 AU). is still poorly constrained by the observations.," As a consequence the occurrence of planetary systems in binaries, and in particular at critical separations $\le100$ AU), is still poorly constrained by the observations." + While the use of a control sample of stars. proposed by Eggenberger et al. (," While the use of a control sample of stars, proposed by Eggenberger et al. (" +2007. 2008). 1s expected to mitigate the impact on the results given by the bias against close binaries applied by radial velocity surveys. other samples of planet-host stars and different techniques may be useful to probe the frequency of planets in binary stellar systems.,"2007, 2008), is expected to mitigate the impact on the results given by the bias against close binaries applied by radial velocity surveys, other samples of planet-host stars and different techniques may be useful to probe the frequency of planets in binary stellar systems." +flare and historically (Harmonetal1997).,flare and historically \citep{har97}. +. Larger soft X-ray (possibly thermal) Iuminosity has been observed. but only very. briefly. not long enough to launch the plasmoid 1998).," Larger soft X-ray (possibly thermal) luminosity has been observed, but only very briefly, not long enough to launch the plasmoid \citep{mir98}." +". There is a small region of solution space wilh energy. [Inxes comparable with the luminosity of these high states of sustained thermal X-ray. emission. {ιν=20 restricted to a verv small range of δὲ where Up, U,."," There is a small region of solution space with energy fluxes comparable with the luminosity of these high states of sustained thermal X-ray emission, $E_{min}= 20$ restricted to a very small range of $R$ where $U_{B} +\gg U_{e}$." + It seems very unlikely that disk radiation pressure can provide the force (hat is necessary (o initiate the ejection of the protonic plasmoids., It seems very unlikely that disk radiation pressure can provide the force that is necessary to initiate the ejection of the protonic plasmoids. + The implication is that magnetic forces would likely be required {ο energize the protonic plasmoicl and eject it al relativistic speeds., The implication is that magnetic forces would likely be required to energize the protonic plasmoid and eject it at relativistic speeds. + There is more information that can be eleaned [rom the protonic models of component C2 as they evolve in time., There is more information that can be gleaned from the protonic models of component C2 as they evolve in time. + This is captured in Figure 12., This is captured in Figure 12. +" This figure compares the solution space of the £,,,=1 and τμ=5 solutions at two epochs. December 6 ancl December 11."," This figure compares the solution space of the $E_{min}=1$ and $E_{min}=5$ solutions at two epochs, December 6 and December 11." +" The solutions for other values of £,,;, were left of the chart. so as not to elutter it. but the trends (hat will be described apply (ο all solutions."," The solutions for other values of $E_{min}$ were left off the chart, so as not to clutter it, but the trends that will be described apply to all solutions." + These plots are formatted differently than what has been shown previously., These plots are formatted differently than what has been shown previously. + This is a plot of (πα) versus δν. the total particle number in (he plasmoid (instead of 2).," This is a plot of $E(\mathrm{lm})$ versus $N$, the total particle number in the plasmoid (instead of $R$ )." + As the plasmoid evolves. one expects the barvon nunmber to be conserved.," As the plasmoid evolves, one expects the baryon number to be conserved." + There is no reason to presume significant entirainment both on cdvnamical grounds since Ielvin-Iehlmholtz instabilities are inefficient means of mixing meclia for relativistic flows. Bicknell(1994).. and empirically the plasmoids in major fares do not seem to clecelerate noticeably from seales of 1 mas to LOO mas (Dhawanetal2000).," There is no reason to presume significant entrainment both on dynamical grounds since Kelvin-Helmholtz instabilities are inefficient means of mixing media for relativistic flows, \citet{bic94}, and empirically the plasmoids in major flares do not seem to decelerate noticeably from scales of 1 mas to 100 mas \citep{dha00}." +. Applying barvon conservation to C2 in Figure 12. shows that as time evolves. the magnetic energy in (he svstem must increase.," Applying baryon conservation to C2 in Figure 12, shows that as time evolves, the magnetic energy in the system must increase." + The vertical dashed lines are drawn {ο help visualize this., The vertical dashed lines are drawn to help visualize this. + The data is color coded., The data is color coded. + The ο=1 data is orange both on the December 6 curve (dashed) and the December 11 curve (solid)., The $E_{min}=1$ data is orange both on the December 6 curve (dashed) and the December 11 curve (solid). + Similarly. the τμ=5 data is purple both on the December 6 curve (dashed) and the December 11 curve (solid).," Similarly, the $E_{min}=5$ data is purple both on the December 6 curve (dashed) and the December 11 curve (solid)." + The vertical dashed lines connect solutions with conserved barvon number in time., The vertical dashed lines connect solutions with conserved baryon number in time. +" The dashed lines are chosen to intersect the four minimum energv solutions: μμ=1. December 6: £4,=1. December 1l: E,=5. December 6: and πμ=5. December 11."," The dashed lines are chosen to intersect the four minimum energy solutions: $E_{min}=1$, December 6; $E_{min}=1$, December 11; $E_{min}=5$, December 6; and $E_{min}=5$, December 11." +" Consider the vertical line farthest io the right (hat intersects the minimum energy configuration at 7,5,=1. December 11."," Consider the vertical line farthest to the right that intersects the minimum energy configuration at $E_{min}=1$, December 11." +" Darvon conservation. implies that the solution is [ar to Che right of the minimum energy point on the plot at for ρω=1 on December 6. where U,zUp."," Baryon conservation, implies that the solution is far to the right of the minimum energy point on the plot at for $E_{min}=1$ on December 6, where $U_{e} \gg U_{B}$." + Thus. the plasmoid is evolving [rom a state of U.>Ug to one of U.zzUy in 5 days.," Thus, the plasmoid is evolving from a state of $U_{e} \gg U_{B}$ to one of $U_{e} \approx U_{B}$ in 5 days." + Since radiation losses are negligible in 5 davs (~10? eres) compared to the mechanical energy in the plasmoid. enerev conservalion implies (hat mechanical energy is being converted (o magnetic energy.," Since radiation losses are negligible in 5 days $\sim 10^{39}$ ergs) compared to the mechanical energy in the plasmoid, energy conservation implies that mechanical energy is being converted to magnetic energy." + In particular. the magnetic enerey increases [from 2.69xLO!10 eres to 5.08x107 eres in 5ΓΕ days in these protonic solutions.," In particular, the magnetic energy increases from $2.69 \times 10^{40}$ ergs to $5.08 \times 10^{42}$ ergs in 5 days in these protonic solutions." + One can svnthesize the deductions from Figures 9. 11 and 12 as follows:," One can synthesize the deductions from Figures 9, 11 and 12 as follows:" +el al. (,et al. ( +2009).,2009). +" An upper limit to the CN fIux density. fea. is obtained from llere. o, is the (dimensionless) uncertainty on the normalized continuum alt the wavelength of the CN band. fj ancl fas (erg 7? | 1) are the [τιν densities at the wavelengths ol the D-(ilter and at3880AÀ.. respectively. and Wea is the width of the portion of the spectrum in which the CN emission is sought."," An upper limit to the CN flux density, $f_{CN}$, is obtained from Here, $\sigma_c$ is the (dimensionless) uncertainty on the normalized continuum at the wavelength of the CN band, $f_B$ and $f_{3880}$ (erg $^{-2}$ $^{-1}$ $^{-1}$ ) are the flux densities at the wavelengths of the B-filter and at, respectively, and $W_{CN}$ is the width of the portion of the spectrum in which the CN emission is sought." + Quantity S4445/55 is the ratio of the reflectiviües at the wavelengths of CN and the D-filter., Quantity $S_{3880}/S_{B}$ is the ratio of the reflectivities at the wavelengths of CN and the B-filter. + Both asteroids are nearly spectrally neutral (Table 3)) and we set κκ = 1., Both asteroids are nearly spectrally neutral (Table \ref{physical}) ) and we set $S_{3880}/S_{B}$ = 1. + Quantity. κοfi). = 0.52 is (he ratio of the {lux densities al the two specified wavelengths in the Solar spectrum (Arvesen et al., Quantity $(f_{3880}/f_{B})_{\odot}$ = 0.52 is the ratio of the flux densities at the two specified wavelengths in the Solar spectrum (Arvesen et al. + 1969)., 1969). + The factor of five corresponds to our deliberately conservative use of a 5o confidence mit., The factor of five corresponds to our deliberately conservative use of a $\sigma$ confidence limit. + We [ist computed σ.. the standard deviation on the reflectivitv in two continuum windows flanking the CN band.," We first computed $\sigma_c$, the standard deviation on the reflectivity in two continuum windows flanking the CN band." +" We used the contimmun windows C, = 3800 - and C5 = 3910 - ancl omitted the wavelengths of the solar IE and Ix lines of Calcium since these were imperfectly cancelled by the computation of the reflectivity spectrum.", We used the continuum windows $C_1$ = 3800 - and $C_2$ = 3910 - and omitted the wavelengths of the solar H and K lines of Calcium since these were imperfectly cancelled by the computation of the reflectivity spectrum. +"— To measure c, we first removed residual trends by fitting a 2nd order polynomial to the 3800 6.6$ keV) that are consistent with originating from highly ionised material (e.g. Fe to Fe )." + In the hieh luminosity end. of the quasar distribution (both racio-loucl anc radio-quiet). the actual strength. of the iron. Ix. line component decreases consideray (Le. from EQW =100150 eV to EQW <50 eV). ooviding strong confirmation of the results in Nandra. (1997b).," In the high luminosity end of the quasar distribution (both radio-loud and radio-quiet), the actual strength of the iron K line component decreases considerably (i.e. from EQW $=100-150$ eV to EQW $<50$ eV), providing strong confirmation of the results in Nandra (1997b)." +. Additionally we also find that the strength. of theneural rellection hump is diminished considerably in the high Iuminosity. quasars., Additionally we also find that the strength of the reflection hump is diminished considerably in the high luminosity quasars. + So how can one explain the observations in the quasars. which seem to contrast with the situation in the Sevífert 1 ealaxies?," So how can one explain the observations in the quasars, which seem to contrast with the situation in the Seyfert 1 galaxies?" + Firstly the energv of the line emission in these quasars implies that the ionisation state of the reprocessing material (the surlace lavers of the putative accretion clisk) is clearly much higher than in the Seyfert) Is., Firstly the energy of the line emission in these quasars implies that the ionisation state of the reprocessing material (the surface layers of the putative accretion disk) is clearly much higher than in the Seyfert 1s. + As has been pointed out from. photoionsation modeling (e.g. see ltoss Fabian 1993: Matt. Fabian Ross 1993: Ross. Fabian Young 1999). the surface lavers of such disks can become substantially photoionised as the (m) of the central engine increases.," As has been pointed out from photoionsation modeling (e.g. see Ross Fabian 1993; Matt, Fabian Ross 1993; Ross, Fabian Young 1999), the surface layers of such disks can become substantially photoionised as the $\dot{m}$ ) of the central engine increases." + Perhaps at the I5ddington limit very little if any iron ἐν enission is seen. as the disk becomes fully ionised down to several Thomson depths.," Perhaps at the Eddington limit very little if any iron K emission is seen, as the disk becomes fully ionised down to several Thomson depths." + This picture is consistent with the most. luminous quasars (either racio-loud or radio-quiet). with very weak iron lines. accreting near the Ecldineton limit.," This picture is consistent with the most luminous quasars (either radio-loud or radio-quiet), with very weak iron lines, accreting near the Eddington limit." + Adcitionally. in the radio-oud objects. the relativistic jet can further weaken the line and rellection component.," Additionally, in the radio-loud objects, the relativistic jet can further weaken the line and reflection component." + Furthermore this wpothesis can also explain the apparent lack of a reflection 1ump fromας material in the high z quasars. found in section 6.3.," Furthermore this hypothesis can also explain the apparent lack of a reflection hump from material in the high z quasars, found in section 6.3." + Indeed it has been postulated. (Itoss. Fabian Young 1999). that the disk becomes more reflective in gh luminosity quasars (as the photoelectric opacity below be Ix decreases at higher ionisation) which can reproduce the apparently featureless spectra of some high z quasars.," Indeed it has been postulated (Ross, Fabian Young 1999), that the disk becomes more reflective in high luminosity quasars (as the photoelectric opacity below Fe K decreases at higher ionisation) which can reproduce the apparently featureless spectra of some high z quasars." + The ack of contrast between the continuum and the reprocessed X-rays can then explain the apparent absence of a reflection ‘hump’., The lack of contrast between the continuum and the reprocessed X-rays can then explain the apparent absence of a reflection `hump'. + Further support for the presence of a highly ionised accretion disk in one object comes from an observation ( with aand RNPLE)) of the luminous quasar PDS 456., Further support for the presence of a highly ionised accretion disk in one object comes from an observation ( with and ) of the luminous quasar PDS 456. + Although the line emission is fairly weak. a deep. highly ionised edge (at. 8.7 keV) is present in the spectrum of this quasar.," Although the line emission is fairly weak, a deep, highly ionised edge (at 8.7 keV) is present in the spectrum of this quasar." + This iron. [x edge. could. originate. from a rellector., This iron K edge could originate from a reflector. + The detailed spectral fitting of this quasar. from aan delata. is discussed in a separate paper (Reeves 2000).," The detailed spectral fitting of this quasar, from and data, is discussed in a separate paper (Reeves 2000)." + The intrinsic neutral column densities for the 62 quasars analvzed are shown in table 2. fitted in the rest. frame of the quasar.," The intrinsic neutral column densities for the 62 quasars analyzed are shown in table 2, fitted in the rest frame of the quasar." + An additional Galactic absorption component was also fitted. in the observers rest. frame. as. described," An additional Galactic absorption component was also fitted in the observers rest frame, as described" +perturbation predicted bv linear theory for any single value of 7. and impose such perturbations to the background equilibrium.,"perturbation predicted by linear theory for any single value of $k$, and impose such perturbations to the background equilibrium." + In order to get a completely sell-consistent initial perturbation. the particle distribution ΠΙΟΙΟ should be perturbed exactly.," In order to get a completely self-consistent initial perturbation, the particle distribution function should be perturbed exactly." + This is very expensive. from a computational point of view. and a shortcut which is verv often emploved is to initialize the particles with a shifted Maxwellian distribution. such that only the current and charge densities are consistent with the limear theory predictions. but not all Cie hieher-order moments of the distribution function.," This is very expensive, from a computational point of view, and a shortcut which is very often employed is to initialize the particles with a shifted Maxwellian distribution, such that only the current and charge densities are consistent with the linear theory predictions, but not all the higher-order moments of the distribution function." + The implicit assumption of such a method is that the PIC code will be able to quickly /sell-adjust. the initial inconsistency. but this approach remains. in our view. not very satisfactory.," The implicit assumption of such a method is that the PIC code will be able to quickly `self-adjust' the initial inconsistency, but this approach remains, in our view, not very satisfactory." + Moreover. the choice of the slope of the initial power spectrum constitutes vel another degree of [reedom in the In this work. we have opted [or a verv general initial perturbation.," Moreover, the choice of the slope of the initial power spectrum constitutes yet another degree of freedom in the In this work, we have opted for a very general initial perturbation." + In (his wav. we do not [ace the problem of choosing some particular modes— to initüialize. and we are also able to study. which mode. if anv. ‘survives’ through the nonlinear cascade.," In this way, we do not face the problem of choosing some particular modes to initialize, and we are also able to study which mode, if any, `survives' through the nonlinear cascade." + Accorcdinely. we initialize our simulations with a background magnetic field in the direction. ancl we superimpose a spectrum of random phase fluctuations in (he magnetic field only.," Accordingly, we initialize our simulations with a background magnetic field in the $x$ direction, and we superimpose a spectrum of random phase fluctuations in the magnetic field only." + We assume that such perturbation is general enough to perturb a large variety of waves in the plasma., We assume that such perturbation is general enough to perturb a large variety of waves in the plasma. + We point out (hat. dillerine from the normal mode initialization described above. (his choice is self-consistent both with Vlasov and Maxwell equations.," We point out that, differing from the normal mode initialization described above, this choice is self-consistent both with Vlasov and Maxwell equations." + The plasma will certainly respond instantaneously to magnetic field gradients by creating currents ancl generating electric fluctuations. anc ultimatelv waves.," The plasma will certainly respond instantaneously to magnetic field gradients by creating currents and generating electric fluctuations, and ultimately waves." + The only requisite that the initial perturbation mist salisly is to be divergence-Iree., The only requisite that the initial perturbation must satisfy is to be divergence-free. +" Hence. we initialize (he magnetic perturbationsas: where L, and L, are the box length. hk,=πινε. kb,=2zxn/L,. m and i are integers which usually range from. —23 to 3. and 6,,4.0,.604.0. are random angles."," Hence, we initialize the magnetic perturbationsas: where $L_x$ and $L_y$ are the box length, $k_x=2\pi m/L_x$, $k_y=2\pi n/L_y$, $m$ and $n$ are integers which usually range from $-3$ to $3$ , and $\phi_{x,y}, \phi_{x}, \phi_{y}, \phi_z$ are random angles." + Note that the, Note that the +LAT bursts have such low radiative efficiencies.,LAT bursts have such low radiative efficiencies. +" This suggests that GBM and LAT detected GRBs are on average more efficient at converting kinetic energy into prompt radiation, which perhaps explains why they are substantially brighter (higher than the BAT bursts with similar afterglow fluence)luminosities."," This suggests that GBM and LAT detected GRBs are on average more efficient at converting kinetic energy into prompt radiation, which perhaps explains why they are substantially brighter (higher fluence) than the BAT bursts with similar afterglow luminosities." +" The LAT bursts are at the high end of the Ey distributions with η>40% for all LAT bursts, and is.-E,η>80% for three of the LAT bursts."," The LAT bursts are at the high end of the $E_{\gamma,iso}$ $E_k$ distributions with $\eta>40\%$ for all LAT bursts, and $\eta>80\%$ for three of the LAT bursts." +" These extreme efficiencies be unphysical and due to a our assumptions: an internalmay shock mechanism as is described in the fireball model a single value of e, and ep, no appreciable Compton component,(??),, and a single universal surrounding medium density."," These extreme efficiencies may be unphysical and due to a our assumptions: an internal shock mechanism as is described in the fireball model \citep{rees98,meszaros02}, , a single value of $\epsilon_e$ and $\epsilon_B$, no appreciable Compton component, and a single universal surrounding medium density." +" We acknowledge that these differences in the distribution of η are degenerate with differences in ες, ep, and the presence of some inverse Compton component."," We acknowledge that these differences in the distribution of $\eta$ are degenerate with differences in $\epsilon_e$, $\epsilon_B$, and the presence of some inverse Compton component." + We also caution that our estimations of for the LAT bursts do not include the extra spectral Eis.power law observed in several of the LAT bursts.," We also caution that our estimations of $E_{\gamma,iso}$ for the LAT bursts do not include the extra spectral power law observed in several of the LAT bursts." +" However, that would make 7 even larger, which perhaps suggests that it is the internal shock model framework that is not valid."," However, that would make $\eta$ even larger, which perhaps suggests that it is the internal shock model framework that is not valid." + The bulk Lorentz factor is a fundamental quantity needed to describe the (T)GRB fireball and therefore interesting to compare for different populations of bursts., The bulk Lorentz factor $\Gamma$ ) is a fundamental quantity needed to describe the GRB fireball and therefore interesting to compare for different populations of bursts. +" Unfortunately, it is also a difficult quantity to accurately measure and there are several methods for placing lower or upper limits on this quantity depending on multiple assumptions."," Unfortunately, it is also a difficult quantity to accurately measure and there are several methods for placing lower or upper limits on this quantity depending on multiple assumptions." +" The most common technique applied to the FermiLAT detected bursts (???) was originally derived by ?,, using the highest energy observed photon to place a lower limit on the pair production attenuation, setting a lower limit on y-rayI’."," The most common technique applied to the }-LAT detected bursts \citep{abdo080916c,abdo090510,abdo090902b} was originally derived by \cite{lithwick01}, using the highest energy observed photon to place a lower limit on the $\gamma$ -ray pair production attenuation, setting a lower limit on $\Gamma$." + This method assumes that the GeV and seed sub-MeV photons are emitted from the same co-spatial region and are produced by internal shocks., This method assumes that the GeV and seed sub-MeV photons are emitted from the same co-spatial region and are produced by internal shocks. + It can produce extreme values of I'>1000 for the LAT bursts., It can produce extreme values of $\Gamma\gtrsim 1000$ for the LAT bursts. + ? and ? suggest modifications for this calculation using a two-zone model that assumes that the sub-MeV and GeV photons are produced at very different radii from the central engine., \cite{zhao10} and \cite{zou10b} suggest modifications for this calculation using a two-zone model that assumes that the sub-MeV and GeV photons are produced at very different radii from the central engine. + This modification lowers [ to approximately a few hundred., This modification lowers $\Gamma$ to approximately a few hundred. + Hascoétt et al. (, Hascoëtt et al. ( +"2011, in-preparation) also demonstrate that when carefully calculating the pair production attenuation taking into account the jet geometry and dynamics, Τ is reduced by a factor of ~2.5.","2011, in-preparation) also demonstrate that when carefully calculating the pair production attenuation taking into account the jet geometry and dynamics, $\Gamma$ is reduced by a factor of $\sim +2.5$." +" When no high energy (GeV) observations are available, the most common method to limit I' is to derive it from the deceleration time of the forward shock which corresponds to the peak time of the optical (????) or X-ray (?) afterglow light curves."," When no high energy (GeV) observations are available, the most common method to limit $\Gamma$ is to derive it from the deceleration time of the forward shock which corresponds to the peak time of the optical \citep{sari99,molinari07,oates09,liang09} or X-ray \citep{liang09} afterglow light curves." +" Often one can only set upper limits on the deceleration time because the peak must have occurred prior to the start of the observations, corresponding to lower limits on I', or be buried under other 'Therecomponents."," Often one can only set upper limits on the deceleration time because the peak must have occurred prior to the start of the observations, corresponding to lower limits on $\Gamma$, or be buried under other components." + are additional alternative methods to determine I including putting upper limits on the forward shock contribution to the keV-MeV prompt emission by looking for deep minima or dips down to the instrumental threshold between peaks in the prompt emission light curves (?).., There are additional alternative methods to determine $\Gamma$ including putting upper limits on the forward shock contribution to the keV-MeV prompt emission by looking for deep minima or dips down to the instrumental threshold between peaks in the prompt emission light curves \citep{zou10a}. + The typical values of these upper limits on I are several hundred., The typical values of these upper limits on $\Gamma$ are several hundred. + ? describe another method that estimate I from the thermal component modeling in the prompt emission spectrum using photosphere modeling., \cite{peer07} describe another method that estimate $\Gamma$ from the thermal component modeling in the prompt emission spectrum using photosphere modeling. + ? describe yet another method to estimate I' using early optical data to constrain the forward and reverse shock components., \cite{zhang03} describe yet another method to estimate $\Gamma$ using early optical data to constrain the forward and reverse shock components. +" The latter two methods are worth further study, but the application of them to the data presented here is beyond the scope of this paper."," The latter two methods are worth further study, but the application of them to the data presented here is beyond the scope of this paper." + We apply the deceleration time of the optical light curves technique to our sample for those GRBs with UVOT light curves and measurements of Ej in Section ??))., We apply the deceleration time of the optical light curves technique to our sample for those GRBs with UVOT light curves and measurements of $E_k$ (derived in Section \ref{sec:eta}) ). +" Unfortunately, due to the lack (derivedof early observations of the LAT bursts, we cannot apply this method to that sample."," Unfortunately, due to the lack of early observations of the LAT bursts, we cannot apply this method to that sample." +" However, we collect estimates of T using the pair-production attenuation technique from the literature, using the typical one-zone model from ??77)), as well as the two-zone estimates from ?,, and compare these limits in Figure 11.."," However, we collect estimates of $\Gamma$ using the pair-production attenuation technique from the literature, using the typical one-zone model from \cite{abdo090902b,abdo080916c,abdo090510,abdo090926a}) ), as well as the two-zone estimates from \cite{zou10b}, and compare these limits in Figure \ref{fig:lf}." + The different methods yield a wide range of I for each burst ranging from a few 10s to more than 1000., The different methods yield a wide range of $\Gamma$ for each burst ranging from a few 10s to more than 1000. +" However, many of these results are upper or lower limits."," However, many of these results are upper or lower limits." + 'The assumptions put into each measurement and method about the geometry and nature of the outflow have a strong influence on the results., The assumptions put into each measurement and method about the geometry and nature of the outflow have a strong influence on the results. +" If we believe that the sub-MeV and GeV photons are generated in the same co-spatial region, and ignore the two-zone model estimates, the lower limits on I' of the LAT bursts are nearly a factor of 2 higher than the BAT and GBM bursts."," If we believe that the sub-MeV and GeV photons are generated in the same co-spatial region, and ignore the two-zone model estimates, the lower limits on $\Gamma$ of the LAT bursts are nearly a factor of 2 higher than the BAT and GBM bursts." +" Unfortunately, we do not have high energy observations of many of the BAT bursts, and we do not have early optical observations of the LAT bursts, therefore one should compare measurements of I for these different samples with caution."," Unfortunately, we do not have high energy observations of many of the BAT bursts, and we do not have early optical observations of the LAT bursts, therefore one should compare measurements of $\Gamma$ for these different samples with caution." + A more careful detailed study of bulk Lorentz factor estimates for the bursts in thissample would perhaps provide more insight into concrete differences between the samples., A more careful detailed study of bulk Lorentz factor estimates for the bursts in thissample would perhaps provide more insight into concrete differences between the samples. +" This would require detailed analysis of all of the prompt emission light curves and spectra of the bursts in our sample, and this is beyond the scope of this study."," This would require detailed analysis of all of the prompt emission light curves and spectra of the bursts in our sample, and this is beyond the scope of this study." +he redshift space volumes occupied by the model groups.,the redshift space volumes occupied by the model groups. +" When the ""interloping galaxies are jettisoned from. the eroups found in the mock catalogues. enough of these extra ow luminosity galaxies are placed along radial lines that hey bias the orientation distribution."," When the `interloping' galaxies are jettisoned from the groups found in the mock catalogues, enough of these extra low luminosity galaxies are placed along radial lines that they bias the orientation distribution." + Increasing X retains a higher fraction of the initially eroupecl galaxies in the eroups. reducing the number of cinterlopers! returned to the ield. and decreasing the number of radially aligned objects ound in the second. pass of the [riends-ol-Eriends algorithm.," Increasing $\chi$ retains a higher fraction of the initially grouped galaxies in the groups, reducing the number of `interlopers' returned to the field, and decreasing the number of radially aligned objects found in the second pass of the friends-of-friends algorithm." + AX value of 4=1.15 produces a mock orientation distribution hat is. according to a Ix-5 test. indistinguishable from that ound in the 2dEGIS.," A value of $\chi=1.15$ produces a mock orientation distribution that is, according to a K-S test, indistinguishable from that found in the 2dFGRS." + This is chosen as the default. value or these 2PBASICC mocks throughout this paper., This is chosen as the default value for these 2BASICC mocks throughout this paper. +" An additional set of 22 mock 2dkORS surveys created rom the Llubble Volume by 2.. as used. by ον, are also analvsed to give some idea of the systematic dillerences resulting from cillerent simulations and implementations of he galaxy formation modelling."," An additional set of 22 mock 2dFGRS surveys created from the Hubble Volume by \citet{2000MNRAS.319..168C}, as used by \citet{2005MNRAS.364..620G}, are also analysed to give some idea of the systematic differences resulting from different simulations and implementations of the galaxy formation modelling." + For these mock catalogues. a value of y=Lil was required. in order to recover the PdAPGRS svstem orientation cistribution.," For these mock catalogues, a value of $\chi=1.11$ was required in order to recover the 2dFGRS system orientation distribution." + In this section. we will first describe the main features and properties of the connected structures found in the 2dECGIUS and then compare with the results from the mock surveys.," In this section, we will first describe the main features and properties of the connected structures found in the 2dFGRS and then compare with the results from the mock surveys." + This comparison will encompass both the whole population of connected svstems as well as the largest objects., This comparison will encompass both the whole population of connected systems as well as the largest objects. + Projections onto the right ascension-redshift plane of all of the connected svstems found in the 2lkPORS are shown in Figs. and 4., Projections onto the right ascension-redshift plane of all of the connected systems found in the 2dFGRS are shown in \ref{twodfrich} and \ref{twodflum}. + A total of 95.010 galaxies are linked. into 7.603 svstems containing at least two members and mean redshifts no greater than 0.12.," A total of $95,010$ galaxies are linked into $7,603$ systems containing at least two members and mean redshifts no greater than $0.12$." + Of these. 3.018 contain only wo members.," Of these, $3,018$ contain only two members." + Almost S7 per cent of galaxies at z:0.12 are Maced. into a connected structure., Almost $87$ per cent of galaxies at $z\le0.12$ are placed into a connected structure. + One large filamentarv-structure stands out in each of the NGP and SGP wedges., One large filamentary-structure stands out in each of the NGP and SGP wedges. + ‘These systems trace out the same overdensities apparent in he 2PIGG cistribution (?).. the smoothed galaxy. density map (7) and the reconstructed. density field. (7). of the 2dECHRS.," These systems trace out the same overdensities apparent in the 2PIGG distribution \citep{2004MNRAS.355..769E}, the smoothed galaxy density map \citep{2004MNRAS.351L..44B} and the reconstructed density field \citep{2004MNRAS.352..939E} of the 2dFGRS." +" The largest NCP object. at z~0.08. corresponds o the large RA end of the ""Sloan Great Wall’ highlighted w 2."," The largest NGP object, at $z\sim0.08$, corresponds to the large RA end of the `Sloan Great Wall' highlighted by \citet{2005ApJ...624..463G}." + At a total by-band luminosity of ο”... his is about 20 per cent more luminous than the largest equivalent in the SP. which lies at z0.11 and RA ~10," At a total $\bj$ -band luminosity of $\sim 7.8\times10^{13}\Lsol$, this is about $20$ per cent more luminous than the largest equivalent in the SGP, which lies at $z\sim0.11$ and RA $\sim10^\circ$." + The extents in RA of these largest. NGP and SCP systems in comoving coordinates are 198.1Mpe and 995.1Alpe respectively., The extents in RA of these largest NGP and SGP systems in comoving coordinates are $\sim198\Mpc$ and $99\Mpc$ respectively. + While the NGDP svstems contains twice as many members as that in the SGP. it is very nearly. broken into two pieces around RA ~185. where the galaxy density drops olf considerably.," While the NGP systems contains twice as many members as that in the SGP, it is very nearly broken into two pieces around RA $\sim185^\circ$, where the galaxy density drops off considerably." + More locally. a continuation to lower ceclinations of the CLA Great Wall (2) is seen at z~0.02 inthe NGL. although our algorithm breaks this up into a few dillerent components.," More locally, a continuation to lower declinations of the CfA Great Wall \citep{1989Sci...246..897G} is seen at $z\sim0.02$ in the NGP, although our algorithm breaks this up into a few different components." + Some average and extreme properties of the systenis identified in the 2dPCGBS are listed in Table 1.., Some average and extreme properties of the systems identified in the 2dFGRS are listed in Table \ref{stats}. + In. more detail. the correlation between the Luminosity and weighted (to account. for the local angular incompleteness of. the survey) membership of connected. structures is shown in Fig. 6..," In more detail, the correlation between the luminosity and weighted (to account for the local angular incompleteness of the survey) membership of connected structures is shown in Fig. \ref{lumrich}." + The second largest svstem contains at least twice as many members as the third. largest. one. and almost 3 times as much luminosity. making the largest. NCP and SGP structures stand. out. from. the remaining svstenis.," The second largest system contains at least twice as many members as the third largest one, and almost 3 times as much luminosity, making the largest NGP and SGP structures stand out from the remaining systems." +metallicities very close to 2.3 (Llarris1996).,metallicities very close to $-2.3$ \citep{harris}. +. Because there were verv few stars with spectroscopy in each elobular cluster. we combined the data from clusters with similar metallicities before plotting the histograms in Figure. 6.," Because there were very few stars with spectroscopy in each globular cluster, we combined the data from clusters with similar metallicities before plotting the histograms in Figure 6." + All of these globular clusters have horizontal branches near gy=16 (the magnitude range for which we have the most complete sample of DIID stars). and thus thespectra have high S/N.," All of these globular clusters have horizontal branches near $g_0=16$ (the magnitude range for which we have the most complete sample of BHB stars), and thus thespectra have high $S/N$." + Figure 6 shows that the SDSS DRT WBC metallicities for 11112 stars tend to. push the metallicities toware 19., Figure 6 shows that the SDSS DR7 WBG metallicities for BHB stars tend to push the metallicities toward $-1.9$. + The measured metallicities are correlated with the published. metallicities of the globular clusters: however. stars that have higher metallicities are measured with metallicities that are too low. and stars with lower metallicities are measured systematically too high.," The measured metallicities are correlated with the published metallicities of the globular clusters; however, stars that have higher metallicities are measured with metallicities that are too low, and stars with lower metallicities are measured systematically too high." + We show for comparison the measured. metallicities of the seven stream stars., We show for comparison the measured metallicities of the seven stream stars. + The measured. metallicity. is lower than that of M92 and NGC 5053., The measured metallicity is lower than that of M92 and NGC 5053. + Because the validity of our stream detection depends on our ability to separate the stream from the stellar halo in metallicity. we need to show that the metallicities in our background. population are accurate.," Because the validity of our stream detection depends on our ability to separate the stream from the stellar halo in metallicity, we need to show that the metallicities in our background population are accurate." + We selected all of the stars with spectra in DRT that have photometry consistent with being a BIID star. as explained in 82. 6745. and 0m57.," We selected all of the stars with spectra in DR7 that have photometry consistent with being a BHB star, as explained in 2, $b>45^\circ$, and $\delta>5^\circ$." + We further restricted the sample by insisting that the WBC estimate of logg. as measured in DIU. was less than 3.75.," We further restricted the sample by insisting that the WBG estimate of $\log g$, as measured in DR7, was less than 3.75." + 1n Figure 7. we show the DRT WBC metallicitv as a function of apparent magnitude.," In Figure 7, we show the DR7 WBG metallicity as a function of apparent magnitude." + We have spectra for stars with 14.5«gy19.15. which span distances of 6 to 50 kpe from the Sun. all at high Galactic latitude.," We have spectra for stars with $14.5< g_0 <19.15$, which span distances of 6 to 50 kpc from the Sun, all at high Galactic latitude." + Phe metallicity distributions for all of the stars brighter than gy<18.5 are similar. with a mean near 1.9 and a sigma of 0.45.," The metallicity distributions for all of the stars brighter than $g_0<18.5$ are similar, with a mean near $-1.9$ and a sigma of 0.45." + In the faintest set of stars. which have apparent magnitudes similar to that of the newly detected stream. the distribution appears considerably broader. but with a similar mean.," In the faintest set of stars, which have apparent magnitudes similar to that of the newly detected stream, the distribution appears considerably broader, but with a similar mean." + We attribute the increased width to the lower S/N in many of these spectra., We attribute the increased width to the lower S/N in many of these spectra. + Phe mean is somewhat lower in the last panel in Figure 7 than in Figure 4. probably clue to a cleaner sample of BULB stars. with less contamination from BS. from the additional restriction in log g.," The mean is somewhat lower in the last panel in Figure 7 than in Figure 4, probably due to a cleaner sample of BHB stars, with less contamination from BS, from the additional restriction in $\log g$ ." + We show for comparison the six stream stars that, We show for comparison the six stream stars that +inclinecl force-[ree magnetosphere.,inclined force-free magnetosphere. +" This altitude. which is not exactly symmetric with respect to the magnetic azimuthal augle o,,. but can be approximated by the value at ©,,=Q. is plotted in Fig."," This altitude, which is not exactly symmetric with respect to the magnetic azimuthal angle $\phi_m$, but can be approximated by the value at $\phi_m=0$, is plotted in Fig." + 8 as purple downward aud blue upward triaugles.," \ref{fig:4.2} + as purple downward and blue upward triangles." + Two linear fitting lines are alsoshown., Two linear fitting lines are alsoshown. +" The altitude ro, decreases with the inclination augle a in both our model aud the separatrix layer model ol a Lorce-Lree maguetospliere.", The altitude $r_{ov}$ decreases with the inclination angle $\alpha$ in both our model and the separatrix layer model of a force-free magnetosphere. + However. the emission region iu tlie separatrix laver model exteucds even outside the light-eylinder. whereas ours is well localized around null points.," However, the emission region in the separatrix layer model extends even outside the light-cylinder, whereas ours is well localized around null points." + Accounting for this differeuce may be inmiportaut for further improvement of the model of the emissiou region based ou a lorce-[ree magnetosphere., Accounting for this difference may be important for further improvement of the model of the emission region based on a force-free magnetosphere. + The thickuess of the gap region. w. is not known. but it is sometimes assumed to decrease with the spin-down luminosity Lop (Wattersetal.2009:Romani&Watters2010).," The thickness of the gap region, $w$, is not known, but it is sometimes assumed to decrease with the spin-down luminosity $ L_{SD}$ \citep{Wa09, RW10}." +. We have w= --rep. if the lower boundary of the gap is fixed as the last-open fiekl line in the vacuum dipole field.," We have $w=1-r_{ov}$, if the lower boundary of the gap is fixed as the last-open field line in the vacuum dipole field." + This assumption is tested in the lower left pauel of Fig. &..," This assumption is tested in the lower left panel of Fig. \ref{fig:4.2}," + in which the relation (1—rq)&(Lsp/10*ergs1jEU? js plotted as a light green curve. (, in which the relation $(1-r_{ov}) \approx (L_{SD} / 10^{33}erg s^{-1})^{-1/2}$ is plotted as a light green curve. ( +The curve is not fitted to the data poiuts.),The curve is not fitted to the data points.) + This suggests that the assumption of maximum altitude. ro.=1.0. is uot a good oue.," This suggests that the assumption of maximum altitude, $r_{ov}=1.0$, is not a good one." + This discovery. allects expected utumber of the 5-ray. pulsars in the observation., This discovery affects expected number of the $\gamma$ -ray pulsars in the observation. + From geometrical reason. the pulsed emissiou by caustics is liuited to a certain range between inclination aud viewing augles.," From geometrical reason, the pulsed emission by caustics is limited to a certain range between inclination and viewing angles." +" Romani&Watters(2010) showed the range of observable pulsars witli ry,0.95. 0.90 aud 0.70 or outer gap model iu their Fig."," \citet{RW10} showed the range of observable pulsars with $r_{ov}=$ 0.95, 0.90 and 0.70 for outer gap model in their Fig." + 16., 16. + We recalculate it auc show the result in Fig. 9.., We recalculate it and show the result in Fig. \ref{fig:4.3}. + The observable ange of viewing augle £ is below the curves., The observable range of viewing angle $\xi$ is below the curves. + Our fiudiug in Fig., Our finding in Fig. +" 8. is that ro, is a function of the inclination angle. which is similar to that of the separatrix laver model."," \ref{fig:4.2} is that $r_{ov}$ is a function of the inclination angle, which is similar to that of the separatrix layer model." + We also show the observable ange by the empirical relation obtained in Fig., We also show the observable range by the empirical relation obtained in Fig. + 8 as black solid line. for which the altitude is chosen as 0.925 times the height of the last-open Geld line iu force-free imagnetosphere.," \ref{fig:4.2} as black solid line, for which the altitude is chosen as 0.925 times the height of the last-open field line in force-free magnetosphere." + The figure slows hat sources with low inclination aud viewing augles become observable., The figure shows that sources with low inclination and viewing angles become observable. +" For example. pulsar with he inclination augle a=30° can be detected for €>607 for rj, —0.95. but for €>307."," For example, pulsar with the inclination angle $\alpha =30^{\circ}$ can be detected for $\xi > 60^{\circ}$ for $r_{ov}=$ 0.95, but for $\xi >30^{\circ}$." + Thus expected number increases approximately twice lor sources with the low inclination auc viewing augles., Thus expected number increases approximately twice for sources with the low inclination and viewing angles. + The caustic model cousidered in Section 3 provides peak positions cousisteut witli observation. but there are also some additional. unseen peaks.," The caustic model considered in Section 3 provides peak positions consistent with observation, but there are also some additional, unseen peaks." + These are interpreted as being prohibited by sole nuechanism., These are interpreted as being prohibited by some mechanism. + In this section. we consider au improvement to our model that takes into account a very simple distribution for the emissivity.," In this section, we consider an improvement to our model that takes into account a very simple distribution for the emissivity." + Detectable 7-rays are raciated with large multiplicity by the pair plasma in the gap region., Detectable $\gamma$ -rays are radiated with large multiplicity by the pair plasma in the gap region. + Therefore. tle mean [ree path of a 5-ray. photou should be less than lighte eylinder radius (Takata&Chane[eJ2007).," Therefore, the mean free path of a $\gamma$ -ray photon should be less than light cylinder radius \citep{TC07}." +. The pair creation mean [ree path is [weeiven by A(r)—5.6pούD?2 Claugetal.2008) lor an assumed limitiug distance to the uull poiut rj7;5.," The pair creation mean free path is given by $\lambda(r)\sim 5.6 P^{13/21}(B_s/10^{12}G)^{-2/7} r$ \citep{Ta08} for an assumed limiting distance to the null point $r_{n,lim}$ ." + The position of the null point of inclined pulsars. where the accelerating electric Ποια arises. depends sienificantlye ou maguetice azimuthal anele.[we so the intensity of y-ray emission," The position of the null point of inclined pulsars, where the accelerating electric field arises, depends significantly on magnetic azimuthal angle, so the intensity of $\gamma$ -ray emission" +adopted to minimize contamination from the extended ejecta.,adopted to minimize contamination from the extended ejecta. +" We refer to Nielsenetal.(2005) and Hillieretal.(2006) for further details on the observations and for an extensive analysis of the HST/STIS ultraviolet spectrum of Eta Car, in particular the dataset obtained in 2002 Jul 04."," We refer to \citet{nielsen05} and \citet{hillier06} for further details on the observations and for an extensive analysis of the /STIS ultraviolet spectrum of Eta Car, in particular the dataset obtained in 2002 Jul 04." +" For the optical range, the G430M and G750M gratings were used, yielding a resolving power of 6000-8000 across the 1100 spectral range."," For the optical range, the G430M and G750M gratings were used, yielding a resolving power of 6000–8000 across the 100 spectral range." + Spectra were extracted using 6 half-pixels (071152)., Spectra were extracted using 6 half-pixels 152). + Table 3 summarizes the (HST/STIS data used in this paper., Table \ref{tab3} summarizes the /STIS data used in this paper. + Herein we discuss the behavior of key line profiles across the two most recent spectroscopic events: 2003.5 (6= 11.0) and 2009.0 (@= 12.0)., Herein we discuss the behavior of key line profiles across the two most recent spectroscopic events: 2003.5 $\phi = 11.0$ ) and 2009.0 $\phi = 12.0$ ). +" While the ideal case would be that all observations were accomplished across the same spectroscopic event, availability of instrumentation did not permit such."," While the ideal case would be that all observations were accomplished across the same spectroscopic event, availability of instrumentation did not permit such." +" We note that the 1998.0 and 2003.5 spectroscopic events were nearly identical in behavior in X-rays (Corcoran2005),, but that the duration of the X-ray minimum was substantially shorter in the 2009.0 spectroscopic event (M. Corcoran et al."," We note that the 1998.0 and 2003.5 spectroscopic events were nearly identical in behavior in X-rays \citep{corcoran05}, but that the duration of the X-ray minimum was substantially shorter in the 2009.0 spectroscopic event (M. Corcoran et al." +" 2010, in prep.)."," 2010, in prep.)." +" However, optical spectroscopy indicated that the Ha line profile was flat-topped in 2003.5 but not in the 1998.0 spectroscopic event (Davidsonetal.2005)."," However, optical spectroscopy indicated that the $\alpha$ line profile was flat-topped in 2003.5 but not in the 1998.0 spectroscopic event \citep{davidson05}." +". Our understanding of the changes in spectroscopic profiles presented here suggests that while there may be small changes in the wind profiles due to the secular variability (Sect. 3.2)),"," Our understanding of the changes in spectroscopic profiles presented here suggests that while there may be small changes in the wind profiles due to the secular variability (Sect. \ref{highvelopd}) )," + the major changes we see are due to the periodic variations caused by the binary nature of Eta Car., the major changes we see are due to the periodic variations caused by the binary nature of Eta Car. +" The 410833 absorption line profile, as displayed in Figure 1,, evolved considerably across the 2009.0 spectroscopic event."," The $\lambda$ 10833 absorption line profile, as displayed in Figure \ref{fig1}, evolved considerably across the 2009.0 spectroscopic event." +" In all recordedspectra a relatively broad (100 Κπις-!), blueshifted emission feature is seen at --250km s!, and is due to gas in the equatorial plane of the Homunculus (Smith2002;Teodoroetal. 2008)."," In all recordedspectra a relatively broad $\sim100~\kms$ ), blueshifted emission feature is seen at $-250~\kms$ , and is due to gas in the equatorial plane of the Homunculus \citep{smith02, teodoro08}." +". The spectrum obtained at $=11.875, well before periastron, shows strong 410833 absorption extending from ~—150kms! up to an edge with velocity Vedge3-750 kms'!, with the strongest absorption occurring at Vblack&—580km s!."," The spectrum obtained at $\phi=11.875$, well before periastron, shows strong $\lambda$ 10833 absorption extending from $\sim-150~\kms$ up to an edge with velocity $\vedge \simeq -750~\kms$ , with the strongest absorption occurring at $\vblack\simeq-580~\kms$ ." + This value of Vplack from He1410833 is remarkablysimilar to those derived from UV resonancelines, This value of $\vblack$ from $\ion{He}{i} \lambda$ 10833 is remarkablysimilar to those derived from UV resonancelines +asteroids is about LO? (times the escape velocity from Scheila.,asteroids is about $^2$ times the escape velocity from Scheila. + At such a high speed. experiments show that a projectile can excavate 10* times its own mass [rom the target.," At such a high speed, experiments show that a projectile can excavate $^3$ times its own mass from the target." + However. the bulk of the ejecta moves too slowly lo escape.," However, the bulk of the ejecta moves too slowly to escape." + Specifically. the mass of the ejecta leaving wilh is comparable to the impactor mass (Figure 4 of Housen and Lolsapple 011).," Specifically, the mass of the ejecta leaving with is comparable to the impactor mass (Figure 4 of Housen and Holsapple 2011)." + Therefore. the impact hypothesis requires that Scheila be struck by a body having mass (Table 2)).," Therefore, the impact hypothesis requires that Scheila be struck by a body having mass (Table \ref{photometry}) )." + HE also of density p = 2000 ke . the impactor diameter would have been and the kinetic energv of the impact (about 0.1 MTonnes TNT equivalent).," If also of density $\rho$ = 2000 kg $^{-3}$, the impactor diameter would have been and the kinetic energy of the impact (about 0.1 MTonnes TNT equivalent)." + The resulting crater on Scheila would be of diameter Another possibility is that the coma is produced by sublimation of surface ice. as in (115816 ancl Jewitt 2006).," The resulting crater on Scheila would be of diameter Another possibility is that the coma is produced by sublimation of surface ice, as in (Hsieh and Jewitt 2006)." + Radio spectral line observations limit the production rate from Scheila to in the period December 14 - January 04. corresponding to mass production rates Fin water (Howell and Lovell 2011).," Radio spectral line observations limit the production rate from Scheila to in the period December 14 - January 04, corresponding to mass production rates in water (Howell and Lovell 2011)." + However. these production limits are model-dependent. and cannot exclude the possibility that Scheila. outgassed more strongly al earlier times. launching dust [rom the surface by the action of eas drag forces.," However, these production limits are model-dependent, and cannot exclude the possibility that Scheila outgassed more strongly at earlier times, launching dust from the surface by the action of gas drag forces." +" The energye. balance equation for sublimatinge ice may be written in which is the Solar Constant. £2, is the heliocentric distance expressed in AU. r, (n) is the nucleus radius. Ais the Bond albedo. e is the emissivitv. 7 (IX) the elfective temperature of the nucleus. L(T) (J +) the temperature-dependent latent heat of sublimation and the rate of sublimation of the ice per unit. area."," The energy balance equation for sublimating ice may be written in which is the Solar Constant, $R_{au}$ is the heliocentric distance expressed in AU, $r_n$ (m) is the nucleus radius, $A$ is the Bond albedo, $\epsilon$ is the emissivity, $T$ (K) the effective temperature of the nucleus, $L(T)$ (J $^{-1}$ ) the temperature-dependent latent heat of sublimation and the rate of sublimation of the ice per unit area." + Parameter 4 in Equation (5)) is a proxy [or the surlace temperature variation over (he surface of (he nucleus. itself dependent on the nucleus shape. thermal properties. rotation period and spin axis direction relative to (he Sun.," Parameter $\chi$ in Equation \ref{equilibrium}) ) is a proxy for the surface temperature variation over the surface of the nucleus, itself dependent on the nucleus shape, thermal properties, rotation period and spin axis direction relative to the Sun." +" To solve Equation (5)) requires additional knowledge of LCD) ancl dinαἱ,", To solve Equation \ref{equilibrium}) ) requires additional knowledge of $L(T)$ and $dm/dt$. + For (this. we use the saturation vapor pressures and latent heat data for ice from Washburn (1926).," For this, we use the saturation vapor pressures and latent heat data for ice from Washburn (1926)." + Allowable values of 4 lie in the range The hieh temperature limit. describes a flat. plate oriented with ils normal pointing towards the Sun. because then the absorbing and radiaiing areas are identical.," Allowable values of $\chi$ lie in the range The high temperature limit, describes a flat plate oriented with its normal pointing towards the Sun, because then the absorbing and radiating areas are identical." + This would approximate. for instance. the heating of the sunware pole on a nucleus whose," This would approximate, for instance, the heating of the sunward pole on a nucleus whose" +"where r=c(R,—R:)n is the equatorial optical depth.",where $\tau = \sigma (R_1-R_2)n_0$ is the equatorial optical depth. + The degree of polarization is given by p=|x|1. and the polarization position angle is given by Ψ=larg z.," The degree of polarization is given by $p=|z^*| = |z|$, and the polarization position angle is given by $\psi = \frac{1}{2} arg \,z$ ." + From Eqs. (29)), From Eqs. \ref{eq:fnorm}) ) +" and (30)). we can calculate the polarization and the scattered flux. using the properties of the two factors Ky and fj, that describe the envelope geometry and source anisotropy."," and \ref{eq:znorm}) ), we can calculate the polarization and the scattered flux, using the properties of the two factors $K_{l'}$ and $f_{l{\rm m}}$ that describe the envelope geometry and source anisotropy." +" Due to the symmetry of the functions chosen to describe the stellar flux and the scatterer density distribution. Ky and fj, are non-zero only for even / and /. respectively."," Due to the symmetry of the functions chosen to describe the stellar flux and the scatterer density distribution, $K_{l'}$ and $f_{l{\rm m}}$ are non-zero only for even $l'$ and $l$ , respectively." +" As mentioned above. the multipoles of the flux fj, are zero only for even /. and the spherical harmonics for />4 are important mainly for fairly large angular distortions of the star from sphericity."," As mentioned above, the multipoles of the flux $f_{l{\rm m}}$ are non-zero only for even $l$, and the spherical harmonics for $l\ge +4$ are important mainly for fairly large angular distortions of the star from sphericity." + As an example. Figures 2aa and b show the variation of fig for an oblate/prolate star distorted onlyalong its c-axis.," As an example, Figures \ref{fig2}a a and b show the variation of $f_{l0}$ for an oblate/prolate star distorted onlyalong its $c-$axis." +all “light” IMFs (Sehiavon et 22000: 33).,all “light” IMFs (Schiavon et 2000; 3). + Star formation likely proceeded very differently in massive elliptical galaxies than in the disks of spiral galaxies., Star formation likely proceeded very differently in massive elliptical galaxies than in the disks of spiral galaxies. + It is now thought that the progenitors of massive ellipticals were very compact. with average densities 220 .ppe? inside the effective radius (e.g.. 2008; 2008).," It is now thought that the progenitors of massive ellipticals were very compact, with average densities $\gtrsim +20$ $^{-3}$ inside the effective radius (e.g., 2008; 2008)." + These densities are similar to giant molecular clouds in the Milky Way. but given the ~kkpe scale of these galaxies the column densities would have been several orders of magnitude higher.," These densities are similar to giant molecular clouds in the Milky Way, but given the $\sim$ kpc scale of these galaxies the column densities would have been several orders of magnitude higher." + It will be interesting to measure the physical conditions in the star-forming progenitors of these galaxies and compare them to measurements in star-forming regions in the Milky Way (see. e.g.. 2010).," It will be interesting to measure the physical conditions in the star-forming progenitors of these galaxies and compare them to measurements in star-forming regions in the Milky Way (see, e.g., 2010)." + This study can be extended in many ways., This study can be extended in many ways. + The comparison between globular clusters and elliptical galaxies itself is model-independent. but we still rely on stellar population synthesis models to quantify how steep the IMF is in elliptical galaxies.," The comparison between globular clusters and elliptical galaxies itself is model-independent, but we still rely on stellar population synthesis models to quantify how steep the IMF is in elliptical galaxies." + The main uncertainty in these models is whether short-lived stellar evolution phases with unusual abundance patterns are missed. and this can be addressed by augmenting the spectral library.," The main uncertainty in these models is whether short-lived stellar evolution phases with unusual abundance patterns are missed, and this can be addressed by augmenting the spectral library." + Radial gradients in Nall and FeH can provide information on the spatial distribution of the dwarfs. which in turn. might reflect different formation mechanisms for the central of ellipticals and their. outskirts (e.g... 2010: 2010).," Radial gradients in I and FeH can provide information on the spatial distribution of the dwarfs, which in turn might reflect different formation mechanisms for the central of ellipticals and their outskirts (e.g., 2010; 2010)." + Some studies find steep gradients in Nall 1991). which might suggest that such effects could be important.," Some studies find steep gradients in I 1991), which might suggest that such effects could be important." + It will also be interesting to extend this study to elliptical galaxies of lower luminosity., It will also be interesting to extend this study to elliptical galaxies of lower luminosity. + There is good evidence that the dynamical M/L ratio of early-type systems scales with velocity dispersion (e.g.. 2006: 2008: 2010)," There is good evidence that the dynamical $M/L$ ratio of early-type systems scales with velocity dispersion (e.g., 2006; 2008; 2010)." + A varying IMF may be responsible for this trend(Treu 2010. Dutton et 22010). although some studies consider dark matter variations a more likely. possibility 2010).," A varying IMF may be responsible for this trend 2010, Dutton et 2010), although some studies consider dark matter variations a more likely possibility 2010)." + As noted by (2006) the dynamical M/L ratios of low luminosity ellipticals may, As noted by (2006) the dynamical $M/L$ ratios of low luminosity ellipticals may +(log ®=7.9).,(log $\Phi$ =7.9). +" We then explored the results of varying the only parameter in our set of assumptions that is not directly determined for the Barnard’s Loop, that is, the relative abundances of the heavy elements (Z/H)."," We then explored the results of varying the only parameter in our set of assumptions that is not directly determined for the Barnard's Loop, that is, the relative abundances of the heavy elements (Z/H)." +" We scaled all of the heavy elements together, thereby ignoring subtleties in things like the N/O ratio changes that can be expected from stellar evolution models."," We scaled all of the heavy elements together, thereby ignoring subtleties in things like the N/O ratio changes that can be expected from stellar evolution models." +" In this case we see that one obtains excellent agreement between the observations and the models with a log (Z/H) abundance enhancement of between 0.1 and 0.2, i.e. a heavy element abundance enhancement of about a factor of 1.4."," In this case we see that one obtains excellent agreement between the observations and the models with a log (Z/H) abundance enhancement of between 0.1 and 0.2, i.e. a heavy element abundance enhancement of about a factor of 1.4." + The more diagnostically useful figure is the low-ionization color-color ratio because of its insensitivity to contamination by scattered light and Figure 5 will be used for discussion., The more diagnostically useful figure is the low-ionization color-color ratio because of its insensitivity to contamination by scattered light and Figure 5 will be used for discussion. +" It is important to understand that the locus of points tracked by the models of various abundances is a result of both the number of elements of that species available for emitting the emission line, but also ((the emissivity of the collisionally excited [S II] and [N II] lines increasing with aand the emissivity of the recombination ddecreasing with Το)."," It is important to understand that the locus of points tracked by the models of various abundances is a result of both the number of elements of that species available for emitting the emission line, but also (the emissivity of the collisionally excited [S II] and [N II] lines increasing with and the emissivity of the recombination decreasing with )." + A track from lowest Z/H to highest Z/H models is a monotonic progression from high to lowΤο., A track from lowest Z/H to highest Z/H models is a monotonic progression from high to low. +" Comparison of our models with varying abundances with the three sets of observations of Barnard's Loop (this study, (Peimbertetal.1975),, (Madsenetal. 2006))) still indicates that the best agreement is when there is an enrichment of heavy elements by between 0.1 and 0.2 dex."," Comparison of our models with varying abundances with the three sets of observations of Barnard's Loop (this study, \citep{pei75}, \citep{mad06}) ) still indicates that the best agreement is when there is an enrichment of heavy elements by between 0.1 and 0.2 dex." + We also considered the high-ionization color-color diagram because the [O III] 5007 lline was detected by Madsenetal.(2006) in several of their samples of Barnard's Loop., We also considered the high-ionization color-color diagram because the [O III] 5007 line was detected by \citet{mad06} in several of their samples of Barnard's Loop. + In each case there was significant disagreement with the models best fitting the low-ionization color-color diagram in the sense that there was excess [O III] emission., In each case there was significant disagreement with the models best fitting the low-ionization color-color diagram in the sense that there was excess [O III] emission. + In the same way, In the same way + , +tests.,tests. + The internal characteristics of four of these models are presented in Table 6 and their echelle diagrams are displayed in Fig., The internal characteristics of four of these models are presented in Table \ref{tab6} and their echelle diagrams are displayed in Fig. + 8 (middle and lower panels)., \ref{fig8} (middle and lower panels). + Models with = 0.001 and 0.002 are undistinguishable from models without overshooting., Models with = 0.001 and 0.002 are undistinguishable from models without overshooting. + The more overshooting is added at the edge of the stellar core. the more the evolutionary time scales are increased. às can be seel in Fig. 7..," The more overshooting is added at the edge of the stellar core, the more the evolutionary time scales are increased, as can be seen in Fig. \ref{fig7}." + The developpement of the convective core Is increased during a longer main sequence phase., The developpement of the convective core is increased during a longer main sequence phase. + The models that have a mean large separation of 90 μΗΖ are not in the same evolutiorary stage. depending on the value ofca. and they do not have the same internal structure.," The models that have a mean large separation of 90 $\mu$ Hz are not in the same evolutionary stage, depending on the value of, and they do not have the same internal structure." +" Models with o, 0.002 are at the beginning of the subgiant branch. as are models without overshooting."," Models with $<$ 0.002 are at the beginning of the subgiant branch, as are models without overshooting." + When Increases. with a value between 0.002 and 0.10. the models are in the phase of contraction of the convective core.," When increases, with a value between 0.002 and 0.10, the models are in the phase of contraction of the convective core." +" And finally. for «a,» 0.10. the nodels are at the end of the main sequence."," And finally, for $>$ 0.10, the models are at the end of the main sequence." +" This difference of evolutionary stages explains that the central helium abundance ts lower for models with a higher overshooting parameter,", This difference of evolutionary stages explains that the central helium abundance is lower for models with a higher overshooting parameter. + We studied the evolution of the oscillation frequencies when increases., We studied the evolution of the oscillation frequencies when increases. + For small values of overshooting = 0.001] and = 0.002). there is no visible influence on the oscillations frequencies.," For small values of overshooting = 0.001 and = 0.002), there is no visible influence on the oscillations frequencies." + For = 0.005. the reduced v is a little higher (y= 1.66) than for the model without overshooting.," For = 0.005, the reduced $\chi^2$ is a little higher $\chi^2=1.66$ ) than for the model without overshooting." + We can see on the echelle diagram (Fig. 8..," We can see on the echelle diagram (Fig. \ref{fig8}," + middle-left panel) that the lines £=ο - ἓ=2 are closer for high frequencies., middle-left panel) that the lines $\ell=0$ - $\ell=2$ are closer for high frequencies. + Por = 0.01. these lines cross at vy = 2.6 mHz. as can be seen in the echelle diagram (Fig. 8..," For = 0.01, these lines cross at $\nu$ = 2.6 mHz, as can be seen in the echelle diagram (Fig. \ref{fig8}," + middle-right panel)., middle-right panel). + The y has increased: 1.73., The $\chi^2$ has increased: 1.73. + For higher values of (a 0.01). the crossing point appears for lower frequencies decreasing for increasing (Fig. 8..," For higher values of $>$ 0.01), the crossing point appears for lower frequencies decreasing for increasing (Fig. \ref{fig8}," + lower panels)., lower panels). + Their y value is high (2.45 and 3.04. respectively).," Their $\chi^2$ value is high (2.45 and 3.04, respectively)." + These models do not fit the observations., These models do not fit the observations. + We conclude from these computations that the overshooting parameter is small in µ Arae. less than 0.01.," We conclude from these computations that the overshooting parameter is small in $\mu$ Arae, less than 0.01." + Let us recall however that in these computations overshooting is simply treated as an extension of the convective core., Let us recall however that in these computations overshooting is simply treated as an extension of the convective core. + We have demonstrated that the seismic analysis of stars is able to give precise constraints on their central mixed zone., We have demonstrated that the seismic analysis of stars is able to give precise constraints on their central mixed zone. + This does not exclude other kinds of mild macroscopic motions. plumes for instance. provided they do not lead to complete mixing.," This does not exclude other kinds of mild macroscopic motions, plumes for instance, provided they do not lead to complete mixing." + This new analysis of the star jj Arae confirms that seismology is very powerful and can provide precise values of the stellar parameters with the help of spectroscopy to raise the final degeneracy between the best computed models., This new analysis of the star $\mu$ Arae confirms that seismology is very powerful and can provide precise values of the stellar parameters with the help of spectroscopy to raise the final degeneracy between the best computed models. + The procedure we use may be summarized as follows., The procedure we use may be summarized as follows. + The parameters found for ij. Arae are given in Table 7.., The parameters found for $\mu$ Arae are given in Table \ref{tab7}. + The uncertainties have been tentatively evaluated by allowing a possible y increase of 0.1 for each set of models and an uncertainty of 0.1 on the mixing length parameter., The uncertainties have been tentatively evaluated by allowing a possible $\chi^2$ increase of 0.1 for each set of models and an uncertainty of 0.1 on the mixing length parameter. + They take into account that all computations done with various sets of chemical parameters converge on the same model values., They take into account that all computations done with various sets of chemical parameters converge on the same model values. + One must keep in mind however that these uncertainties do not include systematic effects which would oceur if stellar physics, One must keep in mind however that these uncertainties do not include systematic effects which would occur if stellar physics +redshift clusters (0.2—:0.8) as still debated.,redshift clusters $0.2100) in cluster is needed so that the relatively few E|A ealaxies can be identified., A statistically representative sample of members $>100$ ) in cluster is needed so that the relatively few E+A galaxies can be identified. + Membership confirmation aud E|A selection can oulv be accomplished reliably by obtaining spectra., Membership confirmation and E+A selection can only be accomplished reliably by obtaining spectra. + Iu addition. ligh resolution imaging is uceded at these redshifts (2>0.3) to determine physical properties such as structural parameters aud morphological tvpe.," In addition, high resolution imaging is needed at these redshifts $z>0.3$ ) to determine physical properties such as structural parameters and morphological type." + Oulv by pairing wide-field HST/WFEDPC?2 tuagine with deep eround-based spectroscopy can we adequately study. the E|A ealaxies iu intermediate redshift clusters., Only by pairing wide-field HST/WFPC2 imaging with deep ground-based spectroscopy can we adequately study the E+A galaxies in intermediate redshift clusters. +" From extensive spectroscopic surveys of CLI358 0.33:7)... MS2053 (2=0,58:ιν and MS1051 (2=0.83:22?) awe select 16 E|A candidates from 500 coufirmes cluster members."," From extensive spectroscopic surveys of CL1358 \citep[$z=0.33$;][]{fisher:98}, MS2053 \citep[$z=0.58$;][]{tran:02}, and MS1054 \citep[$z=0.83$;][]{tran:99,vandokkum:00,tran:02}, we select 46 E+A candidates from $\sim500$ confirmed cluster members." +" Using UST/WEPC2 mosaics taken of each cluster (all to pee;~1h Alpe}. we measure the colors. magnitudes. halflisht radi. bulge-to-tota fractions. deeree of galaxy asvuuuetry., and morplologica type of the cluster members."," Using HST/WFPC2 mosaics taken of each cluster (all to $R_{BCG}\sim1$ Mpc), we measure the colors, magnitudes, half-light radii, bulge-to-total fractions, degree of galaxy asymmetry, and morphological type of the cluster members." +" With LRIS (7?) ou eck. we also have measured internal velocity dispersions for 120 cluster members (27?7,JIK005).."," With LRIS \citep{oke:95} on Keck, we also have measured internal velocity dispersions for 120 cluster members \citep[K00b]{kelson:97,vandokkum:98b,kelson:01,kelson:03a}." + With these measure dispersions. accurate colors. and the Fundamental Plane (27).. we estimate velocity dispersions for the remainder of the sample.," With these measured dispersions, accurate colors, and the Fundamental Plane \citep{faber:87,djorgovski:87}, we estimate velocity dispersions for the remainder of the sample." + Using the E|A’s that satisfy our strict selection criteria. we determine the E|A fraction in intermediate redshift clusters. ideutifv characteristics of their pareut population. address what the desceudauts of these galaxies can boe. aud discuss the Likely downu-siziug of this population.," Using the E+A's that satisfy our strict selection criteria, we determine the E+A fraction in intermediate redshift clusters, identify characteristics of their parent population, address what the descendants of these galaxies can be, and discuss the likely down-sizing of this population." + A brief description of the HIST/WFEPC?2 imagine and eround-based spectroscopy is provided in 822., A brief description of the HST/WFPC2 imaging and ground-based spectroscopy is provided in 2. + We describe our E|A selection criteria and address the discrepancy in the cluster. E|A fraction found. bv. different surveys in 833., We describe our E+A selection criteria and address the discrepancy in the cluster E+A fraction found by different surveys in 3. + After identifvine the cluster E|A population. we exiununme the nature of these systems m 8h.," After identifying the cluster E+A population, we examine the nature of these systems in 4." + We discuss their properties and evolution in $55. and present our conclusions in 866.," We discuss their properties and evolution in 5, and present our conclusions in 6." +" Unless otherwise noted. we use Qa,=0.3.04= 0.7. aud Wy=1005 + in this paper."," Unless otherwise noted, we use $\Omega_M=0.3, +\Omega_{\Lambda}=0.7$ , and $H_0=100h$ $^{-1}$ in this paper." + We select E|A ealaxies from a larec program stucving three N-vayv huuinous clusters at +=0.33.0.58.&0.83 (Table ??.. references therein).," We select E+A galaxies from a large program studying three X-ray luminous clusters at $z=0.33,~0.58,~\&~0.83$ (Table \ref{clusters}, references therein)." + Our dataset combines IST/WEPC2 iosaics (cach to Προς~1 Mpc) of these clusters with exteusive eround-hbased spectroscopy., Our dataset combines HST/WFPC2 mosaics (each to $R_{BCG}\sim1$ Mpc) of these clusters with extensive ground-based spectroscopy. +" Frou the spectroscopy. we determine spectral types for all members (277) aswell as measure internal kinematics for a subset (227?, IKO0b).."," From the spectroscopy, we determine spectral types for all members \citep{fisher:98,vandokkum:00,tran:02} as well as measure internal kinematics for a subset \citep[K00b]{kelson:97,vandokkum:98b,kelson:01,kelson:03a}. ." + From over 1200 redshifts obtained in thethree fields. we isolate ~500 cluster members.," From over 1200 redshifts obtained in thethree fields, we isolate $\sim500$ cluster members." + Here we describe bricty the spectra aud photometry used iu this paper., Here we describe briefly the spectra and photometry used in this paper. +The amount of IGL can be inferred from the stellar light associated with the IGPNe.,The amount of IGL can be inferred from the stellar light associated with the IGPNe. + This can be computed considering the luminosity specific planetary nebulae density (a)., This can be computed considering the luminosity specific planetary nebulae density $\alpha$ ). + In Aguerri et al. (, In Aguerri et al. ( +2005) we discussed the different possible values of a. and used three representative values. which will be the same adopted in the present work.,"2005) we discussed the different possible values of $\alpha$, and used three representative values, which will be the same adopted in the present work." + For HCG44 the [OI] limiting magnitude is 0.62 magnitudes fainter than the PNLF bright cut-off at the distance of the group., For HCG44 the [OIII] limiting magnitude is 0.62 magnitudes fainter than the PNLF bright cut-off at the distance of the group. + This means that the brightest 0.5 magnitude of the PNLF ts accessible to our photometry., This means that the brightest 0.5 magnitude of the PNLF is accessible to our photometry. + Then. we will use the value of «5.5 for computing the stellar ight associated with the IGPNe.," Then, we will use the value of $\alpha_{0.5,B}$ for computing the stellar light associated with the IGPNe." + But. only 4/6 of the selected emission line objects as IGPNe are brighter then M 0.5. being M the PNLF bright cut-off.," But, only 4/6 of the selected emission line objects as IGPNe are brighter then $M^{*}+0.5$ , being $M^{*}$ the PNLF bright cut-off." + We will consider this 41 IGPNe to compute the stellar light associated with them., We will consider this $4^{+1}_{-0}$ IGPNe to compute the stellar light associated with them. + One value of a corresponds to that obtained for the bulge of M31 (Ciardullo et al., One value of $\alpha$ corresponds to that obtained for the bulge of M31 (Ciardullo et al. +" 1989). which is qos,=2.9x107°."," 1989), which is $\alpha_{0.5,B}=2.9\times 10^{-9}$." + Then. the luminosity of the IGL associated to this value in HCG44 is 137x107Lag.," Then, the luminosity of the IGL associated to this value in HCG44 is $\times 10^{9} +L_{\odot,B}$." + The second value of aos=4.12x107 results from the RGB intracluster stellar population observec in Virgo cluster by Durrell et al. (," The second value of $\alpha_{0.5,B}=4.12\times 10^{-9}$ results from the RGB intracluster stellar population observed in Virgo cluster by Durrell et al. (" +2002).,2002). + For that value. the luminosity of the IGL in HCG 44 is 0.97x10?Lis.," For that value, the luminosity of the IGL in HCG 44 is $\times 10^{9} L_{\odot,B}$." + The thirc value of « was taken from the «-color relation discovered by Hui et al. (, The third value of $\alpha$ was taken from the $\alpha$ -color relation discovered by Hui et al. ( +1993).,1993). + The mean B-V of the galaxies of HCG 44 is 0., The mean B-V of the galaxies of HCG 44 is . +757... Then. according to the a-color relation of Hui et al. (," Then, according to the $\alpha$ -color relation of Hui et al. (" +"1993) we have aus,=4.67x107°. the luminosity of the IGL is 100.85xL4.","1993) we have $\alpha_{0.5,B}=4.67\times 10^{-9}$, the luminosity of the IGL is $\times 10^{9} L_{\odot,B}$." + Taking the mean of these numbers we give an upper limit of the luminosity of the IGL in HCG 44 of 1071.06xLen.," Taking the mean of these numbers we give an upper limit of the luminosity of the IGL in HCG 44 of $\times 10^{9} L_{\odot,B}$." + We can compare the luminosity of the [GL with the luminosity of the galaxies of HCG 44., We can compare the luminosity of the IGL with the luminosity of the galaxies of HCG 44. + According to their apparent B. magnitudes (see Table 1) the total light from the HCG44 galaxies is 2.1510!Lj: then the upper limit of the IGL contribution is 4.766.," According to their apparent B magnitudes (see Table 1) the total light from the HCG44 galaxies is $\times +10^{10} L_{\odot,B}$; then the upper limit of the IGL contribution is $\%$." + We have also computed the surface brightness of the diffuse light in HCG44., We have also computed the surface brightness of the diffuse light in HCG44. + The adopted area is given by the circle centered on the group center. and with a radius equal to the distance to the center of the most distant IGPNe in our sample.," The adopted area is given by the circle centered on the group center, and with a radius equal to the distance to the center of the most distant IGPNe in our sample." + This corresponds to an area of 581.06 aremin?., This corresponds to an area of 581.06 $^{2}$. + Thus. the resulting surface brightness of the diffuse light in HCGA4 is Hp=30.04 mag 4aresec7.," Thus, the resulting surface brightness of the diffuse light in HCG44 is $\mu_{B}=30.04$ mag $^{-2}$." + The amount of intragroup light depends on the adopted distance modulus of HCG44., The amount of intragroup light depends on the adopted distance modulus of HCG44. + Williams et al. (, Williams et al. ( +1991) reported an error of 0.2 to the measured distance modulus of this group.,1991) reported an error of 0.2 to the measured distance modulus of this group. + When this error in the distance is taken into account. the number of possible IGPNe would be 41.," When this error in the distance is taken into account, the number of possible IGPNe would be $4^{+1}_{-0}$." + Similar numbers are found when we considered the distance to the group to be 21.7 Mpe as inferred from the Virgo infall model to NGC 3185 and NGC 3190., Similar numbers are found when we considered the distance to the group to be 21.7 $Mpc$ as inferred from the Virgo infall model to NGC 3185 and NGC 3190. + The fraction of diffuse light in the group is 4.7116€ in both cases., The fraction of diffuse light in the group is $4.7^{+1.7}_{-0.2} \%$ in both cases. + Diffuse light has so far always been observed in gravitationally bound systems such as galaxy groups or clusters., Diffuse light has so far always been observed in gravitationally bound systems such as galaxy groups or clusters. + Numerical simulations of galaxy clusters 1n. hierarchical. cosmologies predict that the amount of diffuse light depends directly on the cluster mass (Murante et al., Numerical simulations of galaxy clusters in hierarchical cosmologies predict that the amount of diffuse light depends directly on the cluster mass (Murante et al. + 2004). and the dynamical status (Sommer-Larsen 2006: Rudick et al.," 2004), and the dynamical status (Sommer-Larsen 2006; Rudick et al." + 2006)., 2006). + Simulations also indicate that most of the diffuse light is created during interactions and major mergers resulting in the largest cluster dominant elliptical galaxies (Murante et al..," Simulations also indicate that most of the diffuse light is created during interactions and major mergers resulting in the largest cluster dominant elliptical galaxies (Murante et al.," + in. preparatior, in preparation). + These predictions are consistent with the observations in the Virgo cluster where important amounts of diffuse light have been observed in regions near the dominant galaxy M87 and the subgroup formed by M84 and M86 (Aguerri et al., These predictions are consistent with the observations in the Virgo cluster where important amounts of diffuse light have been observed in regions near the dominant galaxy M87 and the subgroup formed by M84 and M86 (Aguerri et al. + 2005: Mihos et al., 2005; Mihos et al. + 2005)., 2005). + HCG 44 was catalogued by Hickson (1982) as a galaxy group formed by four members., HCG 44 was catalogued by Hickson (1982) as a galaxy group formed by four members. + However. SBF measurements of the elliptical galaxy. NGC 3193. showed that this galaxy is at a larger distance than the rest of the group (Tonry et al.," However, SBF measurements of the elliptical galaxy, NGC 3193, showed that this galaxy is at a larger distance than the rest of the group (Tonry et al." + 2001)., 2001). + Two of the spiral galaxies. NGC 3190 and NGC3187. show morphological distortions which indicate the interaction between them.," Two of the spiral galaxies, NGC 3190 and NGC3187, show morphological distortions which indicate the interaction between them." + This interaction ts also visible through the faint HI bridge between the two galaxies (Williams et al., This interaction is also visible through the faint HI bridge between the two galaxies (Williams et al. +" 1991),", 1991). + Pildis et al. (, Pildis et al. ( +19952) did not find an extended X-ray emission in HCG 44. Ponman et al. (,"1995a) did not find an extended X-ray emission in HCG 44, Ponman et al. (" +"1996) gave an upper limit of the X-ray emission of this group. being Ly<7x10"" erg s7l.","1996) gave an upper limit of the X-ray emission of this group, being $L_{X}<7\times 10^{40}$ erg $^{-1}$." + This probably means that this group does not have a deep potential well., This probably means that this group does not have a deep potential well. + Those results together with the low upper limit of diffuse light in HCG 44 indicate that HCG 44 1s not a dynamically evolved system. or only the two spiral galaxies are group members.," Those results together with the low upper limit of diffuse light in HCG 44 indicate that HCG 44 is not a dynamically evolved system, or only the two spiral galaxies are group members." + This would fit well in the framework of Diatferio et al. (, This would fit well in the framework of Diaferio et al. ( +1994) which suggests that compact groups with low or no X-ray emission and containing galaxies with signs of interactions would have formed only recently.,1994) which suggests that compact groups with low or no X-ray emission and containing galaxies with signs of interactions would have formed only recently. + The fact that HCG 44 15 not a dynamically evolved system opens a long posed question about the dynamical state of these galaxy associations., The fact that HCG 44 is not a dynamically evolved system opens a long posed question about the dynamical state of these galaxy associations. + The Hickson (1982) catalog is basec on projected galaxy properties. and a large fraction of those cataloged às compact groups may not be physically relatec galaxy systems or dynamically evolved systems.," The Hickson (1982) catalog is based on projected galaxy properties, and a large fraction of those cataloged as compact groups may not be physically related galaxy systems or dynamically evolved systems." + As mentioned before the detection of diffuse light in clusters Is always associated with gravitationally bound galaxy associations. anc its amount depends on the dynamical evolution of the system (Sommer-Larsen 2006: Rudick et al.," As mentioned before the detection of diffuse light in clusters is always associated with gravitationally bound galaxy associations, and its amount depends on the dynamical evolution of the system (Sommer-Larsen 2006; Rudick et al." + 2006)., 2006). + Thus. the detectior of diffuse light in galaxy groups can tell us about the dynamical state of the system.," Thus, the detection of diffuse light in galaxy groups can tell us about the dynamical state of the system." + Several studies of diffuse light in groups have been carried out in the past., Several studies of diffuse light in groups have been carried out in the past. + Pilis et al. (, Pilis et al. ( +1995b) studied the diffuse component in 12 Hickson Compact Groups.,1995b) studied the diffuse component in 12 Hickson Compact Groups. + They found that only one of the groups contained a significant amount of diffuse light., They found that only one of the groups contained a significant amount of diffuse light. + Feldmeier et al. (, Feldmeier et al. ( +2003b) and Castro-Rodrigguez et al. (,2003b) and guez et al. ( +2003) searched for IGPNe in the M81 and the Leo groups. respectively.,"2003) searched for IGPNe in the M81 and the Leo groups, respectively." + They found that a few percent ofthe light in these groups is located in the intragroup regions., They found that a few percent ofthe light in these groups is located in the intragroup regions. + In contrast. White," In contrast, White" +of l/(dv./dr/H+1) are not.,of $1 / (dv_r/dr/H + 1)$ are not. +" The bias to higher values is further enhanced when weighted by the local density as in the ὅΤε expression, A/(dv,/dr/Η+1)."," The bias to higher values is further enhanced when weighted by the local density as in the $\delT$ expression, $\Delta / (dv_r/dr/H + 1)$." +" Intuitively, infall in overdense regions causes photons emitted there to travel farther in order to reach fixed relative redshift; therefore the optical depth and 67) are increaseda in 6> regions (?).."," Intuitively, infall in overdense regions causes photons emitted there to travel farther in order to reach a fixed relative redshift; therefore the optical depth and $\delT$ are increased in $\delta > 0$ regions \citep{BL05}." +" To further explore0 this effect and compare our results with simulations, in Fig. 6,,"," To further explore this effect and compare our results with simulations, in Fig. \ref{fig:just_ratios}," +" we plot the ratio of the 21- power spectra, T(z)?A2,(k,z), computed including peculiar velocities to those not including peculiar velocities."," we plot the ratio of the 21-cm power spectra, $\bar{\delT}(z)^2 \Delta^2_{21}(k, z)$, computed including peculiar velocities to those not including peculiar velocities." + The thin solid red curve in the upper panel corresponds to a fully neutral universe at z—9., The thin solid red curve in the upper panel corresponds to a fully neutral universe at $z=9$. +" The hydrodynamic simulations go down to much smaller scales than plotted in Fig. 5,,"," The hydrodynamic simulations go down to much smaller scales than plotted in Fig. \ref{fig:just_ratios_large_box}," +" which are more non-linear and hence show a larger enhancement of power, though we confirm that most of this is due to the evolution in the mean signal, 97;(z)?."," which are more non-linear and hence show a larger enhancement of power, though we confirm that most of this is due to the evolution in the mean signal, $\bar{\delT}(z)^2$." + This enhanced 21-cm power from non-linear peculiar velocities obviously merits more investigation beyond the scope of this paper., This enhanced 21-cm power from non-linear peculiar velocities obviously merits more investigation beyond the scope of this paper. + Therefore we defer further analysis to future work., Therefore we defer further analysis to future work. +" We caution however that it is unclear how well we can estimate this enhancement, due to the misuse of the 1/(dv,/dr/H+1) term in eq. (1))."," We caution however that it is unclear how well we can estimate this enhancement, due to the misuse of the $1/(dv_r/dr/H+1)$ term in eq. \ref{eq:delT}) )." +" This expression assumes that dvu./dr 40$ kyr for any threshold. + Ελπίς is caused. by the eventual growth of the regions in spite of the flickering., This is caused by the eventual growth of the regions in spite of the flickering. + There is some indication that the probabilities for negative changes also decrease at timescales shorter than 1 kyr. specially for Hux- thresholds larger than 50% (see Figs.," There is some indication that the probabilities for negative changes also decrease at timescales shorter than 1 kyr, specially for flux-change thresholds larger than $50~\%$ (see Figs." + S and 9)., 8 and 9). + This is also suggested. from the analysis of the high temporal-resolution data in the next section., This is also suggested from the analysis of the high temporal-resolution data in the next section. + Although Hux increments are more likely than decrements for any given. threshold and time lag. a novel result. of these simulations is that negative [Lux changes do happen. in contrast with the simple expectation of ever growing regions.," Although flux increments are more likely than decrements for any given threshold and time lag, a novel result of these simulations is that negative flux changes do happen, in contrast with the simple expectation of ever growing regions." + We re-ran four time intervals in each of Run A and tun D. spanning a few hundred: vears cach. ancl producing data dumps at each simulation step (10 vr).," We re-ran four time intervals in each of Run A and Run B, spanning a few hundred years each, and producing data dumps at each simulation step $\sim 10$ yr)." + These time intervals were selected to contain a pair of negative/positive lux changes to investigate the correlation of lux variations with physical changes in the region. like size and density (next section).," These time intervals were selected to contain a pair of negative/positive flux changes to investigate the correlation of flux variations with physical changes in the region, like size and density (next section)." + Pherefore. they may not be representative of the entire simulation. but since it is not feasible to re-run the entire simulations producing data dumps at the üehest temporal resolution. we use these data to constrain he expected Hux variations in observable timescales.," Therefore, they may not be representative of the entire simulation, but since it is not feasible to re-run the entire simulations producing data dumps at the highest temporal resolution, we use these data to constrain the expected flux variations in observable timescales." + We, We +galaxies have larger metallicities in the outskirts than in the center (where the center is defined as the maximum of the flux).,galaxies have larger metallicities in the outskirts than in the center (where the center is defined as the maximum of the flux). + About 1/4 of our sample galaxies thus show a positive metallicity gradient at à >Io confidence level (see blue area in 5)., About 1/4 of our sample galaxies thus show a positive metallicity gradient at a $>1\sigma$ confidence level (see blue area in ). + Of these. VVDS220376206 displays a positive gradient with 2c confidence. while in the galaxies VVDS140217425 and VVDS220014252 a positive gradient of ~0.02 is detected with >Sc confidence.," Of these, VVDS220376206 displays a positive gradient with $2\sigma$ confidence, while in the galaxies VVDS140217425 and VVDS220014252 a positive gradient of $\sim0.02$ is detected with $>5\sigma$ confidence." + Among the seven galaxies. four are classified as interacting systems. while the three other are isolated.," Among the seven galaxies, four are classified as interacting systems, while the three other are isolated." + One of the isolated galaxies. the secure case VVDS140217425. appears as a “chained-galaxy™ with large clumps in the outskirts that could be interpreted as minor mergers.," One of the isolated galaxies, the secure case VVDS140217425, appears as a “chained-galaxy”, with large clumps in the outskirts that could be interpreted as minor mergers." + About half (4/8) of the interacting galaxies have a positive metallicity gradient while it concerns only 3/16 (20%)) of the isolated ones., About half (4/8) of the interacting galaxies have a positive metallicity gradient while it concerns only 3/16 $\sim 20$ ) of the isolated ones. + We thus teitatively conclude that the majority of the galaxies showing a positive metallicity gradient are interacting., We thus tentatively conclude that the majority of the galaxies showing a positive metallicity gradient are interacting. + It is interesting to note also that among the four interacting systems. one galaxy only ts classified as a rotating disk.," It is interesting to note also that among the four interacting systems, one galaxy only is classified as a rotating disk." + On the other hand. five galaxies display clear negative metallicity gradients at à >lo confidence level (of which one at 2c and three at >3c confidence level: see and Table 3)).," On the other hand, five galaxies display clear negative metallicity gradients at a $>1\sigma$ confidence level (of which one at $>2\sigma$ and three at $>3\sigma$ confidence level; see and Table \ref{metal}) )." + Among these five galaxies. three are isolated and two are interacting.," Among these five galaxies, three are isolated and two are interacting." + Four of these five galaxies are classified as rotating disks., Four of these five galaxies are classified as rotating disks. + Although rare. this is not the first time that positive gradients of oxygen abundance were found.," Although rare, this is not the first time that positive gradients of oxygen abundance were found." + Recently. ? reported a positive gradient in a local galaxy and proposed several scenarios to explain their discovery: (1) a radial redistribution of the metal-rich gas produced in the nucleus. (11) supernovae blowing out metal-rich gas. enriching the IGM. then falling onto the outer parts of the disk. (im) the result of a past interaction.," Recently, \citet{werk10} reported a positive gradient in a local galaxy and proposed several scenarios to explain their discovery: (i) a radial redistribution of the metal-rich gas produced in the nucleus, (ii) supernovae blowing out metal-rich gas, enriching the IGM, then falling onto the outer parts of the disk, (iii) the result of a past interaction." + At high redshift. ? have recently studied with SINFONI the metallicity distribution of three Lyman-break galaxies at zo 3an the AMAZE/LSD sample.," At high redshift, \cite{cresci10} have recently studied with SINFONI the metallicity distribution of three Lyman-break galaxies at $z\sim 3$ in the AMAZE/LSD sample." + They were able to derive metallicity maps for the three galaxies. with high SNR., They were able to derive metallicity maps for the three galaxies with high SNR. + In each case. they discovered a positive gradient. comparable to the ones we have found.," In each case, they discovered a positive gradient, comparable to the ones we have found." + They favour the scenario m which these positive. gradients would be produced by the infall of metal-poor gas into the center of the disks. diluting the gas and lowering its metallicity in the central regions.," They favour the scenario in which these positive gradients would be produced by the infall of metal-poor gas into the center of the disks, diluting the gas and lowering its metallicity in the central regions." +" The authors claim that the discovery of positive gradients in high-redshift disks. pre-selected to be ""isolated"". is a direct evidence for cold gas accretion as a mechanism of mass assembly."," The authors claim that the discovery of positive gradients in high-redshift disks, pre-selected to be “isolated”, is a direct evidence for cold gas accretion as a mechanism of mass assembly." + Such a conclusion could be balanced arguing that a merger remnant can keep. during a transient phase with a typical timescale of ~0.5 Gyrs. an inversed metallicity gradient (eg.??)..," Such a conclusion could be balanced arguing that a merger remnant can keep, during a transient phase with a typical timescale of $\sim 0.5$ Gyrs, an inversed metallicity gradient \citep[eg.][]{perez11, torrey11}." + In contrast. our study appearss to show that among the seven detected positive gradients. only two galaxies are isolated. the others showing signs of interaction.," In contrast, our study appears to show that among the seven detected positive gradients, only two galaxies are isolated, the others showing signs of interaction." + Cold gas accretion toward the center of disks might thus not be the only process able to lower the central metallicity., Cold gas accretion toward the center of disks might thus not be the only process able to lower the central metallicity. +would argue that a viscosity of some kind is useful we would argue that it is much better to consider a physical viscosity that acts continually.,would argue that a viscosity of some kind is useful we would argue that it is much better to consider a physical viscosity that acts continually. + Llowever. while we do not believe that the artificial Viscosity method is the most instructive it is a method that has served the community for many vears and. as such. one must entertain the possibility that the solutions founc about might in some way be the result of the lack of the inclusion of an artificial viscosity.," However, while we do not believe that the artificial viscosity method is the most instructive it is a method that has served the community for many years and, as such, one must entertain the possibility that the solutions found about might in some way be the result of the lack of the inclusion of an artificial viscosity." + As such. for completeness we here examine the 32° caleulation with the artificial viscosity term included and where €'22.0 as is standard.," As such, for completeness we here examine the $32^{3}$ calculation with the artificial viscosity term included and where $C=2.0$ as is standard." + Εις implies that smoothing is carried out over two cells., This implies that smoothing is carried out over two cells. + Further discussion of the artificial viscosity can be found in Llawley. and Stone&Norman(1992)., Further discussion of the artificial viscosity can be found in \cite{HGB1} and \cite{SN92}. +. Figure 5 shows that the same global trend is witnessed in this case as in the case where there is no artificial viscosity included., Figure \ref{alphafullav} shows that the same global trend is witnessed in this case as in the case where there is no artificial viscosity included. +" ""This shows that the inclusion. of an artificial Viscosity does not change the result found above.", This shows that the inclusion of an artificial viscosity does not change the result found above. + The behaviour witnessed above is fully explained. by an examination of what occurs to the mean of the various components., The behaviour witnessed above is fully explained by an examination of what occurs to the mean of the various components. + Many of these components should formally be zero but the interpolation necessary in the implementation of the shearing boundary conditions give rise to errors as shown in figure 6.., Many of these components should formally be zero but the interpolation necessary in the implementation of the shearing boundary conditions give rise to errors as shown in figure \ref{Bcomps}. + Phese errors have been mentioned before in earlier calculations Hawlev.Gammie&Balbus(1995)., These errors have been mentioned before in earlier calculations \cite{HGB}. +". llowever. many of the carly caleulations were for short time spans and there the error was stated to be about 10.ος,"," However, many of the early calculations were for short time spans and there the error was stated to be about $10^{-3}c_s$." + while we confirm that this is true for small numbers of orbits this is not true in the long term., while we confirm that this is true for small numbers of orbits this is not true in the long term. +" In fact. as figure 6 shows the mean D; and D, fields both grow and tha the By field. &rows to such and extent that it becomes of ereater magnitude."," In fact, as figure \ref{Bcomps} shows the mean $B_z$ and $B_y$ fields both grow and that the By field grows to such and extent that it becomes of greater magnitude." +" We note here that the numerical methoc emplovecl prevents 2, from obtaining significant error.", We note here that the numerical method employed prevents $B_x$ from obtaining significant error. +" The constrained transport forces D, to stay constant to rounc olf because it is evolved. with the emf components ££, am fe. which ave strictly. periodic and hence D, is conserved to round. olf error.", The constrained transport forces $B_x$ to stay constant to round off because it is evolved with the emf components $E_y$ and $E_z$ which are strictly periodic and hence $B_x$ is conserved to round off error. +" Llowever. both D, and D; have some error due to the shearing box interpolation in £5."," However, both $B_y$ and $B_z$ have some error due to the shearing box interpolation in $E_x$." + 1t we are to obtain a valid long-term average for a then we need to remove this error. which compounds to give us an Unintentional switch in the mean field.," If we are to obtain a valid long-term average for $\alpha$ then we need to remove this error, which compounds to give us an unintentional switch in the mean field." + As such we proceed bv forcing all mean values to their mathematically formal values by removing the error at set intervals., As such we proceed by forcing all mean values to their mathematically formal values by removing the error at set intervals. + Obviously the most rigorous correction would be invoke this cleaning procedure every time-step., Obviously the most rigorous correction would be invoke this cleaning procedure every time-step. +" However. this is computationally, demanding."," However, this is computationally demanding." + Vherelore. we choose here to correct the mean," Therefore, we choose here to correct the mean" +Alvich. Me-poor stars in NCC 2808 iust lave Όσοι produced by pollution from a previous stellar generation in the clusters.,"Al-rich, Mg-poor stars in NGC 2808 must have been produced by pollution from a previous stellar generation in the clusters." + Deep mixing has been receutly revisited as an explanation for the extreme chemical abunudances of RGB stars in CC's (sec. eo. D'Autoua&Ventura2007:Lee 20109).," Deep mixing has been recently revisited as an explanation for the extreme chemical abundances of RGB stars in GCs (see, e.g., \citealt{dv07,lee10}) )." +" ILowever. since deep mixing cannot have been responsible for the lieht clement abunudances in the bMS star. it is unlikely to have caused the identical pattern iu evolved RGB stars of NGC 2808,"," However, since deep mixing cannot have been responsible for the light element abundances in the bMS star, it is unlikely to have caused the identical pattern in evolved RGB stars of NGC 2808." + Finally. it is iutercsting to note that the Da abundance. as indicated bv the resonance Ba line at 1551A.. secius the same for the two MS stars.," Finally, it is interesting to note that the Ba abundance, as indicated by the resonance Ba line at 4554, seems the same for the two MS stars." + If coufirmed by more quantitative analysis. this would probably exclude a significant contribution from low-mass AGB stars (c.g.Youngetal.2009) to the pool of gas from which the secoud-eeueration stars originated.," If confirmed by more quantitative analysis, this would probably exclude a significant contribution from low-mass AGB stars \citep[e.g.,][]{yong09} to the pool of gas from which the second-generation stars originated." + The consequence is that the handful of stars observed to have strong chhancement in Da aud other s process elements iu sole CCS must have another origin. likely frou mass transfer from a former ACB companion iu a binary system (see D'Orazietal.2010.in prep.)).," The consequence is that the handful of stars observed to have strong enhancement in Ba and other $s-$ process elements in some GCs must have another origin, likely from mass transfer from a former AGB companion in a binary system (see \citealt{dorazi10}) )." + Iu conclusion. the chemical pattern we found from the first abundance analysis of a star on the ILle-rich MS sequence of NGC 2808 is exactly what is expected if stars on the bMS. formed from ejecta produced by au carly stellar generation via proton-capture reactions nn T-burning at high temperature. accompanied the main outcome of this unclear burning. 1.0. helium.," In conclusion, the chemical pattern we found from the first abundance analysis of a star on the He-rich MS sequence of NGC 2808 is exactly what is expected if stars on the bMS formed from ejecta produced by an early stellar generation via proton-capture reactions in H-burning at high temperature, accompanied the main outcome of this nuclear burning, i.e. helium." + The extreme A] cuhancement and Me depletion observed in the bMS star argues against a deep ήπιο hvpothesis for the extreme chemical abundances of ROB stars in GCs., The extreme Al enhancement and Mg depletion observed in the bMS star argues against a deep mixing hypothesis for the extreme chemical abundances of RGB stars in GCs. + Observations of a larger sample of unevolved stars in this cluster and others with suspected Ie variations would be welcome., Observations of a larger sample of unevolved stars in this cluster and others with suspected He variations would be welcome. + We thauk Paolo Molaro for the nice observations made on behalf of the Italian X-shooter GTO. team and Valeutina D'Odorico for help aud sugeestious with the data reduction., We thank Paolo Molaro for the nice observations made on behalf of the Italian X-shooter GTO team and Valentina D'Odorico for help and suggestions with the data reduction. + The organizing work of Paul Groot and Sofia Rancdich is acknowledged., The organizing work of Paul Groot and Sofia Randich is acknowledged. + Funding come from PRIN-MIUR 2007. the Italian GTO) X-shooter Consortium. and US National Scieuce Foundation erat AST-0908978.," Funding come from PRIN-MIUR 2007, the Italian GTO X-shooter Consortium, and US National Science Foundation grant AST-0908978." + This paper is dedicated to Roberto Pallavicini. late Italian PI of the N-3hooter Consortimu. who speut a lot of time and work for the realization of this fine instrument.," This paper is dedicated to Roberto Pallavicini, late Italian PI of the X-shooter Consortium, who spent a lot of time and work for the realization of this fine instrument." +6 Car.,6 Gyr. + More receutly. Saghaetal.(2010). have made a detailed study of the M31 bulge region using a number of long-slit exposures with the WET.," More recently, \citet{saglia} have made a detailed study of the M31 bulge region using a number of long-slit exposures with the HET." + They find a mean metallicity around solar. aud an age of around 12 Cyr in the immer 1-2 kpc. (," They find a mean metallicity around solar, and an age of around 12 Gyr in the inner 1-2 kpc. (" +Note that they do see a metallicity gradient. reaching up to |0.1l. over the inner 200 pe. the region dominated |Z/II|2by the classical bulge.),"Note that they do see a metallicity gradient, reaching up to [Z/H]=+0.4, over the inner 200 pc, the region dominated by the classical bulge.)" + Sarajedini&Jablonka(2005) used TST/WEPC2 observations to produce a coloranaenitude diagram for ABs bulee at 1.6 kpc from its center. and inferred a muctallicity distribution which peaked near solu.," \citet{ata05} used HST/WFPC2 observations to produce a color-magnitude diagram for M31's bulge at 1.6 kpc from its center, and inferred a metallicity distribution which peaked near solar." + Olseuetal(2006) sununarized near IR color-magnitude diagrams from high spatial resolution studies of M31 to fud that the stellar population iu the imucr few kpc was dominated bw old. nearly solar-metallicity stars.," \citet{olsen} summarized near IR color-magnitude diagrams from high spatial resolution studies of M31 to find that the stellar population in the inner few kpc was dominated by old, nearly solar-metallicity stars." + Tuterestinely. by comparing fields in the bulge with au inner disk field. they found no evidence for an age difference between bulge and disk.," Interestingly, by comparing fields in the bulge with an inner disk field, they found no evidence for an age difference between bulge and disk." + This is uusurprisius if NDAUS bulge is dominated by a bar. since bar stars are merely inner disk stars which have become part of the bar pattern.," This is unsurprising if M31's bulge is dominated by a bar, since bar stars are merely inner disk stars which have become part of the bar pattern." + The mean metallicity of the inteerated light frou field stars thus exceeds the mean metallicity of the elobulars in the inner few kpe: it is closer to the mean of those with 0.6. which show either disk or bar kinematics. (," The mean metallicity of the integrated light from field stars thus exceeds the mean metallicity of the globulars in the inner few kpc; it is closer to the mean of those with $>$ –0.6, which show either disk or bar kinematics. (" +It has Fe/H]»been suggested before that elobular clusters are ornmed less efficiently in metalxicli populations: Straderetal.(2005). calculate that the efficiencies differ by more han a factor of 10 in the Milkv Wax. by comparing ποτάπο]. globular clusters to the bulge huuimositv and imetal-poor numbers to the halo huuimositv.,"It has been suggested before that globular clusters are formed less efficiently in metal-rich populations: \citet{strader05} calculate that the efficiencies differ by more than a factor of 10 in the Milky Way, by comparing metal-rich globular clusters to the bulge luminosity and metal-poor numbers to the halo luminosity." + This nuuber will not be chauged radically if we substitute he thick disk Iuninositv for the bulee Iuminosity iu this calculation.), This number will not be changed radically if we substitute the thick disk luminosity for the bulge luminosity in this calculation.) + Thus a snrple picture can explain the existence of he metalaich globular clusters in M31: they merely xwticipated in the carly formation ofthe iuncr disk aud he onset of the bar instability., Thus a simple picture can explain the existence of the metal-rich globular clusters in M31: they merely participated in the early formation of the inner disk and the onset of the bar instability. + We have discussed accurate kinematical data for old ADAE clusters in its inner regions within 2 kpc of its uajor axis., We have discussed accurate kinematical data for old M31 clusters in its inner regions within 2 kpc of its major axis. + The majority of the metal-rich clusters (those with |Fe/TI]| greater than 0.6) show disk kinematics. aud uauv of the clusters within the imucrmost bar region have he signature of the Tuudlv.," The majority of the metal-rich clusters (those with [Fe/H] greater than –0.6) show disk kinematics, and many of the clusters within the innermost bar region have the signature of the family." + This clearly shows the existence of an ILR and. to our knowledee. this is the first time dt has con. Clearly shown using stellar kinematics.," This clearly shows the existence of an ILR and, to our knowledge, this is the first time it has been clearly shown using stellar kinematics." + In the ouly other known cxample. Teubeuetal.(1986) showed lis using gas kinenmiaties iu the strongly barred galaxy NGC 1365.," In the only other known example, \citet{teuben} showed this using gas kinematics in the strongly barred galaxy NGC 1365." + Our result also gives an estimate of the ILR location. which provides uscful coustraiuts for future dynamical studies of MOI since dt could be used to set limits to the bar pattern speed.," Our result also gives an estimate of the ILR location, which provides useful constraints for future dynamical studies of M31 since it could be used to set limits to the bar pattern speed." + These metal-rich clusters share the population properties (uictallicity aud age) of the integrated light iu the iuner few kpc. which has been studied both wa spectroscopy and via deep color-magnitude diagrams from HIST aud adaptive optics imaging.," These metal-rich clusters share the population properties (metallicity and age) of the integrated light in the inner few kpc, which has been studied both via spectroscopy and via deep color-magnitude diagrams from HST and adaptive optics imaging." + By coutrast. clusters with less than 0.6 within 2 kpc of the|Fo/TI] major axis show little rotational support aud a velocity dispersion which increases as racial distance to the center decreases.," By contrast, clusters with less than –0.6 within 2 kpc of the major axis show little rotational support and a velocity dispersion which increases as radial distance to the center decreases." + Ow data do not probe the small region (200 pc) occupied by AB's classical bulge iu the description of Beatonctal.(2007).. so we cannot comment on its kinematics.," Our data do not probe the small region (200 pc) occupied by M31's classical bulge in the description of \citet{beaton}, so we cannot comment on its kinematics." + [Tlowever. we caution against simply interpreting a high velocity dispersion in M23I3 inner few kpc as a bulge velocity clispersion aud then using it to coustrain M33 black hole mass (asdonemostrecentlybySaghaetal. 2010):: the coutribution of the bar. which dominates the lisht there. needs to be assessed.," However, we caution against simply interpreting a high velocity dispersion in M31's inner few kpc as a bulge velocity dispersion and then using it to constrain M31's black hole mass \citep[as done most recently by ][]{saglia}: the contribution of the bar, which dominates the light there, needs to be assessed." + IILM thanks the NSF for support under erat AS'T-0607518. AJR for erauts AST-Os0s099 αμα AST-909237. and EA the ANR for ANR-06-BLAN-0172.," HLM thanks the NSF for support under grant AST-0607518, AJR for grants AST-0808099 and AST-0909237, and EA the ANR for ANR-06-BLAN-0172." + RPS is supported by Cemini Observatory. which is operated w AURA. Iuc. on behalf of the international Ceci xwtuership of Arecutina. Australia. Brazil. Canada. Chile. the United. Ninedom aud the United States of America.," RPS is supported by Gemini Observatory, which is operated by AURA, Inc, on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom and the United States of America." + We also thank Johu Wiley aud Sous for )ornission to reproduce Figure 2., We also thank John Wiley and Sons for permission to reproduce Figure 2. +suffice for our purpose.,suffice for our purpose. + For first cight stars. the A. values equal one-half of the longitude separation between the two visible peaks. aud are upper nuits because the core/cone distinction is not completely clear iu the profile.," For first eight stars, the $\Delta_{cc}$ values equal one-half of the longitude separation between the two visible peaks, and are upper limits because the core/cone distinction is not completely clear in the profile." + The star types are again as in RL., The star types are again as in R4. + The frst eight stars in Table 2 illustrate the mereine othe core component with one of the conal ones., The first eight stars in Table 2 illustrate the merging of the core component with one of the conal ones. + The last four correspond to he core components being displaced outside the conc., The last four correspond to the core components being displaced outside the cone. + We discuss them oue by One., We discuss them one by one. + 1., 1. + PSR 1802103: “The extremely Ligh linear polarization aud flat positio1 auele of the leaciug conmponeut argue that it is a core or possibly a merged core aud cone. with the trailing compouent being conal (Weishere et al.," PSR 1802+03: ""The extremely high linear polarization and flat position angle of the leading component argue that it is a core or possibly a merged core and cone, with the trailing component being conal"" (Weisberg et al." + 1999)., 1999). + T1ο core thus leads by Lae., The core thus leads by $\le 4.1^\circ$. +" 2,", 2. +" PSR 1822-09: This pulsar has been «escribed variously as “ost iuterestiug"" and “intrigue” (Manchester e al."," PSR 1822-09: This pulsar has been described variously as ""most interesting"" and ""intriguing"" (Manchester et al." + 1980. Rankin 1956. hereafter R3) aud is ideutified as à triple yo).," 1980, Rankin 1986, hereafter R3) and is identified as a one-sided triple $_{1/2}$ )." + Its profile strikingly resembles that of the Crab pulsar (both exhibit inter]]xex)., Its profile strikingly resembles that of the Crab pulsar (both exhibit interpulses). + The uain pulse profile is double with the leading component (precursor) showing conal characteristics.," The main pulse profile is double with the leading component (""precursor"") showing conal characteristics." +" The core component in this star is identified as the leading component of the composite second ~componcut” of the main pulse (1160),"," The core component in this star is identified as the leading component of the composite second ""component"" of the main pulse (R6)." + Fro wa 1612 MIIz profile (Manchester et al., From a 1612 MHz profile (Manchester et al. + 1980: κος also B3). we read the core couponeut lag as 7.57," 1980; see also R3), we read the core component lag as $7.5^\circ$." + 3., 3. + PSR 18512111: Siuluw to PSR 1502105 in lavove (Weisberg et al., PSR 1842+14: Similar to PSR 1802+03 in 1 above (Weisberg et al. + 1999) with core lead MM L, 1999) with core lead $\le 3.9^\circ$. + , 4. +PSR 1859103: Profile is similar to PSRs 1802|03 aud 18512111 but core is identified here from its circular polarization signature (Weisberg et al., PSR 1859+03: Profile is similar to PSRs 1802+03 and 1842+14 but core is identified here from its circular polarization signature (Weisberg et al. + 1999). aud lags by 5.67.," 1999), and lags by $\le 5.6^\circ$ ." + 5., 5. + PSR 1907101 At 21 cim anc lugher frequencies. the leading component is apparcutly conal while the primary componcut is a core. possibly with another weak one merced ou to its trailing edge (Weishere et al.," PSR 1907+10: At 21 cm and higher frequencies, the leading component is apparently conal while the primary component is a core, possibly with another weak one merged on to its trailing edge (Weisberg et al." + 1999)., 1999). +" The core lag is <3.8"".", The core lag is $\le 3.8^\circ$. + 6., 6. + PSR 1920121: Iu this star the core component is so carly that it virtually overlics the leading conal outrider (R6: see also Rankin et al., PSR 1920+21: In this star the core component is so early that it virtually overlies the leading conal outrider (R6; see also Rankin et al. + 1989. hereafter RSW89).," 1989, hereafter RSW89)." + A 1115 MIIZ profile (Weisberg et al., A 1418 MHz profile (Weisberg et al. + 1999) eves the core lead as 1.57., 1999) gives the core lead as $4.5^\circ$. + 7., 7. + PSR 2020|28 Iu the profile of this pulsar as seen iu Sieber et al (1975) aud Cordes ct al (1978). the two conal components obscure the weak core compoucut on the trailing edge of the leading component (R6) which also has beeu termed as a bridec (Weisbere et al.," PSR 2020+28 In the profile of this pulsar as seen in Sieber et al (1975) and Cordes et al (1978), the two conal components obscure the weak core component on the trailing edge of the leading component (R6) which also has been termed as a bridge (Weisberg et al." + 1999)., 1999). + The profile can be modelle as the stm of three κΠΠ ΠΠrents. iv which the steep spectral iudex avove SOO ATTz of the bridge “sugecsS“ that it is a core (Woeisberg et al.," The profile can be modelled as the sum of three Gaussian components, in which the steep spectral index above 800 MHz of the bridge ""suggests"" that it is a core (Weisberg et al." + 1999)., 1999). + From the profile at 130 MIIz iuSicber et al. (, From the profile at 430 MHz inSieber et al. ( +1975). we find that the core leacs by5° ,"1975), we find that the core leads by $5^\circ$ ." +S., 8. + PSR 222165 :, PSR 2224+65 : +Moreover. there is another challenge offered by the Centaurus cluster.,"Moreover, there is another challenge offered by the Centaurus cluster." + From kinematical studies of the clusters in Virgo (Binggeli et al., From kinematical studies of the clusters in Virgo (Binggeli et al. + 1993) and Fornax (Held Mould 1994) we know that the velocity distribution of early-type dwarfs might differ significantly from that of the giants., 1993) and Fornax (Held Mould 1994) we know that the velocity distribution of early-type dwarfs might differ significantly from that of the giants. + This could be due to cluster formation effects and/or evolution of dwarf galaxies in high density environments., This could be due to cluster formation effects and/or evolution of dwarf galaxies in high density environments. + In particular. the observed clumpiness of low density regions in galaxy clusters and the marked spatial and velocity segregation of galaxy types (e.g. Stein 1997) suggest the occurrence of significant late infall of spiral galaxies from the cluster outskirts onto the core (Binggelt 1987).," In particular, the observed clumpiness of low density regions in galaxy clusters and the marked spatial and velocity segregation of galaxy types (e.g. Stein 1997) suggest the occurrence of significant late infall of spiral galaxies from the cluster outskirts onto the core (Binggeli 1987)." + These infalling late-type galaxies are likely to be initially surrounded by a bound population of dwarf satellites. as was found to be the case for the field (Vader Sandage 1991).," These infalling late-type galaxies are likely to be initially surrounded by a bound population of dwarf satellites, as was found to be the case for the field (Vader Sandage 1991)." + It seems to be clear that a significant fraction of bound (dwarf) galaxies can be found in clusters (Ferguson 1992). but it is still not known whether all reach the central cluster region as companions of spirals or whether there are other evolutionary effects involved.," It seems to be clear that a significant fraction of bound (dwarf) galaxies can be found in clusters (Ferguson 1992), but it is still not known whether all reach the central cluster region as companions of spirals or whether there are other evolutionary effects involved." + It has been proposed to extract dynamical information about a cluster using dwarf galaxies as test particles in the cluster potential well (Binggeli 1987). given that their gravitational pull on neighbouring giant galaxies is negligible.," It has been proposed to extract dynamical information about a cluster using dwarf galaxies as test particles in the cluster potential well (Binggeli 1987), given that their gravitational pull on neighbouring giant galaxies is negligible." + In the case of relaxed clusters with a central dominant galaxy up to of the cluster members were found to be possibly bound to the central system (Gebhardt Beers 199]; Merrifield Kent 1991: but see Blakeslee Tonry 1992)., In the case of relaxed clusters with a central dominant galaxy up to of the cluster members were found to be possibly bound to the central system (Gebhardt Beers 1991; Merrifield Kent 1991; but see Blakeslee Tonry 1992). + So far the only studies about bound populations involving distinctions between dwarf and giant galaxies have been Ferguson's (1992) and Binggeli’s (1993) analysis of the Virgo cluster., So far the only studies about bound populations involving distinctions between dwarf and giant galaxies have been Ferguson's (1992) and Binggeli's (1993) analysis of the Virgo cluster. + The aim of the present study is to explore the velocity distributions of different galaxy types in the Centaurus cluster with special weight on the dwarf families., The aim of the present study is to explore the velocity distributions of different galaxy types in the Centaurus cluster with special weight on the dwarf families. + This shall help to give us more insight into the kinematic properties of this complex galaxy aggregation and of type-dependent cluster dynamics in general., This shall help to give us more insight into the kinematic properties of this complex galaxy aggregation and of type-dependent cluster dynamics in general. + The sample selection is discussed in Sect., The sample selection is discussed in Sect. + 2., 2. + A technical description of the spectroscopic observations and of the data reduction follows in Sect., A technical description of the spectroscopic observations and of the data reduction follows in Sect. + 3., 3. + The resulting new redshifts were then used to check the validity of previous membership assignments based on morphological information alone (Sect., The resulting new redshifts were then used to check the validity of previous membership assignments based on morphological information alone (Sect. + 4)., 4). + We present our analysis of the data in Sections 5 and 6. where type-dependent velocity distributions are interpreted and the existence of bound galaxies Is investigated.," We present our analysis of the data in Sections 5 and 6, where type-dependent velocity distributions are interpreted and the existence of bound galaxies is investigated." + Main results are summarized in Sect., Main results are summarized in Sect. + 7., 7. + With the deep photometric Centaurus cluster survey. (Jerjen 1995) an extensive list of new cluster dwarf galaxies became available including accurate positions and high morphological resolution., With the deep photometric Centaurus cluster survey (Jerjen 1995) an extensive list of new cluster dwarf galaxies became available including accurate positions and high morphological resolution. + These latter quantities are based on a fine-scale 20-inch Las Campanas du Pont plate covering the central «1.5 degrees of the cluster., These latter quantities are based on a fine-scale 20-inch Las Campanas du Pont plate covering the central $\times$ 1.5 degrees of the cluster. + The probability of cluster membership was worked out based on pure morphological criteria and is given as or higher for each galaxy included in the catalogue., The probability of cluster membership was worked out based on pure morphological criteria and is given as or higher for each galaxy included in the catalogue. + For our redshift project we selected all galaxies of the outcoming Centaurus cluster catalogue (Jerjen Dressler 1997a. hereafter CCC) with a mean effective D-band surface brightness SB; brighter than 7.," For our redshift project we selected all galaxies of the outcoming Centaurus cluster catalogue (Jerjen Dressler 1997a, hereafter CCC) with a mean effective $B$ -band surface brightness $_{\rm eff}$ brighter than $^{-2}$." + This implies our sample contains a substantial number of newly discovered dwarf galaxies as well as several mainly giant galaxies with known redshifts (Dickens et al., This implies our sample contains a substantial number of newly discovered dwarf galaxies as well as several mainly giant galaxies with known redshifts (Dickens et al. + 1986. hereafter DCL: LC: Stein 1996).," 1986, hereafter DCL; LC; Stein 1996)." + The latter subsample was used for comparison., The latter subsample was used for comparison. + The restriction of our redshift survey onto the inner region of the Centaurus cluster was not only dictated by the area of the photometric survey but is also required to overcome uncontrollable cluster sample contamination by unrelated galaxies located at a Hubble distance of ~kmx., The restriction of our redshift survey onto the inner region of the Centaurus cluster was not only dictated by the area of the photometric survey but is also required to overcome uncontrollable cluster sample contamination by unrelated galaxies located at a Hubble distance of $\sim$. +. In fact. this is a crucial problem for the Centaurus cluster as already emphasized elsewhere (Lucey et al.," In fact, this is a crucial problem for the Centaurus cluster as already emphasized elsewhere (Lucey et al." + 1986b)., 1986b). + Observations were carried out between May 23-206. 1995 at the 3.6 m ESO telescope at La Silla.," Observations were carried out between May 23–26, 1995 at the 3.6 m ESO telescope at La Silla." + We employed the multifibre instrument MEFOS. which has a circular field of view of 1 degree and 29 fibre arms.," We employed the multifibre instrument MEFOS, which has a circular field of view of 1 degree and 29 fibre arms." + Each arm carries one image fibre of «36 aresee and two spectral fibres of 2.5 aresec aperture for simultaneous object and sky acquisition., Each arm carries one image fibre of $\times$ 36 arcsec and two spectral fibres of 2.5 arcsec aperture for simultaneous object and sky acquisition. + The image fibre is meant for the interactive repositioning of spectral fibres onto the object of choice. prior to the spectral exposure.," The image fibre is meant for the interactive repositioning of spectral fibres onto the object of choice, prior to the spectral exposure." + For a detailed study about the performance of MEFOS consult Felenbok 1997., For a detailed study about the performance of MEFOS consult Felenbok 1997. + No beam-switching technique has been applied for subtraction of the night sky spectral contribution (Cuby Mignoli 1994). because the traditional technique with fibre transmission correction (given by the signal under the emission line at AA)) gave suitable results.," No beam-switching technique has been applied for subtraction of the night sky spectral contribution (Cuby Mignoli 1994), because the traditional technique with fibre transmission correction (given by the signal under the emission line at ) gave suitable results." + The 512 pixels of the CCD covered the wavelength range 3800 toAA., The 512 pixels of the CCD covered the wavelength range 3800 to. +. A total exposure time between 5400 and 7200ss per field was chosen., A total exposure time between 5400 and s per field was chosen. + Reduction of the spectroscopic data was done using the MIDAS package on an IBM AIX/RS6000., Reduction of the spectroscopic data was done using the MIDAS package on an IBM AIX/RS6000. + All frames were carefully corrected for pixel-to-pixel variations 1n. sensitivity (flat-fielded)., All frames were carefully corrected for pixel-to-pixel variations in sensitivity (flat-fielded). + Then an optimal extraction algorithm was applied (Horne 1986). which was able to correct for most of the cosmic ray hits.," Then an optimal extraction algorithm was applied (Horne 1986), which was able to correct for most of the cosmic ray hits." + No correction for stray light nor cross-talk between fibres (Lissandrini 1994) was applied. because it could have influenced the precision of the optimal extraction.," No correction for stray light nor cross-talk between fibres (Lissandrini 1994) was applied, because it could have influenced the precision of the optimal extraction." + The resulting one-dimensional spectra were then calibrated in wavelength and the positions of night-sky emission lines were checked against their expected wavelength., The resulting one-dimensional spectra were then calibrated in wavelength and the positions of night-sky emission lines were checked against their expected wavelength. +" Note that no appreciable systematic deviation 1n the position of night-sky lines was found. as opposed to the findings of Felenbok 1997, who comment on their problems with observations taken roughly one year before us."," Note that no appreciable systematic deviation in the position of night-sky lines was found, as opposed to the findings of Felenbok 1997, who comment on their problems with observations taken roughly one year before us." + Prior to sky subtraction the signal of each spectrum (including sky spectra) had to be scaled with respect to the intrinsic transmission efficiency of the corresponding fibre., Prior to sky subtraction the signal of each spectrum (including sky spectra) had to be scaled with respect to the intrinsic transmission efficiency of the corresponding fibre. + To, To +(psrgn(f)) L).. now pushing out to 2Z82010).,"$\rho_{SFR}(t)$ , now pushing out to $z\gap8$." +. These measurements have been augimenuted Y oineasurelents of the obscured SER due to advances in the capabilities of long waveleneth detectors allowing neasurements of hieli-z star formation2005)., These measurements have been augmented by measurements of the obscured SFR due to advances in the capabilities of long wavelength detectors allowing measurements of $z$ star formation. +. Such assessiueut of the SFR has also been mace at ow redshifts by survevs like the Sloan Digital Sky Survey and the Calaxy Evolution Explorer all on the asic properties of SFR versus time., Such assessment of the SFR has also been made at low redshifts by surveys like the Sloan Digital Sky Survey and the Galaxy Evolution Explorer all on the basic properties of SFR versus time. + While carly measurements of psgg(f) showed a peak around +—1.52001).. more recent nieasureienuts have generally put the peak prior to τν22008).. includiug measurements combining the star formation histories (SFUs)}) of Local Group galaxies.," While early measurements of $\rho_{SFR}(t)$ showed a peak around $z\sim1.5$, more recent measurements have generally put the peak prior to $z\sim2$, including measurements combining the star formation histories (SFHs) of Local Group galaxies." + Inside the LG found that pagg(f) was broadly consistent with redshif survevs with no significant coutributiou frou dwiurfs a any epoch. and fouud ar- excess of star formation in recent epochs. dominated bv the disk of the Milkv Way. as well as a recen increase in the contribution from dwarts.," Inside the LG found that $\rho_{SFR}(t)$ was broadly consistent with redshift surveys with no significant contribution from dwarfs at any epoch, and found an excess of star formation in recent epochs, dominated by the disk of the Milky Way, as well as a recent increase in the contribution from dwarfs." + found little difference in the SFUs of the LC dwarfs aud those in a larger volume., found little difference in the SFHs of the LG dwarfs and those in a larger volume. + Oulv one recen measurement. based ou integrated galaxy spectra in the Sloan Digital Sky Sirvey2001).. has found a peak more recent than 2=2.," Only one recent measurement, based on integrated galaxy spectra in the Sloan Digital Sky Survey, has found a peak more recent than $z=2$." + Furthermore. recent analytical caleulatious2003).. scnu-analvtie galaxy formation models2009).. and bydrodvuamic simulations also generally put the peal carlicr than +—2.," Furthermore, recent analytical calculations, semi-analytic galaxy formation models, and hydrodynamic simulations also generally put the peak earlier than $z\sim2$." + For current WAIAP cosiology. this places the peak at lookback times 210 Cyr.," For current WMAP cosmology, this places the peak at lookback times $>$ 10 Gyr." + There is mounting evidence that low-mass galaxies may have later formation, There is mounting evidence that low-mass galaxies may have later formation +2002b).. and in CE315. an AALTCCVai type CV 2001).,", and in CE315, an CVn type CV ." +. In addition. we coufiii the uuusually largeNv/C€1v emission liue dux ratios iu the chvarf novae BZUUNa aud CCve. first detected in data by and (€2002).," In addition, we confirm the unusually large emission line flux ratios in the dwarf novae UMa and Cyg, first detected in data by and ." +. //STIS FUV spectroscopy of JJ2329. CES315. BZUUNa and CCre was obtained using the ClLoL erating and the 52”40.2” aperture roft-hstobs)).," /STIS FUV spectroscopy of J2329, CE315, UMa and Cyg was obtained using the G140L grating and the $52\arcsec\times0.2\arcsec$ aperture \\ref{t-hstobs}) )." + This instrmucutal setup provides aspectral resolution of AHz1000., This instrumental setup provides aspectral resolution of $R\approx1000$. + The data were processed with the latest release of CALSTIS (V2.13b). which takes iuto account the decaving seusitivitv of the GLLlOoL erating.," The data were processed with the latest release of CALSTIS (V2.13b), which takes into account the decaying sensitivity of the G140L grating." + The STIS spectra of JJ25329. CE315. DZUUMGA and (νο are displaved in reff-stisspectra..," The STIS spectra of J2329, CE315, UMa and Cyg are displayed in \\ref{f-stisspectra}." + An apparent similarity between all four systenas ds the unusually large streugth ofA1210. as well as the lack of noticeable1176. or emission.," An apparent similarity between all four systems is the unusually large strength of, as well as the lack of noticeable, or emission." + Despite the short exposure times. the quality of our STIS spectra exceeds that of the previous observations of UUMA and CCve by large factors.," Despite the short exposure times, the quality of our STIS spectra exceeds that of the previous observations of UMa and Cyg by large factors." + The coutiuuuu FUV spectra of UUMa is typical for a short-period dwarf nova. beiug most likely a 1unixture of enission from the accretion disc aud the white dwarf.," The continuum FUV spectrum of UMa is typical for a short-period dwarf nova, being most likely a mixture of emission from the accretion disc and the white dwarf." + The fact that the broad aabsorptiou originating in the white dwarf photosphere is lavecly filled in with emission sugeests that the disc contributes sienificautly iu the FUY., The fact that the broad absorption originating in the white dwarf photosphere is largely filled in with emission suggests that the disc contributes significantly in the FUV. + Iu coutrast to this. the FUW continuum of RXJJ2329 is extremely red. sugecsting that the white dwarf in this system is very cold (veddening is negligible for the distance of 200 ppc determined by 2002b)).," In contrast to this, the FUV continuum of J2329 is extremely red, suggesting that the white dwarf in this system is very cold (reddening is negligible for the distance of $\sim200$ pc determined by )." + The coutiuuuuu slope aud aabsorptiou observed iu CCve is reminiscent of the photospheric emüsson of a white dwarf with Zu-—25000 II. A detailed modelling of the coutiuuuu spectra of JJ2329. UUMA aud CCye. will be preseuted along with the data of additional objects from our snapshot survey iu a separate paper.," The continuum slope and absorption observed in Cyg is reminiscent of the photospheric emission of a white dwarf with $\Twd\sim25\,000$ K. A detailed modelling of the continuum spectra of J2329, UMa and Cyg, will be presented along with the data of additional objects from our snapshot survey in a separate paper." + The STIS spectra of CE315 differs from that of the other three systems in that practically uo coutim£ona enüsson ids detected., The STIS spectrum of CE315 differs from that of the other three systems in that practically no continuum emission is detected. + Furthermore. noue of the usual enussion lines of silicon are present in the spectrum.," Furthermore, none of the usual emission lines of silicon are present in the spectrum." + Most of the weak emission lines are likely due to Ni., Most of the weak emission lines are likely due to . + The identifications of emission features at LITOA.. ~1300AA. ~1190 aud c1560AÀ. iedain somewhat uncertain.," The identifications of emission features at $\sim1170$, $\sim1300$, $\sim1490$ and $\sim1560$ remain somewhat uncertain." + With respect to the last line. we stress. however. that tlis feature is clearly not related to enission ofIv.," With respect to the last line, we stress, however, that this feature is clearly not related to emission of." +" We have measured the enuüsson hne fluxes ofI210.105.1550. and in JJ2329. CE315. DZUUMGA and EYνο adopting the following two methods: (1) We fitted a sinall interval around the ceutral waveleugth with a linear function plus a Gaussian line (in the case of two (ναοίασ), aud computed the line flux from the Gaussian fit parameters: (2) we used the columand in the suite to interactively determine the coutiuuun level aud iutegrate the flux of the cussion line(s) above this coutinumm."," We have measured the emission line fluxes of, and in J2329, CE315, UMa and Cyg adopting the following two methods: (1) We fitted a small interval around the central wavelength with a linear function plus a Gaussian line (in the case of two Gaussians), and computed the line flux from the Gaussian fit parameters; (2) we used the command in the suite to interactively determine the continuum level and integrate the flux of the emission line(s) above this continuum." + The results fro these two methods were found to be in good aerecineut. and the average of the liue fluxes from both 1ieasuremoents are reported in roft-hinetiuxes..," The results from these two methods were found to be in good agreement, and the average of the line fluxes from both measurements are reported in \\ref{t-linefluxes}." + Note that we did not detect at a statistically significant level in amy of the four stars., Note that we did not detect at a statistically significant level in any of the four stars. + Iu addition. were not detected in CE315.," In addition, were not detected in CE315." + Iu order to constrain the aud line fluxes we have added to the STIS spectra Gaussian profiles of simular width as the observed lines and analysed the svuthetic cussion lines as described above., In order to constrain the and line fluxes we have added to the STIS spectra Gaussian profiles of similar width as the observed lines and analysed the synthetic emission lines as described above. +" We repeated this process. decreasing the line fluxes of the added Gaussian lines, until reaching the detection threshold."," We repeated this process, decreasing the line fluxes of the added Gaussian lines, until reaching the detection threshold." + The upper lamits on the line fluxes derived im that way are giveu in roft-linetiuxes.., The upper limits on the line fluxes derived in that way are given in \\ref{t-linefluxes}. + For completeness. we compare thev enüssion line fluxes obtained from our STIS spectra of DZUUMGA aud CCyve with the values derived from archival observations (the other lines are too weal in the spectra to permit anv useful measurement}.," For completeness, we compare the emission line fluxes obtained from our STIS spectra of UMa and Cyg with the values derived from archival observations (the other lines are too weak in the spectra to permit any useful measurement)." + Iu the case of BZUUNIa. two SWP spectra are available (32778. 32183). which coutainNv atf a similar flux level as our STIS spectrum (6028510P ecs)).," In the case of UMa, two SWP spectra are available (32778, 32783), which contain at a similar flux level as our STIS spectrum $\sim60\pm5\times10^{-13}$ )." + In the case of CCve. the two availabe SWP spectra that have a sufficient signal-to-noise ratio sugecst that iu this svstem the hue may wav significantly (33128: 20+1s10+ees: 1208 L043«4lo1H ecs)).," In the case of Cyg, the two availabe SWP spectra that have a sufficient signal-to-noise ratio suggest that in this system the line may vary significantly (33428: $20\pm4\times10^{-14}$; 31304: $10\pm3\times10^{-14}$ )." + Secoud-epoch STIS observatious of CCre would be desirable to coufiii the variability., Second-epoch STIS observations of Cyg would be desirable to confirm the variability. + To our kuowledge. 10. CVs have so far been reported to display anomalously high enuüssion line flux ratios: AAqry1980).. BYCCam1987).. CCol1991). W1309O00n1996).. Uva2001)... CCrve 2002). DZUUMGA 2002)). CCom1995).. JJ2329. and CE315.," To our knowledge, 10 CVs have so far been reported to display anomalously high emission line flux ratios: Aqr, Cam, Col, Ori, Hya, Cyg ), UMa ), Com, J2329, and CE315." + We show in reff-lineratios the line flux ratios vs.1v aud vs. of these “anomalous” CVs. except for CE315 (iu which neither norSil are detected. reffstisspectra)) aud CCom Ga which is not detected. and iis not included in the wavelength rauge covered by the //FOS observations}.," We show in \\ref{f-lineratios} the line flux ratios vs. and vs. of these “anomalous” CVs, except for CE315 (in which neither nor are detected, \\ref{f-stisspectra}) ) and Com (in which is not detected, and is not included in the wavelength range covered by the /FOS observations)." + The line flix measurements are taken from the study of(1997).. except for OO0ri 2001).. να 2001).. CCol 19913). the lineratios were measured as described above from the spectra SWPO00502L and SWP31129L). aud JJ2329. DZUUMa. aud (νο roft-lineftuxes)).," The line flux measurements are taken from the study of, except for Ori , Hya , Col ), the lineratios were measured as described above from the spectra SWP00502L and SWP34129L), and J2329, UMa, and Cyg\\ref{t-linefluxes}) )." +that the free diffusion predominance is merely an effect of insufficient. times of integration.,that the free diffusion predominance is merely an effect of insufficient times of integration. + If one extends the integration time to sufficient limits. the asvimptolic behaviour with the slope index ~—5/3. characteristic of the Lévvy flights in the given problem. should become apparent.," If one extends the integration time to sufficient limits, the asymptotic behaviour with the slope index $\sim -5/3$, characteristic of the Lévvy flights in the given problem, should become apparent." + several actual multiple stars are known nowadavs to be near the edge of the stability region in the phase space of the motion. in particular. WD 40887. WD 76644 (ADS 7114— i Uma). ID 217675 (o And). ILD 222326 (ADS 16904) (Orlov&Zhuchkov2005).," Several actual multiple stars are known nowadays to be near the edge of the stability region in the phase space of the motion, in particular, HD 40887, HD 76644 (ADS $=$ $\iota$ Uma), HD 217675 $o$ And), HD 222326 (ADS 16904) \citep{Or05}." +. Numerical integrations. based on initial data from further high-precision astrometric observations ol these svstems. would allow one to reveal long-term evolution features. in particular. the theoretically. predicted Lévvy flights in the orbital periods and (he eeonmetrical sizes of the svslens.," Numerical integrations, based on initial data from further high-precision astrometric observations of these systems, would allow one to reveal long-term evolution features, in particular, the theoretically predicted Lévvy flights in the orbital periods and the geometrical sizes of the systems." +" This work was partially supported by (the Russian Foundation for Basic Research (project 09-02-00267-a). the Programme of Fundamental Research of the Russian Academy of sciences ""Fundamental Problems in Nonlinear Dynamics. and the President. Programme for Support the Leading Scientilic Schools (project 3290.2010.2)."," This work was partially supported by the Russian Foundation for Basic Research (project 09-02-00267-a), the Programme of Fundamental Research of the Russian Academy of Sciences “Fundamental Problems in Nonlinear Dynamics”, and the President Programme for Support the Leading Scientific Schools (project 3290.2010.2)." +gamma-raay and possible ultra-high energy (UHE) cosmic-ray emitter.,ay and possible ultra-high energy (UHE) cosmic-ray emitter. +ο) surface density play an important role in semi-analytical models and simulations (e.g.Springeletal.2005).,) surface density play an important role in semi-analytical models and simulations \citep[e.g.][]{spr05}. +. These empirical relations. or star formation “recipes” are generally derived from observations of large spiral galaxies.," These empirical relations, or star formation ”recipes” are generally derived from observations of large spiral galaxies." + On the other hand. since in hierarchical models of galaxy formation. small objects form first. and merge together later to form large galaxies. the star formation laws governing small. gas rich. galaxies are of particular interest.," On the other hand, since in hierarchical models of galaxy formation, small objects form first, and merge together later to form large galaxies, the star formation laws governing small, gas rich, galaxies are of particular interest." + Gas in the smallest galaxies does not settle into a thin. dynamically cold disk. and the shallow potential wells of these galaxies would make their ISM more susceptible to disruption due to energy input from star formation.," Gas in the smallest galaxies does not settle into a thin, dynamically cold disk, and the shallow potential wells of these galaxies would make their ISM more susceptible to disruption due to energy input from star formation." + As such. it seems probable that star formation in the smallest galaxies proceeds in a manner that is different from that in large spirals.," As such, it seems probable that star formation in the smallest galaxies proceeds in a manner that is different from that in large spirals." + To the extent that the nearby extremely faint dwarf irregular galaxies could be regarded as proxies for galaxies in the early universe. it is interesting to look for correlations. if any. between the gas density and the star formation rate in them.," To the extent that the nearby extremely faint dwarf irregular galaxies could be regarded as proxies for galaxies in the early universe, it is interesting to look for correlations, if any, between the gas density and the star formation rate in them." + In this paper we use HI data from the GMRT based FIGGS survey (Begumetal.2008) and publicly available data to look ‘or star formation recipes in a sample of extremely faint dwarf irregular galaxies., In this paper we use HI data from the GMRT based FIGGS survey \citep{ay08} and publicly available data to look for star formation recipes in a sample of extremely faint dwarf irregular galaxies. + For ease of comparison with the existing large body of work on star formation recipes for galaxies. we examine in detail two particular recipes.CL) the existence of a threshold column density below which star formation is quenched and (2) a power aw relation between the gas column density and the star formation rate density above this threshold.," For ease of comparison with the existing large body of work on star formation recipes for galaxies, we examine in detail two particular recipes, (1) the existence of a threshold column density below which star formation is quenched and (2) a power law relation between the gas column density and the star formation rate density above this threshold." + It is has long been suggested that there is a threshold column density below which star formation is quenched (Toomre1964:Spitzer1968:Quirk 1972).," It is has long been suggested that there is a threshold column density below which star formation is quenched \citep{t64, spi68, qui72}." +. Cold gas in a thin rotating disk is unstable to gravitationally collapse above a critical column density (Safronov1960:Toomre1964).," Cold gas in a thin rotating disk is unstable to gravitationally collapse above a critical column density \citep{safronov60,t64}." + In large spiral galaxies therefore. such a threshold might be related to global disk instabilities.," In large spiral galaxies therefore, such a threshold might be related to global disk instabilities." + Sharp thresholds to the Ha emission have indeed been observed in normal spirals (Kennicutt.1989:Martin&Kennicutt2001).. leading credence to the idea that a threshold for star formation does in fact exist.," Sharp thresholds to the $\alpha$ emission have indeed been observed in normal spirals \citep{ken89,mar01}, leading credence to the idea that a threshold for star formation does in fact exist." + Our sample galaxies are unlikely to have thin. dynamically cold disks. since for dwarfs in this luminosity range the gas velocity dispersion is typically comparable in magnitude to the rotation velocity (Youngetal.2003:Begum&Chengalur2003.2004:Begumetal. 2006).," Our sample galaxies are unlikely to have thin, dynamically cold disks, since for dwarfs in this luminosity range the gas velocity dispersion is typically comparable in magnitude to the rotation velocity \citep{young03,begum03,begum04,begum06}." +.. A threshold for star formation in dwarf galaxies may still exist as a consequence of a critical amount of dust shielding required for molecular gas to form (Skillman1987)., A threshold for star formation in dwarf galaxies may still exist as a consequence of a critical amount of dust shielding required for molecular gas to form \citep{ski87}. + The suggestion that there is a power law relation between and has a similarly long history., The suggestion that there is a power law relation between and has a similarly long history. + Schmidt(1959) related the volume densities of young stars and gas in the Galactic disk.viz.," \cite{s59} related the volume densities of young stars and gas in the Galactic disk,viz." +" psp=apu. tthe “Schnmudt law"")", $\rm {\rho_{SFR} = a~\rho{_{gas}^n}}$ (the “Schmidt law”). + A more convenient parametrization for external galaxies is in terms of the surface densities. viz. ωμή=ANE.," A more convenient parametrization for external galaxies is in terms of the surface densities, viz. $\rm {\Sigma_{SFR} = A~\Sigma{_{gas}^N}}$." + There have been several measurements of the power law indexN. derived from observations of various samples and using various tracers of the star formation and the gas density.," There have been several measurements of the power law index, derived from observations of various samples and using various tracers of the star formation and the gas density." + Kennicutt (Kennicutt.1997) compiled a summary of the distribution of derived values ofN. which had a broad peak betweenN = 0.8 andN = 2.5. and a full range ofN = +3.5.," Kennicutt \citep{ken97} compiled a summary of the distribution of derived values of, which had a broad peak between = 0.8 and = 2.5, and a full range of = $\pm$ 3.5." + He concluded that the large dispersion could be only be partly attributed to observational factors. such as beam smearing effects or fitting to only the atomic or molecular gas densities.," He concluded that the large dispersion could be only be partly attributed to observational factors, such as beam smearing effects or fitting to only the atomic or molecular gas densities." + Much of the scatter is real. being caused by suchfactors as deviations from a power law or spatial variations inN across a galaxy.," Much of the scatter is real, being caused by suchfactors as deviations from a power law or spatial variations in across a galaxy." +" Kennicutt (Kennicutt1989.1998) also investigated the possibility of a composite Schmidt law. using data ranging from normal spiral galaxies (star formation traced using Ha. gas density traced using both HI and CO. observations) to. eireumnuclear starburst galaxies (star formation traced using Far Infrared. gas density traced using CO observations. HI gas being negligible). and arrived at the widely used (foreg.Springel&Hernquist2004:KrumholzThompson2007.etc.) ""Kennicutt-Schmidt law: We use this as a template to compare with the relations that we find in our sample of extremely faint dwarfs."," Kennicutt \citep{ken89, ken98} also investigated the possibility of a composite Schmidt law, using data ranging from normal spiral galaxies (star formation traced using $\alpha$, gas density traced using both HI and CO observations) to circumnuclear starburst galaxies (star formation traced using Far Infrared, gas density traced using CO observations, HI gas being negligible), and arrived at the widely used \citep[for eg.~][~etc.]{spr00,nag04,kru07} “Kennicutt–Schmidt” law: We use this as a template to compare with the relations that we find in our sample of extremely faint dwarfs." + As mentioned above. one point of departure from earlier studies is the fact that our sample is composed of extremely faint dwarfs.," As mentioned above, one point of departure from earlier studies is the fact that our sample is composed of extremely faint dwarfs." + Another is the spatial resolution that we use., Another is the spatial resolution that we use. + Most classical studies of star formation used either globally averaged surface densities or azimuthally averaged radial profiles., Most classical studies of star formation used either globally averaged surface densities or azimuthally averaged radial profiles. + This may be relevant in situations where. for e.g. global processes like large scale disk instabilities play a role in controlling star formation.," This may be relevant in situations where, for e.g. global processes like large scale disk instabilities play a role in controlling star formation." + For dwarf galaxies on the other hand. the low gas densities result in inefficient cloud formation as compared to inner part of spirals (Dong.Lin&Murray2003:Li.Mordecai-MarkKlessen2005).," For dwarf galaxies on the other hand, the low gas densities result in inefficient cloud formation as compared to inner part of spirals \citep{don03, li05}." +. Local processes are expected to dominate in dwarf galaxies (Elmegreen&Hunter 2006).. and star formation is observed in HI clouds or complexes where the average gas density is much below the Toomre critical density (eg.deBlok&Walter20060.," Local processes are expected to dominate in dwarf galaxies \citep{elm06}, , and star formation is observed in HI clouds or complexes where the average gas density is much below the Toomre critical density \citep[eg.][]{deB06}." + We hence study the small scale (i.e. 7400 pe and ~ 200 pe) relation between the gas and star formation rate in our sample galaxies by doing “pixel by pixel” correlations. in addition to looking at the correlation between globally averaged quantities.," We hence study the small scale (i.e. $\sim$ 400 pc and $\sim$ 200 pc) relation between the gas and star formation rate in our sample galaxies by doing “pixel by pixel” correlations, in addition to looking at the correlation between globally averaged quantities." + We also depart from many earlier studies in that we use only HI data to determine thegas column density. i.e. the contribution of the molecular gas is ignored.," We also depart from many earlier studies in that we use only HI data to determine thegas column density, i.e. the contribution of the molecular gas is ignored." + CO is notoriously difficult to detect in dwarf galaxies (eg.Taylor.Kobulnicky.&Skillman1998).. and the CO to He conversion factor in dwarf galaxies may be substantially different from that in our own galaxy (eg.Maddenetal.1997:Israel1997).," CO is notoriously difficult to detect in dwarf galaxies \citep[eg.][]{taylor98}, and the CO to $_2$ conversion factor in dwarf galaxies may be substantially different from that in our own galaxy \citep[eg.][]{madden97,israel97}." +. Further the calibration we use to convert the UV flux into a star formation rate assumes a standard Salpeter IMF with solar metallicity., Further the calibration we use to convert the UV flux into a star formation rate assumes a standard Salpeter IMF with solar metallicity. + We discuss the implications of these assumptions for our results in Sec. 4.., We discuss the implications of these assumptions for our results in Sec. \ref{sec:dis}. + Our sample consists of 23 galaxies drawn from the FIGGS HI 21em survey (Begumetal.2008).. for which there is publicly available data.," Our sample consists of 23 galaxies drawn from the FIGGS HI 21cm survey \citep{ay08}, for which there is publicly available data." + The galaxies are listed in Table 1: the columns in the table are: Columntl) the galaxy name. Columnst2)&(3) the equatorial coordinates. (2000)... Column (4). the absolute blue magnitude (corrected for galactic extinction). Columns) the distance in Mpe. Columnt6) the group membership of the galaxy.," The galaxies are listed in Table \ref{tab:samp}; the columns in the table are: Column(1) the galaxy name, (3) the equatorial coordinates (J2000), Column (4) the absolute blue magnitude (corrected for galactic extinction), Column(5) the distance in Mpc, Column(6) the group membership of the galaxy." + All of this data has been taken from Begumetal.(2008)., All of this data has been taken from \citet{ay08}. +. Column(7) the de Vaucouleurs (25 mag/aresec?) diameter of the optical disk., Column(7) the de Vaucouleurs (25 $^2$ ) diameter of the optical disk. + For dwarf low surface brightness galaxies from the KK lists (KK14. KK65. KK144. KKH98). the diameters correspond to the Holmberg system ( 26.5 mag arcsec 7).," For dwarf low surface brightness galaxies from the KK lists (KK14, KK65, KK144, KKH98), the diameters correspond to the Holmberg system ( 26.5 mag $^{-2}$ )." + Column(8) the optical axis ratio., Column(8) the optical axis ratio. + Data for column (7) and (8) have been taken from taken from Karachentsevetal. 004)..., Data for column (7) and (8) have been taken from taken from \citet{kar04}. . + Columnt9) the assumed inclination angle., Column(9) the assumed inclination angle. + The data is from Begumetal. (2008).. except forthe starred galaxies. for which the inclination angle is measured from the coarsest resolution HI maps.," The data is from \citet{ay08}, , except forthe starred galaxies, for which the inclination angle is measured from the coarsest resolution HI maps." +The role of disks in the formation of high-mass (1.e. O- and early B-type) stars has been extensively discussed in a number of reviews (see e.g. Cesaront et al. 2006.. 2007)).,"The role of disks in the formation of high-mass (i.e. O- and early B-type) stars has been extensively discussed in a number of reviews (see e.g. Cesaroni et al. \cite{natu}, , \cite{ppv}) )." + Disks are important because they focus the aceretion onto the forming star and allow some of the stellar photons to escape along the disk axis (see Krumholz et al., Disks are important because they focus the accretion onto the forming star and allow some of the stellar photons to escape along the disk axis (see Krumholz et al. + 2009. and references therein)., \cite{krum} and references therein). + The combined effects of these two mechanisms might prevent radiation pressure from halting the infalling gas. thus allowing growth of the stellar mass beyond the otherwise maximum value of ~8M. (Palla Stahler 1993)).," The combined effects of these two mechanisms might prevent radiation pressure from halting the infalling gas, thus allowing growth of the stellar mass beyond the otherwise maximum value of $\sim8~M_\odot$ (Palla Stahler \cite{past}) )." + For these reasons. the detection of disks around early-type (proto)stars could be used to prove that the formation of such stars is à scaled up version of that of solar-type stars.," For these reasons, the detection of disks around early-type (proto)stars could be used to prove that the formation of such stars is a scaled up version of that of solar-type stars." + Despite the numerous searches made in recent years with (sub)millimeter interferometers. no true. (Le. self-gravitating. dynamically stable) circumstellar disk has been found associated with early O-type (proto)stars.," Despite the numerous searches made in recent years with (sub)millimeter interferometers, no true (i.e. self-gravitating, dynamically stable) circumstellar disk has been found associated with early O-type (proto)stars." + There is. however. growing evidence of Keplerian disks around early type stars and iis an exemplary case.," There is, however, growing evidence of Keplerian disks around early B-type stars and is an exemplary case." + This 107L. young stellar object (YSO) has been the subject of a long series of studies. with angular resolution spanning from a few tto a few milli-aresec (mas).," This $10^4~L_\odot$ young stellar object (YSO) has been the subject of a long series of studies, with angular resolution spanning from a few to a few milli-arcsec (mas)." + Here. we note some findings most relevant to the present article. namely: Such an overwhelming quantity of information made it possible to determine a number of physical parameters of the star-disk-outflow system.," Here, we note some findings most relevant to the present article, namely: Such an overwhelming quantity of information made it possible to determine a number of physical parameters of the star-disk-outflow system." + Among these. the most important are the stellar mass and luminosity. which allows one to identify this object as an early B-type protostar.," Among these, the most important are the stellar mass and luminosity, which allows one to identify this object as an early B-type protostar." + However. the values on which this conclusion is based depend on the distance. d. which is poorly known.," However, the values on which this conclusion is based depend on the distance, $d$, which is poorly known." + The value quoted in the literature (1.7 kpe) was adopted under the assumption that lies in the Cyg-X region (see Shinnaga et al., The value quoted in the literature (1.7 kpc) was adopted under the assumption that lies in the Cyg-X region (see Shinnaga et al. + 2008. for a discussion of the distance determination)., \cite{shin} for a discussion of the distance determination). + In a previous study. we tried to constrain the distance to the source using the observed proper motions of the mmaser spots associated with it (see Moscadelli et al.," In a previous study, we tried to constrain the distance to the source using the observed proper motions of the maser spots associated with it (see Moscadelli et al." + 2005. for details)., \cite{mosca05} for details). + We concluded that sshould be located farther than. 1.2 kpe. but this result. beside being a very loose constraint. is also model dependent.," We concluded that should be located farther than 1.2 kpc, but this result, beside being a very loose constraint, is also model dependent." + In conclusion. one cannot exclude the possibility that this YSO is much less massive than expected. if d«1.7 kpe. or much more. if d>1.7 kpe.," In conclusion, one cannot exclude the possibility that this YSO is much less massive than expected, if $d\ll1.7$ kpc, or much more, if $d\gg1.7$ kpc." + The former possibility would dramatically reduce the values of stellar mass and luminosity. thus “destroying” the most convincing example of an accretion disk around an early B-type protostar.," The former possibility would dramatically reduce the values of stellar mass and luminosity, thus “destroying” the most convincing example of an accretion disk around an early B-type protostar." + In turn. this would have implications for the formation scenario of high-mass stars. as previously explained.," In turn, this would have implications for the formation scenario of high-mass stars, as previously explained." + Hence. it is of fundamental importance to obtain an accurate estimate of d.," Hence, it is of fundamental importance to obtain an accurate estimate of $d$." + Recently. several studies (see Reid et al.," Recently, several studies (see Reid et al." + 2009b and references therein) have proved the potential of maser parallax measurements for distance determinations., \cite{reid09b} and references therein) have proved the potential of maser parallax measurements for distance determinations. + We have applied this method to the mmasers in aand in Sect., We have applied this method to the masers in and in Sect. + 4. we report on the results obtained., \ref{spara} we report on the results obtained. + Another crucial issue in Galactic studies is that ofthe reference system used to determine absolute proper motions., Another crucial issue in Galactic studies is that ofthe reference system used to determine absolute proper motions. +We svnthesize five Monte Carlo populations of LAINBs. whose spins are such that their gravitational radiation reaction torque exactly balances the accretion torque.,"We synthesize five Monte Carlo populations of LMXBs, whose spins are such that their gravitational radiation reaction torque exactly balances the accretion torque." + We assume that cach simulated LAINB population uncergoes magnetic burial according to one of the live EOS in Table 1.., We assume that each simulated LMXB population undergoes magnetic burial according to one of the five EOS in Table \ref{table:eos}. + Phe number of neutron stars in each population is chosen large enough (~107) to vield an accurate cumulative spin distribution., The number of neutron stars in each population is chosen large enough $(\sim10^{5})$ to yield an accurate cumulative spin distribution. + We assume fiducial neutron star. parameters (see Section 3)) and solve for the equilibrium spin frequency. assuming the wobble anele a tends to a=x/2 due to GW back reaction (2) or crustcore coupling (2)..," We assume fiducial neutron star parameters (see Section \ref{section_3}) ) and solve for the equilibrium spin frequency, assuming the wobble angle $\alpha$ tends to $\alpha = \pi/2$ due to GW back reaction \citep{cutler2002} or crust–core coupling \citep{alpar1988}." + The aceretion rates are. selected from the empirical luminosity function of Galactic LAINB sources (?).. where £ is the apparent luminosity in the 2.10keV band. and Lus is the cut-oll luminosity. combined with the Iuminositv-dependent. mass fraction of the Galaxy which is visible to the All-Sky Monitor sec fig.," The accretion rates are selected from the empirical luminosity function of Galactic LMXB sources \citep{grimm2002}, , where $L$ is the apparent luminosity in the $2-10 \ \mathrm{keV}$ band, and $L_{\mathrm{max}}$ is the cut-off luminosity, combined with the luminosity-dependent mass fraction of the Galaxy which is visible to the All-Sky Monitor [see fig." + 11 of ?]., 11 of \citet{grimm2002}] ]. + The long-term average bolometric luminosity is related: crucely to. the accretion rate by the familiar expression., The long-term average bolometric luminosity is related crudely to the accretion rate by the familiar expression. + The results of the Monte Carlo simulations are shown in Fig. 12..," The results of the Monte Carlo simulations are shown in Fig. \ref{fig:cumulative_spins}," + where we compare the cumulative distribution function of our spin-equilibrium models with the observed distribution of nuclear-powered milliseconcl pulsars (NMPs) (i.c. sources that show brightness oscillations in the tails of Type L X-ray bursts). accretion-powered. milliseeoncl pulsars (AALPS) (i.e. sources that exhibit N-ray. pulsations) and accreting millisecond X-ray pulsars (AAINDs) (i.e. sources that exhibit. either millisecond burst. oscillations. X-rav pulsations or both).," where we compare the cumulative distribution function of our spin-equilibrium models with the observed distribution of nuclear-powered millisecond pulsars (NMPs) (i.e. sources that show brightness oscillations in the tails of Type I X-ray bursts), accretion-powered millisecond pulsars (AMPs) (i.e. sources that exhibit X-ray pulsations) and accreting millisecond X-ray pulsars (AMXPs) (i.e. sources that exhibit either millisecond burst oscillations, X-ray pulsations or both)." + We obtain cata on the spins of these objects from table 1 of ?7.., We obtain data on the spins of these objects from table 1 of \citet{watts2008}. + To be consistent with contemporary literature on millisecond X-ray. binarics (?7).. we adopt the following naming convention for these sources: accreting millisecond. pulsars are AALPs. burst oscillation sources are NALIPs. ancl we combine these two »»)pulations intoAMNXDPs?.," To be consistent with contemporary literature on millisecond X-ray binaries \citep{chakrabarty2003, galloway2008a}, we adopt the following naming convention for these sources: accreting millisecond pulsars are AMPs, burst oscillation sources are NMPs, and we combine these two populations into." +. Vo distinguish between the confirmed. and uncontirmec sources. we plot all/confirmed λος (thin/thiek triple-dot.dashed: ereen lines) AAIPs (thick orange line) and. all/eonfirmed AAINPs (thin/thick dashed blue lines).," To distinguish between the confirmed and unconfirmed sources, we plot all/confirmed NMPs (thin/thick triple-dot–dashed green lines), AMPs (thick orange line) and all/confirmed AMXPs (thin/thick dashed blue lines)." + Curves represent cumulative distribution 'unctions of models A (dot.dashed black curves). D (triple-dot.dashed. red curves). C (short-dashed. &reen curves). D (long-clashecl blue curves) and LE (solid. purple curves).," Curves represent cumulative distribution functions of models A (dot–dashed black curves), B (triple-dot--dashed red curves), C (short-dashed green curves), D (long-dashed blue curves) and E (solid purple curves)." + We update the spin of EXO 0748676 [rom 45 to 552Lz (η. and we do not discriminate between intermittent pulsars and AMPS (i.e. those sources which exhibit intermittent or »ersistent N-rav. pulsations during outburst. respectively).," We update the spin of EXO 0748–676 from $45$ to $552 \ \mathrm{Hz}$ \citep{galloway2010}, and we do not discriminate between intermittent pulsars and AMPs (i.e. those sources which exhibit intermittent or persistent X-ray pulsations during outburst, respectively)." +" The luminosity function is defined for the Monitor catalogue (210keV band). which is Ilux-inited below ~10°""ergsloge (οι. r"," The luminosity function is defined for the All-Sky Monitor catalogue $2-10 +\ \mathrm{keV}$ band), which is flux-limited below $\sim 10^{35} \ \mathrm{erg} +\ \mathrm{s}^{-1}$ \citep{grimm2002}." +pPwo maximum. luminosity. cut-olfs are investigated. namely Zu;—2.75107ergs (to include the mostluminous LMXD Seo N-1) ancl 3.2107*ergs+ (most luminous AMP Aql N-10). encompassing he lumünositv range of all confirmed. ancl unconfirmed AAINDPs.," Two maximum luminosity cut-offs are investigated, namely $L_{\mathrm{max}} = 2.7\times10^{38} \ \mathrm{erg} \ +\mathrm{s}^{-1}$ (to include the mostluminous LMXB Sco X-1) and $3.2\times10^{37} \ \mathrm{erg} \ \mathrm{s}^{-1}$ (most luminous AMP Aql X-1), encompassing the luminosity range of all confirmed and unconfirmed AMXPs." + All sources are assumed to follow the same scaling of the luminosity function., All sources are assumed to follow the same power-law scaling of the luminosity function. + The Alb-Sky Alonitor underestimates μοι true xÀometric luminosity. and hence the aceretion rate. due to the presence of significant hard X-ray tails 10keV in LAINB X-ray spectra (2)..," The All-Sky Monitor underestimates the true bolometric luminosity, and hence the accretion rate, due to the presence of significant hard X-ray tails $\gtrsim 10 \ \mathrm{keV}$ in LMXB X-ray spectra \citep{barret2001}." + Although this can be corrected (?).. we do not attempt to do so here. because equation (23)) is approximate anyway. equation (21)) depends weakly on M. and the bolometric correction factors differ bv up to =40 per cent between sources.," Although this can be corrected \citep{galloway2008b}, we do not attempt to do so here, because equation \ref{accretion_rate}) ) is approximate anyway, equation \ref{spin_equilibrium}) ) depends weakly on $\dot{M}$, and the bolometric correction factors differ by up to $\approx 40$ per cent between sources." +" Considering tvpical LAINB lifetimes of ~107vr (2).. the aceretec masses in these systems are evaluated. to. be in the range of 10ALAL,10°."," Considering typical LMXB lifetimes of $\sim 10^{8} \ \mathrm{yr}$ \citep{podsiadlowski2002}, the accreted masses in these systems are evaluated to be in the range of $10^{-4} \lesssim +M_{\mathrm{a}}/\mathrm{M}_{\sun} \lesssim 10^{1}$." + Therefore. enough matter has been transferred. in these systems to reach the characteristic masses and saturation cllipticitics for the mocels in Table L.. given initial magnetic fields of 10777Ci.," Therefore, enough matter has been transferred in these systems to reach the characteristic masses and saturation ellipticities for the models in Table \ref{table:eos}, given initial magnetic fields of $10^{12.5} \ \mathrm{G}$." + Ilence. for cach simulated LAINB population. we assign the ellipticities of the neutron stars to be the saturation values for the respective EOS in Table 1..," Hence, for each simulated LMXB population, we assign the ellipticities of the neutron stars to be the saturation values for the respective EOS in Table \ref{table:eos}." + From Fig. 12.," From Fig. \ref{fig:cumulative_spins}," +" we see that an isothermal magnetic mountain (model A) stalls the star at 1.1Uz(B./1017€)V7. where the B, scaling follows from AL,xB? of equation. (30} in PAIOL ancl equation (21))."," we see that an isothermal magnetic mountain (model A) stalls the star at $\nu_{\mathrm{s}} \sim 1 \ \mathrm{Hz} \ +(B_{\ast}/10^{12.5} \ \mathrm{G})^{-4/5}$, where the $B_{\ast}$ scaling follows from $M_{\mathrm{c}} \propto B_{\ast}^{2}$ of equation (30) in PM04 and equation \ref{spin_equilibrium}) )." +" One would therefore need D,zm107€ to fit the observed. spin distribution. contradicting population svnthesis studies of isolated pulsars (???).."," One would therefore need $B_{\ast} \approx 10^{10} \ \mathrm{G}$ to fit the observed spin distribution, contradicting population synthesis studies of isolated pulsars \citep{hartman1997, arzoumanian2002, faucher-giguere2006}." + Adiabatic magnetic mountains (models BE) are generally in better agreement. with the observed. spin. distribution., Adiabatic magnetic mountains (models B–E) are generally in better agreement with the observed spin distribution. + In fact. models DB. € and I2 produce a good fit to all of the observec spin distributions.," In fact, models B, C and E produce a good fit to all of the observed spin distributions." +" Equation (D26)) in Appendix B for ⇀∖∫⋅↿∖∠≩↴⊐↕↓↥↓↓≻↓↕∢⋅≻∕∕∖xD,140 ⇂∎∪↓⋅⊔↓⇜⇂⋖⋅↓⊳∖∐⋜⋯∠⇂∐⋡⋜⋯∠ ⇂∪↓⋅⊔↓⋯⇂⋖⋅⊔⋡↓⋯⊳∖⊳⋜↧∣⋈⋅∏⋖⋅↓⋅↕∐↿∪↥↓↥⋖⊾⋖⋅⊔↓↓≻↓↓⋅⊔∼∥N/A e Cp ⋅ ↔ spin clistributions can be obtained for models D and € if the ficlucial magnetic field in the range of 1071075C. rather than 10177Ci. is considered."," Equation \ref{characteristic_mass_adiabatic}) ) in Appendix \ref{appendix:gs_analytic} for $M_{\mathrm{c}}(B_{\ast})$ implies $\nu_{\mathrm{s}} \propto B_{\ast}^{-4/9}$ for models B and D, and $\nu_{\mathrm{s}} \propto B_{\ast}^{-8/15}$ for model C. Thus, a better fit to the empirical spin distributions can be obtained for models B and C if the fiducial magnetic field in the range of $10^{12}-10^{13} \ \mathrm{G}$, rather than $10^{12.5} \ \mathrm{G}$, is considered." + Although model. D. canno match the observed. spin distribution in this range. it is possible that Ohmic dilfusion can improve the agreemen by allowing the mountain to spread. resulting in a lower saturation ellipticitv ancl hence higher equilibrium. spin frequencies.," Although model D cannot match the observed spin distribution in this range, it is possible that Ohmic diffusion can improve the agreement by allowing the mountain to spread, resulting in a lower saturation ellipticity and hence higher equilibrium spin frequencies." + ]t appears that the equilibrium. spin frequencies of confirmed. NAIPs are systematically higher than those of AAIPs: their cumulative distributions are olfset to the right and left of the AMIN distribution. respectively (see Fig. 12)).," It appears that the equilibrium spin frequencies of confirmed NMPs are systematically higher than those of AMPs; their cumulative distributions are offset to the right and left of the AMXP distribution, respectively (see Fig. \ref{fig:cumulative_spins}) )." + This is qualitatively consistent with the CAV spin stallingmechanism. as the median time-averaged accretion luminosities of NAIPs are ~20 times higher than those of AAIPs. resulting in higher equilibrium spin frequencies by a factor of z(20)7/7LS (under the assumption of similar ellipticities in these systems).," This is qualitatively consistent with the GW spin stallingmechanism, as the median time-averaged accretion luminosities of NMPs are $\sim 20$ times higher than those of AMPs, resulting in higher equilibrium spin frequencies by a factor of $\approx (20)^{1/5} \approx 1.8$ (under the assumption of similar ellipticities in these systems)." + This roughly corresponds to the frequency. separation between the observed. NALP and AMP distributions in Fig. 12..," This roughly corresponds to the frequency separation between the observed NMP and AMP distributions in Fig. \ref{fig:cumulative_spins}, ," + supporting the GW, supporting the GW +of enhanced cluster formation between 5-15 Myr and at 90 Myr.,of enhanced cluster formation between 5-15 Myr and at 90 Myr. +" Their cluster sample contains ages for 164 associations, which is the reason why their sample reaches down to ages of —3 Myr."," Their cluster sample contains ages for 164 associations, which is the reason why their sample reaches down to ages of $\sim$ 3 Myr." +" In the combined sample three episodes of enhanced cluster formation are detectable, the youngest around 6.5 Myr, followed by 8 second peak around 160 Myr, and a third around 630 Myr."," In the combined sample three episodes of enhanced cluster formation are detectable, the youngest around 6.5 Myr, followed by a second peak around 160 Myr, and a third around 630 Myr." +" The analysis in the age range of the oldest peak is limited by the depth of the photometry, while the youngest peak mostly comes from the associations adopted from C06."," The analysis in the age range of the oldest peak is limited by the depth of the photometry, while the youngest peak mostly comes from the associations adopted from C06." + The difference between the oldest peak found in our study and by C06 lies within the given uncertainties for the clusterages —0.3)., The difference between the oldest peak found in our study and by C06 lies within the given uncertainties for the clusterages $\sigma_{log(age)}$ =0.3). +" For the LMC, PU00 detected three (0;55(45«)periods of enhanced cluster formation at about 7 Myr, 125 Myr, and 800 Myr, which are similar to the findings of G95."," For the LMC, PU00 detected three periods of enhanced cluster formation at about 7 Myr, 125 Myr, and 800 Myr, which are similar to the findings of G95." + No associations and nebulae were considered in the study of PUO00 and therefore the age distribution of the combined LMC sample does not reach as young an age as the combined SMC sample., No associations and nebulae were considered in the study of PU00 and therefore the age distribution of the combined LMC sample does not reach as young an age as the combined SMC sample. +" The youngest clusters in PUOO's sample have ages of ~5 Myr, but come with high age uncertainties as stated by the authors."," The youngest clusters in PU00's sample have ages of $\sim$ 5 Myr, but come with high age uncertainties as stated by the authors." + The age determination of the oldest clusters in our sample with ages close to 1 Gyr is highly uncertain 3)., The age determination of the oldest clusters in our sample with ages close to 1 Gyr is highly uncertain (class 3). + Clusters with uncertainties smaller than class 3 (classwere discarded and therefore the oldest peak is very weak., Clusters with uncertainties smaller than class 3 were discarded and therefore the oldest peak is very weak. +" In the combined sample an increased number of clusters appears at ~9 Myr and 630 Myr, which is in very good agreement with G95 and P00."," In the combined sample an increased number of clusters appears at $\sim$ 9 Myr and 630 Myr, which is in very good agreement with G95 and P00." + The most enhanced peak occurs at about 125 Myr., The most enhanced peak occurs at about 125 Myr. +" In both the SMC and the LMC, we find evidence for periods of enhanced cluster formation, which appear to have occurred during the same periods."," In both the SMC and the LMC, we find evidence for periods of enhanced cluster formation, which appear to have occurred during the same periods." +" The peaks at 7-125 and 160 Myr, respectively, are very pronounced in both galaxies and are probably correlated."," The peaks at $\sim$ 125 and 160 Myr, respectively, are very pronounced in both galaxies and are probably correlated." + The difference between the peaks is within the given uncertainties for the cluster ages (difference in log(age)=0.1)., The difference between the peaks is within the given uncertainties for the cluster ages (difference in log(age)=0.1). +" Model calculations performed by e.g., Bekki&Chiba and Kallivayaliletal.(2006a,b) showed that(2005) the MW, the LMC, and the SMC have only interacted long enough to produce the Magellanic Stream."," Model calculations performed by e.g., \citet{Bekki05} and \citet{Kalli06a,Kalli06b} showed that the MW, the LMC, and the SMC have only interacted long enough to produce the Magellanic Stream." +" According to these models, the last close encounter between SMC and LMC occurred about 100-200 Myr ago."," According to these models, the last close encounter between SMC and LMC occurred about 100-200 Myr ago." +" The SMC star formation rate increases, if the LMC orbit leads to a close encounter with the SMC and vice versa."," The SMC star formation rate increases, if the LMC orbit leads to a close encounter with the SMC and vice versa." +" The star formation rate decreases again when the LMC recedes from SMC, thus leading to episodic cluster formation."," The star formation rate decreases again when the LMC recedes from SMC, thus leading to episodic cluster formation." +" Hence, this increase in cluster formation some 100-200 Myr ago may have been triggered by a tidal interaction with the neighboring galaxy (e.g. Gar-vayaliletal."," Hence, this increase in cluster formation some 100-200 Myr ago may have been triggered by a tidal interaction with the neighboring galaxy \citep[e.g., ][]{gardiner96,Bekki05,Kalli06a,Kalli06b}." +" The youngest peaks, however, might have another 2006a,b)..origin."," The youngest peaks, however, might have another origin." +" Probably they are caused by associations, which did not yet dissolve."," Probably they are caused by associations, which did not yet dissolve." + High velocity cloud-cloud collisions are another trigger mechanism of cluster formation (Zhangetal.2001;Bekki 2004)..," High velocity cloud-cloud collisions are another trigger mechanism of cluster formation \citep{zhang01,bekki04}. ." + These collisions are particularly effective during galaxy interactions and mergers., These collisions are particularly effective during galaxy interactions and mergers. + High-speed motions, High-speed motions +outside the main-on state.,outside the main-on state. + We now proceed by. discussing some physical interpretations for our results., We now proceed by discussing some physical interpretations for our results. + The complex. multipeaked structure of the pulse profile of ller X-1 above ~1 keV and its evolution pattern over the beat evele is the subject of several studies.," The complex, multipeaked structure of the pulse profile of Her X-1 above $\sim 1$ keV and its evolution pattern over the beat cycle is the subject of several studies." +" The basic features of the pulse profile are nominally explained by the oblique rotator model (Lamb. Pethick Pines 1973). but. there are still many unresolved. questions regarding the details of the mechanism. such as whether the radiation. pattern is best. described: by a superposition of ‘fan’ and ""pencil beams ancl whether the obscuring material that naioclifics the visibility of the direct. beams from the neutron star contributes to the pulse formation."," The basic features of the pulse profile are nominally explained by the oblique rotator model (Lamb, Pethick Pines 1973), but there are still many unresolved questions regarding the details of the mechanism, such as whether the radiation pattern is best described by a superposition of `fan' and `pencil' beams and whether the obscuring material that modifies the visibility of the direct beams from the neutron star contributes to the pulse formation." + Particularly. successful in explaining the pattern observed byANTE ancl is the accretion column model by Scott et al. (, Particularly successful in explaining the pattern observed by and is the accretion column model by Scott et al. ( +2000).,2000). + This moclel invokes the successive obscuration of a cirect beam (that originates from the polar caps of the neutron star). two fan beams focussed in the antipodal direction (possibly due to evclotron backscattering) ancl a more extended scattered halo.," This model invokes the successive obscuration of a direct beam (that originates from the polar caps of the neutron star), two fan beams focussed in the antipodal direction (possibly due to cyclotron backscattering) and a more extended scattered halo." + As the main-on progresses. the inner edge of the accretion disk cover first one of the fan beam components. then the direct pencil beam and then the second fan beam. component.," As the main-on progresses, the inner edge of the accretion disk cover first one of the fan beam components, then the direct pencil beam and then the second fan beam component." + In contrast. the pulsation detected: below ~1 keV usingAT (Oggelmen Trümmpoer 1955).ROSAL (Alavromatakis 1993). ancl (Oosterbrock οἱ al.," In contrast, the pulsation detected below $\sim 1$ keV using (Öggelmen Trümmper 1988), (Mavromatakis 1993), and (Oosterbroek et al." + 1997. 2000. 2001) is broad and cquasi-sinusoidal.," 1997, 2000, 2001) is broad and quasi-sinusoidal." + “Phis emission is thermal and. probably originates in the inner edge of the disk. that partially intercepts ancl reprocesses the hard X-rays from the neutron star.," This emission is thermal and probably originates in the inner edge of the disk, that partially intercepts and reprocesses the hard X-rays from the neutron star." + data taken during the main-on have an excellent signal to noise ratio and allow us to resolve a substructure in the soft. X- light curve., data taken during the main-on have an excellent signal to noise ratio and allow us to resolve a substructure in the soft X-ray light curve. + The 0.3-0.7. keV. pulse profile observed. at 035; —0.02 clearly shows the presence of two separate pulses. ab Ospin~0.0—0. and Ospin~0.30.1 in Figure 4 (the value of the absolute spin phase is arbitrary).," The 0.3-0.7 keV pulse profile observed at $\Phi_{35}$ =0.02 clearly shows the presence of two separate pulses, at $\phi_{spin} \sim 0.0-0.1$ and $\phi_{spin} \sim 0.3-0.4$ in Figure \ref{spin_hard} (the value of the absolute spin phase is arbitrary)." +" Similar features are also evident in data taken later in the beat evele: at 55,—0.17 the pulse profile shows two maxima (al Ospin~OT and ον~0.9 in Figure 4)) and à small ""notch"" like feature preceding the main pulse (at 02, —0.4 in Figure 4)).", Similar features are also evident in data taken later in the beat cycle: at $\Phi_{35}$ =0.17 the pulse profile shows two maxima (at $\phi_{spin} \sim 0.7$ and $\phi_{spin} \sim 0.9$ in Figure \ref{spin_hard}) ) and a small “notch” like feature preceding the main pulse (at $\phi_{spin}$ =0.4 in Figure \ref{spin_hard}) ). + During the short on (5; —0.60). the soft. X- mocdulation is broader. more sinusoidal. and. exhibits a complex substructure in the Leading edge of the pulse Followed by a faster decay.," During the short on $\Phi_{35}$ =0.60), the soft X-ray modulation is broader, more sinusoidal, and exhibits a complex substructure in the leading edge of the pulse followed by a faster decay." + Whether these features rellect an intrinsic complexity in the thermal and geometrical properties of the reprocessing region or keep memory of the structure of the illuminating beams) is unclear., Whether these features reflect an intrinsic complexity in the thermal and geometrical properties of the reprocessing region or keep memory of the structure of the illuminating beam(s) is unclear. + However. it is worth noticing that during all three beat. phases with bright emission. the features detected in the soft light curves qualitatively resemble those of the corresponding hard band.," However, it is worth noticing that during all three beat phases with bright emission, the features detected in the soft light curves qualitatively resemble those of the corresponding hard band." + Phe two maxima observed in the softer band during the main-on (P5;—0.02. 0.17) have a phase separation similar to that of the two main peaks observed in the 2-10. keV. range. Le. ελών~0.0.3.," The two maxima observed in the softer band during the main-on $\Phi_{35}$ =0.02, 0.17) have a phase separation similar to that of the two main peaks observed in the 2-10 keV range, i.e. $\Delta \phi_{spin} \sim 0.2-0.3$." + Similarlv. the small “notch” preceeding the main pulse ab @s5=0.17 μιαν be associated. with the atypical pulse observed at higher energies (both precede the main peak by ελών~0.25.0.3).," Similarly, the small “notch” preceeding the main pulse at $\Phi_{35}$ =0.17 may be associated with the atypical pulse observed at higher energies (both precede the main peak by $\Delta \phi_{spin} \sim 0.25-0.3$ )." +" I these associations are correct. Le. if at least some of the main characteristics of the neutron star beam are not ""washed out during the reprocessing of hard X-rays. this means that the radiative time scale in the inner edge of the disk is much smaller than the photon travel time."," If these associations are correct, i.e. if at least some of the main characteristics of the neutron star beam are not “washed out' during the reprocessing of hard X-rays, this means that the radiative time scale in the inner edge of the disk is much smaller than the photon travel time." + Moreover. the reprocessing region cannot be too extenled in size.," Moreover, the reprocessing region cannot be too extended in size." + “Phis may be explained by a high inclination angle of 10 disk and/or a highly warped inner edge. in which case αν a fraction of the inner region of the disk. intercepts 10 neutron star beam.," This may be explained by a high inclination angle of the disk and/or a highly warped inner edge, in which case only a fraction of the inner region of the disk intercepts the neutron star beam." + Alternatively. the reprocessing of 1ο neutron star beam may be dominated by a shocked. yplically thick hot spot. instead. of being distributed: over 1e entire inner edge.," Alternatively, the reprocessing of the neutron star beam may be dominated by a shocked, optically thick hot spot instead of being distributed over the entire inner edge." + A similar situation is observed in SAV Vlex stars (see e.g. Dhillon et al., A similar situation is observed in SW Sex stars (see e.g. Dhillon et al. + 1997. Ciroot et al.," 1997, Groot et al." + 2000 and weir Figure 6). where the hot spot region is formed through a shock that occurs along the stream. trajectory. but well inside the accretion disk.," 2000 and their Figure 6), where the hot spot region is formed through a shock that occurs along the stream trajectory, but well inside the accretion disk." + Given the complexity of πο source..— pulse-phase spectroscopy is of paramount importance in. cisentangling the different spectral components observed in. Her. X-1.," Given the complexity of the source, pulse-phase spectroscopy is of paramount importance in disentangling the different spectral components observed in Her X-1." + Past observations using (MeGray et al., Past observations using (McGray et al. + 1953} aneBeppoSax (Oosterbrock at al., 1982) and (Oosterbroek at al. + LOOT. 2000) showed. that. during the main-on state. the maximum of the therma component and the power-law components. are. shiftec wo2507.," 1997, 2000) showed that, during the main-on state, the maximum of the thermal component and the power-law components are shifted by $\sim +250^\circ$." + The departure from a phase shift of. 1807 is usually associated with a disk having a tilt angle. under the assumption that the soft. N-ravs originate in the lavers of he disk that intercept and reprocess the neutron star beam.," The departure from a phase shift of $180^\circ$ is usually associated with a disk having a tilt angle, under the assumption that the soft X-rays originate in the layers of the disk that intercept and reprocess the neutron star beam." + The first evidence for a change in the pulse dillerence. as nmieasured at three dillerent. Φος usingNALALNewtou. has oen reported by RO2.," The first evidence for a change in the pulse difference, as measured at three different $\Phi_{35}$ using, has been reported by R02." + 102 found that during the main-on state (550.17) the soft and the hard. X-ray pulse profiles were strongly anti-correlated. and that the phase shift xtween the soft ancl hard maxima was 1507., R02 found that during the main-on state $\Phi_{35}$ =0.17) the soft and the hard X-ray pulse profiles were strongly anti-correlated and that the phase shift between the soft and hard maxima was $\sim150^{\circ}$. + This was in contrast το previous observations mace during the main-on., This was in contrast to previous observations made during the main-on. + Moreover. the phase shift. between these components was significantly different in the observations performed at 935;—0.26 and 0.60.," Moreover, the phase shift between these components was significantly different in the observations performed at $\Phi_{35}$ =0.26 and 0.60." + “Vhis led to the suggestion that. during the first three exposures. the tilt angle. of the acerction disk was changing substantially (RO2).," This led to the suggestion that, during the first three exposures, the tilt angle of the accretion disk was changing substantially (R02)." + In contrast with past observations (Oosterbroek ct al., In contrast with past observations (Oosterbroek et al. + 2000). 1102 did not detect a svimmetric state at 5s~0.0.5.," 2000), R02 did not detect a symmetric state at $\Phi_{35} \sim 0, 0.5$." + Lf the reprocessing region is located at or near the inner region of the disk. such lack of svmimetry may indicate that the disk is strongly warped (lecmskerk van Paraclijs 1989).," If the reprocessing region is located at or near the inner region of the disk, such lack of symmetry may indicate that the disk is strongly warped (Heemskerk van Paradijs 1989)." + In order to further monitor the phase shift over the beat evele. we presented a new measure of the pulse dillerence. taken during the main-on (45;= 0.02).," In order to further monitor the phase shift over the beat cycle, we presented a new measure of the pulse difference, taken during the main-on $\Phi_{35} = 0.02$ )." + We find that the trend detected by RO2 is confirmed. and the change in the," We find that the trend detected by R02 is confirmed, and the change in the" +1n reft-ftthbrt we see that it appears certain that the faint. N-rav sources show a significant correlation with sub-mim sources while it appears that the bright X-ray sources are. less correlated.,In \\ref{f-ftbrt} we see that it appears certain that the faint X-ray sources show a significant correlation with sub-mm sources while it appears that the bright X-ray sources are less correlated. + In Table 1.. alongside the data for the full X-ray sample. we also show the numbers of detected and expected X-rav-sub-mim pairs for faint and bright sources.," In Table \ref{t-smxray}, alongside the data for the full X-ray sample, we also show the numbers of detected and expected X-ray-sub-mm pairs for faint and bright sources." + We confirm the strong significance of the correlation for the faint sources., We confirm the strong significance of the correlation for the faint sources. + Out to 8«20” wwe find 58 pairs of sub-mm and faint X-ray sources compared to an expectation of 23.8. a 7.00 excess assuming Poisson statistics which we have determined to be reliable at these separations.," Out to $\theta<20$ we find 58 pairs of sub-mm and faint X-ray sources compared to an expectation of 23.8, a $7.0\sigma$ excess assuming Poisson statistics which we have determined to be reliable at these separations." + Any excess for the bright X-ray sources is less significant. although. the statistics become poorer and the possibility that the bright and faint X-ray sources are drawn from the same population cannot be ruled out.," Any excess for the bright X-ray sources is less significant, although the statistics become poorer and the possibility that the bright and faint X-ray sources are drawn from the same population cannot be ruled out." + Neverthelesss. it appears certain that the strong. cross-correlation found in reff-smallx originates mostly in the fainter X-ray sources (see also Barecr ct al..," Neverthelesss, it appears certain that the strong cross-correlation found in \\ref{f-smallx} originates mostly in the fainter X-ray sources (see also Barger et al.," + 2001)., 2001). + Figs. 2, Figs. \ref{f-ftbrt} + and show the equivalent correlations between X-ray sources and the 24 and 70 micron sources in the ECDES., and show the equivalent correlations between X-ray sources and the 24 and 70 micron sources in the ECDFS. + Here. strong correlations are seen split. broaclly evenly between the faint anc bright. sources.," Here, strong correlations are seen split broadly evenly between the faint and bright sources." + Lf anything. 1ο brighter X-ray sources may show a stronger correlation aan the fainter ones. contrary to the tentative indication in 10 sub-mm.," If anything, the brighter X-ray sources may show a stronger correlation than the fainter ones, contrary to the tentative indication in the sub-mm." + One possible explanation would be the dilferent k-corrections in these wavebands at here is à strong negative A-correction. increasing the detection of high-redshilt sources. while at and he &Á-correction is positive. favouring lower redshifts.," One possible explanation would be the different $k$ -corrections in these wavebands – at there is a strong negative $k$ -correction, increasing the detection of high-redshift sources, while at and the $k$ -correction is positive, favouring lower redshifts." + This could account for the dillerent results in reff-ftbrt.., This could account for the different results in \\ref{f-ftbrt}. + To test this. we cross-correlate the πμ ssources with bright and faint X-ray sources in the redshift catalogue. imposing redshift cuts of z20.5 and 2>1: we find that the results are not alfected.," To test this, we cross-correlate the and sources with bright and faint X-ray sources in the redshift catalogue, imposing redshift cuts of $z>0.5$ and $z>1$; we find that the results are not affected." + Dillerent cust temperatures might explain any dillerence in the sub-nim anc 247O micron properties of the bright ancl faint X-ray populations., Different dust temperatures might explain any difference in the sub-mm and 24–70 micron properties of the bright and faint X-ray populations. + Lo the faint. sources include the more absorbed ACN. it may be that more absorbed sources have cooler dust temperatures this idea is discussed further in section 7..," If the faint sources include the more absorbed AGN, it may be that more absorbed sources have cooler dust temperatures – this idea is discussed further in section \ref{s-disc}." + Any temperature —dillerence between bright and faint (lux X-ray sources is unlikely to be be driven by warmer dust in more luminous sources. since Lutz et ((2010) have shown that Ly>10! XX-ray sources have brighter sub-mim lluxes.," Any temperature difference between bright and faint flux X-ray sources is unlikely to be be driven by warmer dust in more luminous sources, since Lutz et (2010) have shown that $L_X>10^{44}$ X-ray sources have brighter sub-mm fluxes." + We therefore next directly consider the luminosity dependence of. the sub-mam properties of the ECDES. N-rayv sources to test Lutz et al, We therefore next directly consider the luminosity dependence of the sub-mm properties of the ECDFS X-ray sources to test Lutz et al. +os result.,'s result. + refEsnillxtum shows our sub-mm stacking analysis for high- and low-Iuminosity X-ray sources. divided at Ly=1011 I.," \\ref{f-smflxlum} shows our sub-mm stacking analysis 2) for high- and low-luminosity X-ray sources, divided at $L_X=10^{44}$ ." + Here we focus on a stacking analysis to be consistent with Lutz et (2010)., Here we focus on a stacking analysis to be consistent with Lutz et (2010). + We find a clear cüllerence between the low and high. £x sources in the sense that the high-£x. sources are brighter in the sub-nim. confirming the result of Lutz et al.," We find a clear difference between the low and high $L_X$ sources in the sense that the $L_X$ sources are brighter in the sub-mm, confirming the result of Lutz et al." + In this analysis we have used a catalogue of 277 X-ray sources with confirmed spectroscopic redshifts. combining sources in the catalogues of Pozzi ct ((2006) and Treister et ((2009).," In this analysis we have used a catalogue of 277 X-ray sources with confirmed spectroscopic redshifts, combining sources in the catalogues of Tozzi et (2006) and Treister et (2009)." + Thus high-Iuminosity X-ray sources are stronger sub-mum sources than Low-Iuminosity X-ray. sources. whereas in ποορ owe found that fainter [lux X-ray sources were significant sub-mni emitters.," Thus high-luminosity X-ray sources are stronger sub-mm sources than low-luminosity X-ray sources, whereas in \\ref{f-ftbrt} we found that fainter flux X-ray sources were significant sub-mm emitters." + To make the comparison with refi-smllxlum. easier. in reff-smstacks we show the stacked sub-nim flux around faint. and bright X-ray sources.," To make the comparison with \\ref{f-smflxlum} easier, in \\ref{f-smstacks} we show the stacked sub-mm flux around faint and bright X-ray sources." + TPhis again shows that the faint-Iux sources are at least as powerful sub-min sources as the bright., This again shows that the faint-flux sources are at least as powerful sub-mm sources as the bright. + llowever. this comparison between the [ux and luminosity. results could also be alleetecd by the incompleteness of the spectroscopic redshift (spec-z) sample used to produce the Ly result.," However, this comparison between the flux and luminosity results could also be affected by the incompleteness of the spectroscopic redshift $z$ ) sample used to produce the $L_X$ result." + In |reff-smstacks and. we show the equivalent results for the spec-z ancl photometric samples., In \\ref{f-smstacks} and we show the equivalent results for the $z$ and photometric samples. + Comparing reff-smstacks to reff-smstacks empha.. it seems that the spec-z sample looks more similar to the Lx result in reff-smllxIum.. with the brighter [ux sources appearing more sub-mnmi bright than their fainter counterparts.," Comparing \\ref{f-smstacks} to \\ref{f-smstacks} , it seems that the $z$ sample looks more similar to the $L_X$ result in \\ref{f-smflxlum}, with the brighter flux sources appearing more sub-mm bright than their fainter counterparts." + Therefore. the spec-z sample may not be a representative subset of the X-ray sources in terms of the sources’ sub-mm propertics.," Therefore, the $z$ sample may not be a representative subset of the X-ray sources in terms of the sources' sub-mm properties." + Comparing the left and central panels of reff-smstacks| suggests that there is a population of sources in the full ECDES catalogue which have faint X-ray Buxes but are bright atSTOtum.. which are missing from the spec-z sample.," Comparing the left and central panels of \\ref{f-smstacks} suggests that there is a population of sources in the full ECDFS catalogue which have faint X-ray fluxes but are bright at, which are missing from the $z$ sample." + HEthese faint sources also have lower X-ray luminosities. it would. cast some doubt on the idea that sub-mim emission. arises from. high-Iuminositv. sources only.," If these faint sources also have lower X-ray luminosities, it would cast some doubt on the idea that sub-mm emission arises from high-luminosity sources only." + We therefore next consider the dillerences between the spectroscopic sample and the full catalogue., We therefore next consider the differences between the spectroscopic sample and the full catalogue. + We have seen that there is some indication of a dillerence between the sub-mam properties of N-rav. sources in. the full catalogue and. of those in the spec-z subset. ancl we therefore attempt to identify ways in which the latter is unrepresentative of the former.," We have seen that there is some indication of a difference between the sub-mm properties of X-ray sources in the full catalogue and of those in the $z$ subset, and we therefore attempt to identify ways in which the latter is unrepresentative of the former." + We first find that the spec-z sample is missing faint-Dux. low-Iuminosity N-rav sources at high redshifts. with a particularly significant dearth of faint X-ray sources in the range 1.3«z<2.5 relElumiz)).," We first find that the $z$ sample is missing faint-flux, low-luminosity X-ray sources at high redshifts, with a particularly significant dearth of faint X-ray sources in the range $1.35, then this is the minimum rate at which we would expect the gas to be cooling over 2«z5."," If is reionized at $z > 5$, then this is the minimum rate at which we would expect the gas to be cooling over $2 < z < 5$." +" We show an example thermal asymptote in Figure 13,, which has been normalized to intersect our mmeasurements at z>4.4."," We show an example thermal asymptote in Figure \ref{fig:T0}, which has been normalized to intersect our measurements at $z \ge 4.4$." +" This trend falls well below our measured values of aat z«4, even in the case of y~1.5, which sets a lower limit for the temperature."," This trend falls well below our measured values of at $z < 4$, even in the case of $\gamma \sim 1.5$, which sets a lower limit for the temperature." + The observed rise in ffrom z=4.4 to z~3 therefore requires an additional source of heating beyond what can be achieved in photoionization equilibrium., The observed rise in from $z = 4.4$ to $z \sim 3$ therefore requires an additional source of heating beyond what can be achieved in photoionization equilibrium. + The expected temperature increase for a parcel of gas due to rreionization is approximately (?) where (E) is the mean energy of the ionizing photons.," The expected temperature increase for a parcel of gas due to reionization is approximately \citep{furoh2008b} + where $\langle E \rangle$ is the mean energy of the ionizing photons." +" In the optically thin limit, the mean energy will be weighted by the ionization cross section, σιοςE?."," In the optically thin limit, the mean energy will be weighted by the ionization cross section, $\sigma_{i} \propto E^{-3}$." +" For an ionizing spectrum J,«xν΄, this will produce (E)thin=54.4(a+2)~* eV, which for a quasar-likespectrum (a=1.5;?) gives ATinin©4000 KK. In the optically thick limit, all ionizing photons will be absorbed and (EF)nick=54.4(o—1)!eV, or ATinick&30000 KK. The increase in iin Figure 13 can easily be accommodated within this range."," For an ionizing spectrum $J_{\nu} \propto \nu^{-\alpha}$, this will produce $\langle E \rangle_{\rm thin} = 54.4\, (\alpha + 2)^{-1}\, {\rm eV}$ , which for a quasar-likespectrum \citep[$\alpha = 1.5$;][]{telfer2002} gives $\Delta T_{\rm thin} \approx 4\,000$ K. In the optically thick limit, all ionizing photons will be absorbed and $\langle E \rangle_{\rm thick} = 54.4 \, (\alpha - 1)^{-1}\,{\rm eV}$, or $\Delta T_{\rm thick} \approx 30\,000$ K. The increase in in Figure \ref{fig:T0} can easily be accommodated within this range." +" We emphasize, however, that the temperatures we are measuring are averaged over large volumes."," We emphasize, however, that the temperatures we are measuring are averaged over large volumes." +" During an extended reionization process, the first regions to ionize will have time to cool before the overall process completes."," During an extended reionization process, the first regions to ionize will have time to cool before the overall process completes." + The maximum increase in the globally-averaged wwill therefore be smaller than the increased experienced by an individual parcel of gas., The maximum increase in the globally-averaged will therefore be smaller than the increased experienced by an individual parcel of gas. + We leave detailed modeling of the rise in ffor future work., We leave detailed modeling of the rise in for future work. +" Assuming that the heating of the density IGM at these redshifts is indeed dominated by pphotoheating, however, we can already formulate two basic conclusions: (i) that rreionization occurs at z«5, and (ii) that the process is extended, beginning at z>4.4 and potentially extending to Z~ 3, consistent with the end of rreionization inferred from the evolution in the"," Assuming that the heating of the low-density IGM at these redshifts is indeed dominated by photoheating, however, we can already formulate two basic conclusions: (i) that reionization occurs at $z < 5$, and (ii) that the process is extended, beginning at $z \ge 4.4$ and potentially extending to $z \sim 3$ , consistent with the end of reionization inferred from the evolution in the" +clusters of A901/2.,clusters of A901/2. + Thirdh. we note that a second mass concentration is measured at z20.1. higher up in the plot.," Thirdly, we note that a second mass concentration is measured at $z\simeq0.4$, higher up in the plot." + This has a peal pixel S/N of 2.8. 5ο is certainly significant.," This has a peak pixel S/N of 2.8, so is certainly significant." + While the signal-to-noise on this eround-based application of the 3-D reconstruction is low. this clearly demonstrates the method.," While the signal-to-noise on this ground-based application of the 3-D reconstruction is low, this clearly demonstrates the method." + With higher uunibers of sources i space-based surveys. we cau expect to map out the dark matter distribution iu 3-D over a significant fraction of the ITIubble volume.," With higher numbers of sources in space-based surveys, we can expect to map out the dark matter distribution in 3-D over a significant fraction of the Hubble volume." + Such 3-D dark matter catalogues can then be used as the basis for constructing mass-sclected cluster catalogues with uo projection effects., Such 3-D dark matter catalogues can then be used as the basis for constructing mass-selected cluster catalogues with no projection effects. + While the combination of shear aud redshift information can be use to directly map the 3-D dark matter. an orthogonal application can also be made to probe the dark energv component of the Universe.," While the combination of shear and redshift information can be use to directly map the 3-D dark matter, an orthogonal application can also be made to probe the dark energy component of the Universe." + The dark euergv makes itself felt via its effect on the evolution of the universe aud in particular the Wibble piraueter. f[(o).," The dark energy makes itself felt via its effect on the evolution of the universe and in particular the Hubble parameter, $H(a)$." + This effects both the evolution of dark matter. and the geometrv of the Universe.," This effects both the evolution of dark matter, and the geometry of the Universe." + This effect has been utilised by. for example. Thi (2002). HIuterer (2002). Abazajian Dodelson (2002). Teavens (2003). Refregier et al (2003). Knox (2003) aud Linder Jeukius (2003).," This effect has been utilised by, for example, Hu (2002), Huterer (2002), Abazajian Dodelson (2002), Heavens (2003), Refregier et al (2003), Knox (2003) and Linder Jenkins (2003)." + Receutly Jain Taxlor (2003) have proposed a new method based purely ou the ecometric effect of dark euerev on gravitational lensing., Recently Jain Taylor (2003) have proposed a new method based purely on the geometric effect of dark energy on gravitational lensing. + This involves a particularly simple cross-correlation statistic: the average tangential shear around massive foreground halos associated with galaxy eroups aud galaxy clusters., This involves a particularly simple cross-correlation statistic: the average tangential shear around massive foreground halos associated with galaxy groups and galaxy clusters. + We show that cross-correlation tomoeraply measures ratios of augular diameter distances over a range of redshifts., We show that cross-correlation tomography measures ratios of angular diameter distances over a range of redshifts. +" The distances are eiven bv integrals of the expansion rate. which in turu depencls ou the equation of state of the dark οιον,"," The distances are given by integrals of the expansion rate, which in turn depends on the equation of state of the dark energy." + Thus the lensing toiiographliv we propose cau coustrain the evolution of dark energwv., Thus the lensing tomography we propose can constrain the evolution of dark energy. + Leus tomoeraply has also been studied as a valuable means of introducing redshift information mto shear power spectra as a ecueral method for improving parameter estimation (see e.g. Seljalk 1998. Thi 1999. 2002. ITuterer 2002. Nine Schneider 20020].," Lens tomography has also been studied as a valuable means of introducing redshift information into shear power spectra as a general method for improving parameter estimation (see e.g. Seljak 1998, Hu 1999, 2002, Huterer 2002, King Schneider 2002b)." + The dark οποίον has equation of state p=wp. with «e=1 corresponding to a cosmological constant.," The dark energy has equation of state $p=w\rho$, with $w=-1$ corresponding to a cosmological constant." + The Hubble parameter Z7(0) is given by where fy is the Hubble parameter today., The Hubble parameter $H(a)$ is given by where $H_0$ is the Hubble parameter today. + The comoving distance is r(o)=da!fa?I(a).," The comoving distance is $ +r(a) = \int_0^a d a'/a'^2 H(a') $." + We consider the leusing mduced cross-correlation between massive foreground INhalos. which are traced by galaxies. aud the tangential shear with respect to the halo ceuter (denoted here ~ jr.(0)=foneOn(04) where #¢(@) is the nuuboer density of foreground galaxies with moeau redshift £25). observed in the direction @ iu the sky and 8n2(0)=(μεθ).ne)fie.," We consider the lensing induced cross-correlation between massive foreground halos, which are traced by galaxies, and the tangential shear with respect to the halo center (denoted here $\gamma$ ): $\omega_\times(\theta)\equiv \left<\delta n_{\rm f}(\hth)\gamma(\hth^\prime)\right>$ where $n_{\rm f}(\hth)$ is the number density of foreground galaxies with mean redshift $\langle z_{\rm f}\rangle$, observed in the direction $\hth$ in the sky and $\delta n_{\rm f}(\hth) \equiv (n_{\rm f}(\hth)-{\bar{n}_{\rm f}})/{\bar{n}_{\rm f}}$." + Tho angele between directions @ and 0 is 0., The angle between directions $\hth$ and $\hth^\prime$ is $\theta$ . + The cross-correlation is Given by (Mooessuer Jain 1998. Ciuzik Soljak 2002): (0) 260 6xduaeM[ejm where g(r) is the lensing ecometry averaged over the normalized distribution of background. galaxies Wut) 4drAy as the haloanass cross-power spectruii. and Vg is the foreground halo redshift distribution.," The cross-correlation is given by (Moessner Jain 1998, Guzik Seljak 2002): )= ^2 d r }(r) where $g(r)$ is the lensing geometry averaged over the normalized distribution of background galaxies $W_{\rm b}(\chi)$ $P_{\rm hm}(r, k)$ is the halo-mass cross-power spectrum, and $W_{\rm f}$ is the foreground halo redshift distribution." +" The Bessel function J), has subscript i—2 for the tangential shear aud go=0 for the convergence.", The Bessel function $J_\mu$ has subscript $\mu=2$ for the tangential shear and $\mu=0$ for the convergence. + The measurement of the mean taugenutial shear around foreground galaxies is called galaxy-galaxy leusiug., The measurement of the mean tangential shear around foreground galaxies is called galaxy-galaxy lensing. + We will consider a generalization of this to massive halos that span galaxy eroups aud clusters., We will consider a generalization of this to massive halos that span galaxy groups and clusters. + Tf the, If the +requencies are found near expected radial modes. which are oedieted to have values of 12.155. 15.700. 19.442. 23.195. 26.060. 30.704. 34.4G9 evele+ from the fundamental to he 6th overtone pulsator.,"frequencies are found near expected radial modes, which are predicted to have values of 12.155, 15.700, 19.442, 23.195, 26.960, 30.704, 34.469 cycle$^{-1}$ from the fundamental to the 6th overtone pulsator." + These values are calculated. for he model with IPot62.5 km , These values are calculated for the model with $V_{\rm rot} = 62.5$ km $^{-1}$. +As jb was noted earlier in tus Secjon. the mocerate rotation does not influence the raclia mode frequencies. significantly: if we it the frequency of the racial fundamental. mode to the observed: value o£ 2.154 evele the frequency of the 6th racial overtone changes [rom 34.536 evele 1 to 342845 evevele when the equatorial rotational velocity. changes from 49 kms to SI kms |.," As it was noted earlier in this Section, the moderate rotation does not influence the radial mode frequencies significantly: if we fit the frequency of the radial fundamental mode to the observed value of 12.154 cycle $^{-1}$, the frequency of the 6th radial overtone changes from 34.536 cycle $^{-1}$ to 34.345 cycle $^{-1}$ when the equatorial rotational velocity changes from 49 km $^{-1}$ to 81 km $^{-1}$." + For lower overtones the effect will be proportionally smaller., For lower overtones the effect will be proportionally smaller. + Therefore. our result tha the [recuency pairs cluster around. the racial modes would be valid Lor every reasonable value of the rotational velocity.," Therefore, our result that the frequency pairs cluster around the radial modes would be valid for every reasonable value of the rotational velocity." + The agreement suggests. that an accumulation of nonracdial modes around. the racial frequencies may. occur., The agreement suggests that an accumulation of nonradial modes around the radial frequencies may occur. + The situation seems to be similar to that observed in Bd Lyrac stars (Olech et al., The situation seems to be similar to that observed in RR Lyrae stars (Olech et al. + 1999)., 1999). + Another observational fact mav link the Blazhko Elect in RR Lyrac and 0 Seuti stars: in most close pairs the components have very cillerent amplitudes (Γαία 1)., Another observational fact may link the Blazhko Effect in RR Lyrae and $\delta$ Scuti stars: in most close pairs the components have very different amplitudes (Table 1). + Important. dillerences between two types of stars also exist: in RRO Lyrac stars. the racial modes always dominate in the frequeney spectrum.," Important differences between two types of stars also exist: in RR Lyrae stars, the radial modes always dominate in the frequency spectrum." + Also. the frequeney spectrum of nonracial mocles is much sparser ancl mode trapping is less cllective in 9 Scuti stars than in RAR Lyrae stars.," Also, the frequency spectrum of nonradial modes is much sparser and mode trapping is less effective in $\delta$ Scuti stars than in RR Lyrae stars." + FO Vir has such an extensive photometric cata coverage with excellent frequency. resolution that the relationship between the amplitude ancl phase variations ο»uld ro examined in detail., FG Vir has such an extensive photometric data coverage with excellent frequency resolution that the relationship between the amplitude and phase variations could be examined in detail. + “Phe results. presented. in the previous sections fully support the interpretation of beating between two (or maybe more) close frequencies., The results presented in the previous sections fully support the interpretation of beating between two (or maybe more) close frequencies. +" LE we consider t [act that more than 75 frequencies have been detected. for p Vir"" with. values between 5.7- and 44.3. evele 1 7. t question arises of whether such an agreement could"," If we consider the fact that more than 75 frequencies have been detected for FG Vir with values between 5.7 and 44.3 cycle $^{-1}$ , the question arises of whether such an agreement could be" +spectroscopic variability aud lack of contenporaucous photometry render the hunuiuosities of individual RSCs uncertain. aud further observations are required to place them firmuly on the IIR. diagram.,"spectroscopic variability and lack of contemporaneous photometry render the luminosities of individual RSGs uncertain, and further observations are required to place them firmly on the HR diagram." + Nevertheless. the M1.δα spectral types derived from TiO. baud streugths appear robust (Clarkotal.2010a).. and are clearly discrepant with respect to current theoretical predictions.," Nevertheless, the M1–5Ia spectral types derived from TiO band strengths appear robust \citep{clark10}, and are clearly discrepant with respect to current theoretical predictions." + magnetar (Muuoetal.2006.2007) hes 1.7 from the centre of Wdl. corresponding to 2.3(7/5kpce) pe in. projection.," The magnetar \citep{muno06, muno07} lies 1'.7 from the centre of Wd1, corresponding to $(d/5\text{kpc})$ pc in projection." +" The negligible likelihood of the magnetar beige a chance association and the preseuce of ~OsV stars in Wal provide strong evidence for a massive progenitor (Munoetal.2006).. a result confirmed by our direct neasurement of the mass of which rules out a nmaeguetar progenitor below —25M.. aud strongly supports a progenitor mass di excess ο πολ Εν, unless nass fransfer within is unexpectedly conservative."," The negligible likelihood of the magnetar being a chance association and the presence of $\sim$ O8V stars in Wd1 provide strong evidence for a massive progenitor \citep{muno06}, a result confirmed by our direct measurement of the mass of which rules out a magnetar progenitor below $\sim$ $_\odot$ and strongly supports a progenitor mass in excess of $\sim$ $_\odot$ unless mass transfer within is unexpectedly conservative." + This is cousistent with the expected initial masses of he most evolved WR stars in Wel. ane also progenitor asses derived for other maenetars: a I8 29ND. progenitor nass is foul. for the magnetar based ou its assuned menboersdip of a massive cluster at CUO.0-0.3 (Bibbyctal—2008). while an expanding III shell around the magnetar is inferred to be a wind-blown bubble from a. ~30 LOAD. progenitor (Cracusleretal.2005).," This is consistent with the expected initial masses of the most evolved WR stars in Wd1, and also progenitor masses derived for other magnetars: a $48^{+20}_{-8}$ $_\odot$ progenitor mass is found for the magnetar based on its assumed membership of a massive cluster at G10.0-0.3 \citep{bibby}, while an expanding HI shell around the magnetar is inferred to be a wind-blown bubble from a $\sim$ $_\odot$ progenitor \citep{gaensler}." +. The progenitor of has a significantly lower Lass (Clarketal—2008:Daviesctal. 2009).. nuplving a nunber of formation patlwwars exist.," The progenitor of has a significantly lower mass \citep{clark08, davies}, implying a number of formation pathways exist." + However. the cerived mass of is stronely influenced by the distance to the lost cluster obtained from spectroscopic observations. aud our results place the first constraints on a duassve lmaguctar progenitor.," However, the derived mass of is strongly influenced by the distance to the host cluster obtained from spectroscopic observations, and our results place the first constraints on a massive magnetar progenitor." + Tudecd. our results IEEE that may have the hiehes dvuamically-constrained progenitor mass of confirmed neutron star.," Indeed, our results suggest that may have the highest dynamically-constrained progenitor mass of confirmed neutron star." + The highauass N-rav binary coutains a QG.5Iaf! mass donor with mass HAELIAL.. but the nature of the LE£XE0.27M. conipact object remains uncertain (Clarketal.2002).. while the o» [32 10M... liehle-busnous Bila! lavpergiant iu the N-rav binary qiia. have evolved via quasi-conservative Case A trausfer iua 23.5 day binary with lnitial masses 2OAD.. 25\0.. (Wellsteiu&Lanecr1999:Isaper," The high-mass X-ray binary contains a $^+$ mass donor with mass $\pm$ $_\odot$ but the nature of the $\pm$ $_\odot$ compact object remains uncertain \citep{clark02}, while the $\sim$ $\pm$ $_\odot$, highly-luminous $^+$ hypergiant in the X-ray binary may have evolved via quasi-conservative Case A transfer in a 3.5 day binary with initial masses $_\odot$ $_\odot$ \citep{wellstein, kaper}." +etal. 2006).. NTT/Sofl A.bauad agingOo rules out a current 2 1M... companion to the magnetar (Munoetal.2006).. a result we confirm using deep VET/NACO J-. Π- aud Kdv.-bandl imagineeine (€(Clark et ab.," NTT/SofI $K_\text{s}$ -band imaging rules out a current $\ge1$ $_\odot$ companion to the magnetar \citep{muno06}, a result we confirm using deep VLT/NACO $J$ -, $H$ - and $K_\text{s}$ -band imaging (Clark et al.," + iu prep.)., in prep.). + Nevertheless. eiven the hiel ynary fraction amonuest the WR population (Crowtheretal.2006) and the need for a low pre-supernova core niass to avoid direct (or fallback) black hole formation (c.g. Feveretal. 2002)) it would appear likely that the magnetar progenitor part of a (now-dizxupted) close binary svstenà (Clarkctal.2008).," Nevertheless, given the high binary fraction amongst the WR population \citep{crowther06} and the need for a low pre-supernova core mass to avoid direct (or fallback) black hole formation (e.g. \citealt{fryer}) ) it would appear likely that the magnetar progenitor part of a (now-disrupted) close binary system \citep{clark08}." +. Support for this hvpothesis comes from population svuthesis models. which can oulyform a neutron star from an isolated «ΝΕ. progenitor within the «Όλα age of Wal if mass loss rates fro stellar winds are greatly chhanced (Belezvuski&Tiuun.," Support for this hypothesis comes from population synthesis models, which can onlyform a neutron star from an isolated $\sim$ $_\odot$ progenitor within the $\sim$ 5Myr age of Wd1 if mass loss rates from stellar winds are greatly enhanced \citep{bel}." +"2008).. In a close ary scenario. however. renova of the ivdrogeenuaich outer iantle via Case A mass transfer resisina reduced post-MS ποια core. aud ougoiug Case D trausfer during shell burning will leave a low mass ( 2.1$ m)." + For simplicity. we model the beame-formed response of each tile as that of a single cross-dipole.," For simplicity, we model the beam-formed response of each tile as that of a single cross-dipole." + We assume a continuous antenna density. profile. faXr7. within a 750 m radius with a constant core density. of approximately one tile per 36 im.," We assume a continuous antenna density profile, $\rho_{\rm a} \propto r^{-2}$, within a 750 m radius with a constant core density of approximately one tile per 36 $^2$." + Section. Al of the Appendix gives more detail on the fiducial array configuration considered., Section \ref{Fiducial array configuration} of the Appendix gives more detail on the fiducial array configuration considered. + The integrated complex polarisation over each frecqucney channel will suller from depolarisation due to the deconstructive summation of linear polarisation vectors within the small but finite range of frequencies in. cach channel., The integrated complex polarisation over each frequency channel will suffer from depolarisation due to the deconstructive summation of linear polarisation vectors within the small but finite range of frequencies in each channel. + The integrated complex polarisation for a channel with frequency range f£X£Xνο ds given hy Given a channel of width Av=νονι centred. on οGn|ve)f2. such that Avi.xml. where a=20AQNwfp.. and d ds assumed pis independent. of frequency.," The integrated complex polarisation for a channel with frequency range $\nu_1 \leq \nu \leq \nu_2$ is given by Given a channel of width $\Delta\nu = \nu_2 - \nu_1$ centred on $\nu_{\rm c} = (\nu_1 + \nu_2)/2$, such that $\Delta\nu/\nu_{\rm c} \ll 1$, where $\alpha = 2\phi\lambda_{\rm c}^2\Delta\nu/\nu_{\rm c}$, and it is assumed $p$ is independent of frequency." + Figure 4. shows the bandwidth depolarisation for the MIWA centred on v=143 MlIZ and 204 Mllz (corresponding to the redshifted 21l-enm emission frequeney for 2=9 ancl 6 respectively)., Figure \ref{MWAdepol} shows the bandwidth depolarisation for the MWA centred on $\nu = 143$ MHz and 204 MHz (corresponding to the redshifted 21-cm emission frequency for $z = 9$ and 6 respectively). + We include the cllects of bandwidth: clepolarisation by generating over-sampled. svnthetic Stokes Q and. C spectra. ancl then summing the contributions over each. channel to. produce the final spectra with the desired number of channels., We include the effects of bandwidth depolarisation by generating over-sampled synthetic Stokes $Q$ and $U$ spectra and then summing the contributions over each channel to produce the final spectra with the desired number of channels. + Note that the detectable range and sampling resolution of Faraday. depth can be found in the following way., Note that the detectable range and sampling resolution of Faraday depth can be found in the following way. + The sinc-[actor cHeetively enveloping £24 vanishs when a=7/2., The sinc-factor effectively enveloping $P_{\rm ch}$ vanishs when $\alpha = \pi/2$. +" Solving for ó when £24,=0 gives where AjDo. is the corresponding. central value ofB A72 given. by Equation (16)).", Solving for $\phi$ when $P_{\rm ch} = 0$ gives where $\lambda^2_0$ is the corresponding central value of $\lambda^2$ given by Equation \ref{eq:lambda_0_squared}) ). + From this. the Faraday depth sampling interval is Note that the central [ag channel GL Noy ds. odd. otherwise the central two channels) contains all signals with lo*Ao.," From this, the Faraday depth sampling interval is Note that the central lag channel (if $N_{\rm ch}$ is odd, otherwise the central two channels) contains all signals with $| \phi | < \Delta\phi$." + Due to the finite length. of the longest. baseline. racio interferometers have ᾱ- corresponcingly finite angular resolution.," Due to the finite length of the longest baseline, radio interferometers have a correspondingly finite angular resolution." + This can be quantified in terms of the synthesised beamwidth. given by where A is the wavelength of observing and. D isthe maximum baseline length.," This can be quantified in terms of the synthesised beamwidth, given by where $\lambda$ is the wavelength of observing and $D$ isthe maximum baseline ." +. When calculating the actual angular resolution achievable in the field. of observation. the projection of the basclines onto the skv-plane must be taken into consideration.," When calculating the actual angular resolution achievable in the field of observation, the projection of the baselines onto the sky-plane must be taken into consideration." + Phroughout this work we assume observations of a zenith-field onA, Throughout this work we assume observations of a zenith-field only. +using the relation showed in Table 1 (second row) in ? (see also Fig.,using the relation showed in Table 1 (second row) in \citealp{Lin-2004} (see also Fig. + 9 in their paper)., 9 in their paper). +" The values measured for our clusters have 0.35X;Nsoo/Nat,localS0.8."," The values measured for our clusters have $0.35\lesssim N_{500}/N_{\rm fit, local} \lesssim 0.8$." +" This result is in stark contrast to the results of the re-analysis by Lin and collaborators of the ? intermediate-z cluster sample, also shown in Figure 8,, which indicate normalised Λου values typically between 1—4 for clusters in the range 0.20.85 more data and better redshift sampling are required to establish accurate trends."," In fact, our value of $\gamma$ indicates a significant trend with $z$ at $\sim3 \sigma$ level; although with only 3 points at $z\geq0.85$ more data and better redshift sampling are required to establish accurate trends." + We are in fact also consistent with ? at ~2σ level., We are in fact also consistent with \citet{Lin-2006} at $\sim 2 \sigma$ level. +" Unfortunately we cannot test our results by using ? data points to repeat our fit, since their values are calculated within FR»ooo. Turning to the study of the concentration parameter, the value of c;—2.8*55 found for the observed sample at z~ 1, is consistent within lo with the one of ? at z~0.06 (cg= 2.9076:55)."," Unfortunately we cannot test our results by using \citet{Lin-2006} data points to repeat our fit, since their values are calculated within $R_{2000}$ Turning to the study of the concentration parameter, the value of $c_{\rm g}=2.8_{-0.8}^{+1}$ found for the observed sample at $z\sim 1$ , is consistent within $1\sigma$ with the one of \citet{Lin-2004} at $z\sim 0.06$ $c_{\rm g}=2.90_{-0.22}^{+0.21}$ )." +" However, the latter value is quite different from the ones measured at similar redshifts (e.g., ?))."," However, the latter value is quite different from the ones measured at similar redshifts (e.g., \citealp{Rines-2006}) )." +" In Figure 10 the current measure of cg is plotted, together with the values found in the literature, as a function of log(z+1)."," In Figure \ref{fig:Figure10} the current measure of $c_{\rm g}$ is plotted, together with the values found in the literature, as a function of $\log (z+1)$." +" A comparison with the predictions of ? for dark matter haloes (see Section 6.2.2)) at the same redshift as the median of the clusters studied here is also carried out, showing thatour value of cg=2.8*1, is consistent with this prediction (Cam= 3.55)(see Fig. 10))."," A comparison with the predictions of \citet{Gao-2008} for dark matter haloes (see Section \ref{subsubsec:subsubsec6.2.2}) ) at the same redshift as the median of the clusters studied here is also carried out, showing thatour value of $c_{\rm g}=2.8_{-0.8}^{+1}$ is consistent with this prediction $c_{\rm dm}=3.55$ )(see Fig. \ref{fig:Figure10}) )." +" Turning to the results obtained for the simulations, the values of Nsoo measuredfrom mock clusters (0-$ 35.0) is seen." + The flat jut of the curve of erowth is surprising aud suggestsOO that hese lines have saturated aud are formed im a region with a well-defined outer radius., The flat part of the curve of growth is surprising and suggests that these lines have saturated and are formed in a region with a well-defined outer radius. + We note that the size of this reeion is not the same for every series. but increaseswitli ower quanti level.," We note that the size of this region is not the same for every series, but increaseswith lower quantum level." + Tn order to understand better the nature of the line ormnation in ~ Cas. we show in Fie.," In order to understand better the nature of the line formation in $\gamma$ Cas, we show in Fig." + 5 the line streneth EW/A. where ETE is the liue equivalent. width measured with respect to the{οσα continuun as a function of wavelength.," \ref{fig:vel} the line strength $\overline{EW}$ $\lambda$, where $\overline{EW}$ is the line equivalent width measured with respect to the continuum, as a function of wavelength." + Also shown in Fig., Also shown in Fig. + 5 is the line EWIIM versus waveleugth., \ref{fig:vel} is the line FWHM versus wavelength. + Both EW /A and the PWIIM. show a characteristic wavelength dependence: for cach series. EW /A increases and then saturates to a value of G«10 HL while the line FWIDAL decreases and reaches a roughly coustaut value of 250-300 lan |.," Both $\overline{EW}$ $\lambda$ and the FWHM show a characteristic wavelength dependence: for each series, $\overline{EW}$ $\lambda$ increases and then saturates to a value of $\times$ $^{-4}$, while the line FWHM decreases and reaches a roughly constant value of 250-300 km $^{-1}$." + Iu other words. the lines reach a coustaut Lue over continu ratio of about 1.3 at a coustaut. FWIIM of 250-300 kins |i.," In other words, the lines reach a constant line over continuum ratio of about 1.3 at a constant FWHM of 250-300 km $^{-1}$." +" Ouly the à aud 3 limes of cach series deviate from this behaviour: their Lue over continuum ratio is larecr aud their FATA σαο,", Only the $\alpha$ and $\beta$ lines of each series deviate from this behaviour: their line over continuum ratio is larger and their FWHM smaller. + The decrease of FWHAL with increasing line strength Is expected or lines formed in a rotating disc iu which the rotational velocity decreases with distance: as more line flux is conune from the outer. more slowly rotating regions. the iue width will decrease.," The decrease of FWHM with increasing line strength is expected for lines formed in a rotating disc in which the rotational velocity decreases with distance; as more line flux is coming from the outer, more slowly rotating regions, the line width will decrease." + This is direct proof of the rotating nature of the liue cmitting region., This is direct proof of the rotating nature of the line emitting region. + It is relnarkable that the weakest lines of cach series have a very high. FWIIM of more than 550 kan +., It is remarkable that the weakest lines of each series have a very high FWHM of more than 550 km $^{-1}$. + Such hieh velocities are not expected given the plhotospheric sin ii of 230 kin + (?).. , Such high velocities are not expected given the photospheric $\sin$ i of 230 km $^{-1}$ \citep{1982ApJS...50...55S}. . +This suggests that the inner disc is rotating more rapidly than the star., This suggests that the inner disc is rotating more rapidly than the star. + However. line broadening due to clectrom scattering could also cause," However, line broadening due to electron scattering could also cause" +angular quadrature and 20 logarithmically-spaced energy groups with group centers from 3 to 300MeV.,angular quadrature and 20 logarithmically-spaced energy groups with group centers from 3 to 300. +. Previous studies (Mezzacappa&Bruenn1993a:Liebendórferetal.2004) with hhave shown that 20-group energy resolution is adequate in removing artifacts seen at lower (12-group) energy resolution. and their 12- and 20-group runs exhibited no differences in outcomes.," Previous studies \citep{MeBr93a,LiMeMe04} with have shown that 20-group energy resolution is adequate in removing artifacts seen at lower (12-group) energy resolution, and their 12- and 20-group runs exhibited no differences in outcomes." + Moreover. 20-group energy resolution matches. or exceeds. the resolution used for supernova models computed with the multidimensional codes we discuss in refsec:codes..," Moreover, 20-group energy resolution matches, or exceeds, the resolution used for supernova models computed with the multidimensional codes we discuss in \\ref{sec:codes}." + The discretization scheme is designed to simultaneously conserve lepton number and energy as described in. Liebendérferetal.(2004)., The discretization scheme is designed to simultaneously conserve lepton number and energy as described in \citet{LiMeMe04}. +.. Since we do not include any physics to distinguish between muon- and tau-flavored leptons. we use the combined species Vie= ο mue=Ve.," Since we do not include any physics to distinguish between muon- and tau-flavored leptons, we use the combined species $\numt = \{\numu,\nutau\}$ and $\numtbar = \{\numubar,\nutaubar\}$." +" For all [Ugmodels we use the [Mynuclear. electron. and photon equations of state (EoS) of Lattimer&Swesty(1991) with the bulk incompressibility of nuclear matter +,=220MeV."" This matches the current experimental value of ας=210+20MeV (Shlomoetal.2006) better than the value of 180 mmore commonly used with LS EoS in the past. though the value of &, in LS EoS has been shown to be of little consequence during the early phases of core-collapse supernova evolution shown here (Swestyetal.1994;Thomp-sonetal.2003"," For all models we use the nuclear, electron, and photon equations of state (EoS) of \citet{LaSw91} with the bulk incompressibility of nuclear matter $\kappa_s = 220 \, \mev$ This matches the current experimental value of $\kappa_s = 240 \pm 20 \, \mev$ \citep{ShKoCo06} better than the value of 180 more commonly used with LS EoS in the past, though the value of $\kappa_s$ in LS EoS has been shown to be of little consequence during the early phases of core-collapse supernova evolution shown here \citep{SwLaMy94,ThBuPi03,LeHiBa10}." +":Lentz 2010)... the “iron” core is treated as an ideal gas of Matterοἱthatoutside""flashes"" instantaneously to nuclear statistical equilibrium when the temperatureexceeds 0.47MeV.", Matter outside the “iron” core is treated as an ideal gas of } that “flashes” instantaneously to nuclear statistical equilibrium when the temperatureexceeds 0.47. +. The stellar progenitor used for all models reported here is the ssolar-metalicity progenitor of Woosley&Heger(2007)., The stellar progenitor used for all models reported here is the solar-metalicity progenitor of \citet{WoHe07}. +. We have mapped the inner 1.5V... of the progenitor onto 108 mass shells of the adaptive radial grid.," We have mapped the inner $1.8 \, \msun$ of the progenitor onto 108 mass shells of the adaptive radial grid." + The base. or full. opacity set (FullOp)) includes emission. absorption. and scattering on. free nucleons (Reddyetal. 1998):: isoenergetic scattering on «-particles and heavy nuclei (Bruenn1985): scattering of neutrinos on electrons (NES) and positrons(NPS) (Schinder&Shapiro 1982): production of neutrino pairs from ο¢ annihilation (Schinder&Shapiro1982) απά bremsstrahlung (Hannestad&Raffelt1998):: and electron capture (EC) on nuclet using the LMSH EC table of Langankeetal.(2003).. which utilizes the EC rates of Langanke&Martínez-Pinedo(2000).," The base, or full, opacity set ) includes emission, absorption, and scattering on free nucleons \citep{RePrLa98}; isoenergetic scattering on $\alpha$ -particles and heavy nuclei \citep{Brue85}; scattering of neutrinos on electrons (NES) and positrons(NPS) \citep{SchSh82}; production of neutrino pairs from $e^+e^-$ annihilation \citep{SchSh82} and bremsstrahlung \citep{HaRa98}; and electron capture (EC) on nuclei using the LMSH EC table of \citet{LaMaSa03}, which utilizes the EC rates of \citet{LaMa00}." +. The full angle and energy exchange for scattering between the neutrinos and electrons. positrons. and nucleons is included. while scattering on nuclei is isoenergetic (IS).," The full angle and energy exchange for scattering between the neutrinos and electrons, positrons, and nucleons is included, while scattering on nuclei is isoenergetic (IS)." + Bremsstrahlung and ccl annihilation are the only sources of aand17., Bremsstrahlung and $e^-e^+$ annihilation are the only sources of and. + For our reduced opacity set (ReducOp)) we replace the LMSH EC table for electron capture on nuclei with an independent particle approximation (IPA) (Fuller1982) using the implementation described in Bruenn(1985).. which cuts off when the mean neutron number of the heavy nuclei ANO10.," For our reduced opacity set ) we replace the LMSH EC table for electron capture on nuclei with an independent particle approximation (IPA) \citep{Full82} using the implementation described in \citet{Brue85}, which cuts off when the mean neutron number of the heavy nuclei $N \geq 40$." + We also drop all scatterings (NIS) that couple neutrino-energy groups., We also drop all scatterings (NIS) that couple neutrino-energy groups. + The primary contribution of electron and positron scattering opacities is through neutrino-energy down-seattering (Mezzacappa&Bruenn 1993c).. not through their contribution to the total scattering opacity: therefore. we omit them completely from the oopacity set.," The primary contribution of electron and positron scattering opacities is through neutrino-energy down-scattering \citep{MeBr93c}, , not through their contribution to the total scattering opacity; therefore, we omit them completely from the opacity set." + We also replace the NIS nucleon scattering opacities of Reddyetal.(1998) with the more approximate IS equivalents from Bruenn(1985)., We also replace the NIS nucleon scattering opacities of \citet{RePrLa98} with the more approximate IS equivalents from \citet{Brue85}. +. For consistency. we also replace the neutrino emission and absorption opacities of Reddyetal.(1998) with their Bruenn(1985) equivalents.," For consistency, we also replace the neutrino emission and absorption opacities of \citet{RePrLa98} with their \citet{Brue85} equivalents." + Ion-ion correlations and weak magnetism are omitted from both opacity sets., Ion-ion correlations and weak magnetism are omitted from both opacity sets. + The two opacity sets are summarized in Table |.., The two opacity sets are summarized in Table \ref{tab:opac}. + As noted in refsec:noc.. the Lagrangian formulation in aand the use of the specific neutrino distribution function. F=fp. which ts needed to properly account for number and energy conservation (seediscussiononthenecessitycappa2003. sIV.B).. require care in the definition of a no-observer-corrections model.," As noted in \\ref{sec:noc}, the Lagrangian formulation in and the use of the specific neutrino distribution function, $F=f/\rho$, which is needed to properly account for number and energy conservation \citep[see discussion on the necessity of using $F$ for Lagrangian models in][ \S IV.B]{CaMe03}, require care in the definition of a no-observer-corrections model." + Moreover. time derivatives at fixed Lagrangian mass coordinates on à moving grid must be handled with care (seeLiebendórferetal.2004. 83.2).," Moreover, time derivatives at fixed Lagrangian mass coordinates on a moving grid must be handled with care \citep[see][ \S 3.2]{LiMeMe04}. ." +". Therefore. for model N-ReducOp-NOC.. we implement the ""compression"" term inthe no-observer-corrections transport equation (12)) by re-expressing the time derivative of density as a spatial divergence. using the continuity equation."," Therefore, for model , we implement the “compression” term inthe no-observer-corrections transport equation \ref{eq:lagnoc}) ) by re-expressing the time derivative of density as a spatial divergence, using the continuity equation," +(2005).,. +". In Figure 8 we demonstrate the fraction distributions of γις for pseudo-bulges (dashed line) and classical bulges (solid line), with the superimposed vertical dashed line giving the position of Ly/L4=6."," In Figure 8 we demonstrate the fraction distributions of $r_{1.5}$ for pseudo-bulges (dashed line) and classical bulges (solid line), with the superimposed vertical dashed line giving the position of $L_{\rm b}/L_{\rm d}=6$." +" We can see that the media values of r;5 (arrows in the figure) are 1.7 and 8.2, for pseudo-bulges and classical bulges respectively, which indicates that about a half of the spectra for the pseudo-bulge sample, whereas only a small fraction of the classical bulge sample, are seriously contaminated (Ly/La« 2) by the light from the disk."," We can see that the media values of $r_{1.5}$ (arrows in the figure) are 1.7 and 8.2, for pseudo-bulges and classical bulges respectively, which indicates that about a half of the spectra for the pseudo-bulge sample, whereas only a small fraction of the classical bulge sample, are seriously contaminated $L_{\rm b}/L_{\rm d}<2$ ) by the light from the disk." +" Therefore, we need to check to what extent our results can be reliably retrieved."," Therefore, we need to check to what extent our results can be reliably retrieved." +" To the above purpose, we draw subsamples with r;5>6 both for the pseudo-bulge and classical bulge samples."," To the above purpose, we draw subsamples with $r_{1.5} \geq 6$ both for the pseudo-bulge and classical bulge samples." +" As listed in Table 1, the subsamples of pseudo-bulges and classical bulges contain 7 and 13 member galaxies, respectively."," As listed in Table 1, the subsamples of pseudo-bulges and classical bulges contain 7 and 13 member galaxies, respectively." + The mean values of the parameters presented in Section 3.2 for these two subsamples are also given in Table 1., The mean values of the parameters presented in Section 3.2 for these two subsamples are also given in Table 1. +" It is interesting to find that, in general, the differences of the derived parameters between the two subsamples and their parent samples are small, which indicates that the bulge and inner disk might have similar stellar populations."," It is interesting to find that, in general, the differences of the derived parameters between the two subsamples and their parent samples are small, which indicates that the bulge and inner disk might have similar stellar populations." +" Therefore, our results might not be much affected by the contamination by the disk."," Therefore, our results might not be much affected by the contamination by the disk." +" However, these two subsamples, especially the pseudo-bulge subsample, are much smaller than their parent samples, which can lead to much uncertainty."," However, these two subsamples, especially the pseudo-bulge subsample, are much smaller than their parent samples, which can lead to much uncertainty." +" Our results need to be checked using a much larger sample that covers the entire Hubble types of spiral galaxies, while already these results provide important clues for bulge formation and evolution models."," Our results need to be checked using a much larger sample that covers the entire Hubble types of spiral galaxies, while already these results provide important clues for bulge formation and evolution models." + Y. Zhao is grateful for the financial supports from the NSF of China (grant No., Y. Zhao is grateful for the financial supports from the NSF of China (grant No. +" 10903029), and greatly appreciates the anonymous referee for her/his careful reading and constructive comments."," 10903029), and greatly appreciates the anonymous referee for her/his careful reading and constructive comments." +" The project is supported by the Brazilian agencies CNPq, CAPES and FAPESP and by the France-Brazil CAPES/Cofecub program."," The project is supported by the Brazilian agencies CNPq, CAPES and FAPESP and by the France-Brazil CAPES/Cofecub program." +" This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."," This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + All the authors acknowledge the work of the Sloan Digital Sky Survey (SDSS) team., All the authors acknowledge the work of the Sloan Digital Sky Survey (SDSS) team. +" Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is http://www.sdss.org/li The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. +" The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Universitylj of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics the Kavli Institute for Particle Astrophysics and Cosmology,"," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology," +less active star.,less active star. + This would uaturally explain why the loss active stars are relatively more variable., This would naturally explain why the less active stars are relatively more variable. + Structure functions are often used to. explore the variability timescales present in time-resolved observations of quasars (ee.??).," Structure functions are often used to explore the variability timescales present in time-resolved observations of quasars \citep[e.g.][]{Simonetti1985,MacLeod2011}." + They represent the change observed between two neasurenieuts of some variable quantity. typically broadband fux in the case of quasars. as a function of the time between measurements (At).," They represent the change observed between two measurements of some variable quantity, typically broadband flux in the case of quasars, as a function of the time between measurements $\Delta$ t)." + It is expected that if the ομούναί variability operates on a characteristic timescale (7). then for At < τ. the measurements will be correlated.," It is expected that if the observed variability operates on a characteristic timescale $\tau$ ), then for $\Delta$ t $<$ $\tau$, the measurements will be correlated." + The variability auplitude will increase with ereater tine separation as the observations sample more of the total variability ranee until At = 7., The variability amplitude will increase with greater time separation as the observations sample more of the total variability range until $\Delta$ t = $\tau$. + For At > r. the structure function maintaius a constaut amplitude as the measurements are nucorrelated and raudomly sample the full variability range.," For $\Delta$ t $>$ $\tau$, the structure function maintains a constant amplitude as the measurements are uncorrelated and randomly sample the full variability range." + We enmplov structure functions here to quautify the typical change in the equivalent width measurements for active Al dwarf spectra ii may bius of time separation. At. and to coustrain the characteristic timescale of variability. 7.," We employ structure functions here to quantify the typical change in the equivalent width measurements for active M dwarf spectra in many bins of time separation, $\Delta$ t, and to constrain the characteristic timescale of variability, $\tau$." +" We divide our suuples at the median value of the fractional variability metric iu Figure 6 into the less active but more-variable stars (oryyf EWA) (0.16). aud the more active but less-variable stars (oEgWwj4LíA/CEWILA, < 0.16)."," We divide our samples at the median value of the fractional variability metric in Figure \ref{lhalbol} into the less active but more-variable stars $\sigma_{EWHA}$ $\langle$ $\rangle$ $>$ 0.16), and the more active but less-variable stars $\sigma_{EWHA}$ $\langle$ $\rangle$ $<$ 0.16)." + We then calculate the change in Ta cussion as a fraction of the mean value. AEWIIA/(EWILA;. between every pair of repeated measurements for the same M. dir.," We then calculate the change in $\alpha$ emission as a fraction of the mean value, $\Delta$ $\langle$ $\rangle$, between every pair of repeated measurements for the same M dwarf." + To illustrate how the structure function amplitude is caleulated. the distributions for three SDSS. time bius from the less-variable (more activo) subsample are presented in Fieure 7..," To illustrate how the structure function amplitude is calculated, the distributions for three SDSS time bins from the less-variable (more active) subsample are presented in Figure \ref{strfunchist}." + Each time bin (the At ranee indicated on the Figure) contributes one poiut ou the structure function., Each time bin (the $\Delta$ t range indicated on the Figure) contributes one point on the structure function. + The typical change between nuüeasureiments for a eiven At lin is taken as the RAIS of the AEWTIA/(EWTIA) distribution. normalized by the uunber of samples in that time bin.," The typical change between measurements for a given $\Delta$ t bin is taken as the RMS of the $\Delta$ $\langle$ $\rangle$ distribution, normalized by the number of samples in that time bin." + This accounts for the uneven saupliug of time separations in our datasets., This accounts for the uneven sampling of time separations in our datasets. + The normalized RAIS values for these three bius crease rom 0.13 to 0.16 with increasing At. The SDSS structure πιοος were constructed frou similar normalized RAIS values that were calculated for Ll time bius spanning he cutire range of At sampled by our data., The normalized RMS values for these three bins increase from 0.13 to 0.16 with increasing $\Delta$ t. The SDSS structure functions were constructed from similar normalized RMS values that were calculated for 14 time bins spanning the entire range of $\Delta$ t sampled by our data. + The time jus were chosen to provide good statistics at short At intervals (15 minutes to 2 hours). where there are may observations. aud to cluster around typical At values for oueer intervals (e.g. one day. several davs).," The time bins were chosen to provide good statistics at short $\Delta$ t intervals (15 minutes to 2 hours), where there are many observations, and to cluster around typical $\Delta$ t values for longer intervals $e.g.$ one day, several days)." + The Uyvdra structure functions were only computed for a few time intervals. reflecting the approximately hourly cadence of he observations.," The Hydra structure functions were only computed for a few time intervals, reflecting the approximately hourly cadence of the observations." + Figure saa illustrates the SDSS) (black asterisks) and Uvera (blue filles circles) structure ΠιοΊο» or the high-variability sample (στju A/(EWILA) 16). aud Figure 8Sbb gives the structure functions for he low-variability sample (στη 4/EWILA? < 0.16).," Figure \ref{strfunc}a a illustrates the SDSS (black asterisks) and Hydra (blue filled circles) structure functions for the high-variability sample $\sigma_{EWHA}$ $\langle$ $\rangle >$ 0.16), and Figure \ref{strfunc}b b gives the structure functions for the low-variability sample $\sigma_{EWHA}$ $\langle$ $\rangle <$ 0.16)." + The timescales range from 15 muünutes to 20 ον»., The timescales range from 15 minutes to 20 days. + The iresuluw binning in At reflects the non-uuiforii separations of the measurements in time due to the salplue cadences of the surveys., The irregular binning in $\Delta$ t reflects the non-uniform separations of the measurements in time due to the sampling cadences of the surveys. + We also require that the shortest time bins (At 2 hows) iu the SDSS structure function contain at least 150 measurement pairs. iu order to obtain well-defined normalized RAIS values (see Figure 7)).," We also require that the shortest time bins $\Delta$ t $<$ 2 hours) in the SDSS structure function contain at least 150 measurement pairs, in order to obtain well-defined normalized RMS values (see Figure \ref{strfunchist}) )." + At lareer time separations. the saluple sizes are smaller aud the error bars on the structure function amplitudes are correspoudiuelv larecr.," At larger time separations, the sample sizes are smaller and the error bars on the structure function amplitudes are correspondingly larger." + The low-variability structure function for the SDSS siuuple in Figure 8bb shows a significant trend with time. indicating increasing variability up to a timescale of at cast an hour.," The low-variability structure function for the SDSS sample in Figure \ref{strfunc}b b shows a significant trend with time, indicating increasing variability up to a timescale of at least an hour." + The plateau at timescales shorter than At ~ 0.1 hours suggests that measurement uncertainties nay dominate any variability amplitude effects below hat time separation., The plateau at timescales shorter than $\Delta$ t $\sim$ 0.4 hours suggests that measurement uncertainties may dominate any variability amplitude effects below that time separation. + The high-variabilitv structure function (Figure saa). ou the other laud. shows a flat distribution at all nues for the SDSS sample.," The high-variability structure function (Figure \ref{strfunc}a a), on the other hand, shows a flat distribution at all times for the SDSS sample." + The structure function auplitude is much larger. which is inclicative of the ueher level of variability seen iu this sample.," The structure function amplitude is much larger, which is indicative of the higher level of variability seen in this sample." + The measurement uncertainties are much less than the detected RAIS (structure fiction amplitude). idicatiug hat the variability timescale is shorter than our smallest," The measurement uncertainties are much less than the detected RMS (structure function amplitude), indicating that the variability timescale is shorter than our smallest" +these simulations for completeness.,these simulations for completeness. + In the following subsections we summarise the main results., In the following subsections we summarise the main results. + The level of clustering in the simulations has been first assessed qualitatively by investigating the densities achieved throughout the box., The level of clustering in the simulations has been first assessed qualitatively by investigating the densities achieved throughout the box. + Fig., Fig. +" 12 shows the particles with an associated density greaterthan 10°, 5-10? and 10° times the average density; the results are from the redshift zero snapshots of the 128? and 256? simulations."," \ref{dens_thres} shows the particles with an associated density greaterthan $10^5$ , $5 \cdot 10^5$ and $10^6$ times the average density; the results are from the redshift zero snapshots of the $128^3$ and $256^3$ simulations." +" The densities have been computed in the SPH fashion, using 60 neighbours for all the runs."," The densities have been computed in the SPH fashion, using $60$ neighbours for all the runs." +" As one can see, the runs with adaptive softening reach higher particles densities."," As one can see, the runs with adaptive softening reach higher particles densities." +" Noticeably, the regions where this enhancement of clustering is observed correspond to the high density regions of the 256? simulation; indeed, moving from left to right (i.e. from the fixed softening case to the fully adaptive one) the same areas can be seen to be more and more populated."," Noticeably, the regions where this enhancement of clustering is observed correspond to the high density regions of the $256^3$ simulation; indeed, moving from left to right (i.e. from the fixed softening case to the fully adaptive one) the same areas can be seen to be more and more populated." +" The numbers in the upper-right corner corresponds to the total number of particles surviving the density threshold; interestingly, the number of these high- particles in the 256? simulation correspond to a mass of ez:23000,10000,300 particles at the 128? resolution On a more quantitative level, we have also analysed the clustering by means of the two-point correlation function £(r)."," The numbers in the upper-right corner corresponds to the total number of particles surviving the density threshold; interestingly, the number of these high-density particles in the $256^3$ simulation correspond to a mass of $\approx 23000,\; 10000,\; 300$ particles at the $128^3$ resolution On a more quantitative level, we have also analysed the clustering by means of the two-point correlation function $\xi(r)$." +" This statistics represents the excess probability, compared to a uniform random distribution, of finding pairs of particles at a given spatial separation."," This statistics represents the excess probability, compared to a uniform random distribution, of finding pairs of particles at a given spatial separation." + Fig., Fig. +" 13 shows the ratio of the correlation functions obtained in the different runs to the result of the 256? simulation; the curves are shown at z=0 and starting from separations of 10h!kpc, which correspond roughly to the resolution scale at the 256? level."," \ref{conv_corr_fct} shows the ratio of the correlation functions obtained in the different runs to the result of the $256^3$ simulation; the curves are shown at $z=0$ and starting from separations of $10 \; h^{-1}\mathrm{kpc}$, which correspond roughly to the resolution scale at the $256^3$ level." +" Other than for some discrepancies at separation of severalmegaparsecs!, the correlation functions of the three runs with fixed softening overlap almost perfectly down to 100 h~'kpc."," Other than for some discrepancies at separation of several, the correlation functions of the three runs with fixed softening overlap almost perfectly down to $100\; h^{-1}\mathrm{kpc}$ ." + Below thatscale the differences in resolution result in a progressively larger amplitude., Below thatscale the differences in resolution result in a progressively larger amplitude. + Since the behaviour of £(r) at the, Since the behaviour of $\xi(r)$ at the +"À-h/R. where A corresponds to the semi-thickness of the warm gas dise and R is its radius. and the dynamo numbers R,=aoR/RuQR?η.","$\lambda=h/R$, where $h$ corresponds to the semi-thickness of the warm gas disc and $R$ is its radius, and the dynamo numbers $R_\alpha=\alpha_0 R/\eta, R_\omega=\Omega_0 R^2/\eta$." + 2 must be à small parameter., $\lambda$ must be a small parameter. + y is the turbulent diffusivity. assumed uniform. and or.Qo are typical values of the a-coefficient and angular velocity respectively.," $\eta$ is the turbulent diffusivity, assumed uniform, and $\alpha_0, \Omega_0$ are typical values of the $\alpha$ -coefficient and angular velocity respectively." + Thus the dynamo equations become in cylindrical polar coordinates 67@.3) where z does not appear explicitly.," Thus the dynamo equations become in cylindrical polar coordinates $(r, \phi, z)$ where $z$ does not appear explicitly." + This equation has been calibrated by introduction of the factors 27/4 in the vertical diffusion terms., This equation has been calibrated by introduction of the factors $\pi^2/4$ in the vertical diffusion terms. +" Of course. in principle in the aw approximation the parameters R,.R,, can be combined into a single dynamo number D=R,R,. but for reasons of convenience and clarity of interpretation we choose to keep them separate."," Of course, in principle in the $\alpha\omega$ approximation the parameters $R_\alpha, +R_\omega$ can be combined into a single dynamo number $D=R_\alpha +R_\omega$, but for reasons of convenience and clarity of interpretation we choose to keep them separate." + In the current implementation the code is now written in cartesian coordinates x.y.z. with z-axis parallel to the rotation axis.," In the current implementation the code is now written in cartesian coordinates $x, y, z$, with $z$ -axis parallel to the rotation axis." +" Length. time and magnetic field are non-dimensionalized inunits of ΑΔ. /i/j and the equipartition field strength B, respectively."," Length, time and magnetic field are non-dimensionalized inunits of $R$, $h^2/\eta$ and the equipartition field strength $B_{\rm eq}$ respectively." +" A naive algebraic a-quenching nonlinearity is assumed. oq=ao/(l+B where B4, is the strength of the equipartition field in [Biathe general disc environment. not necessarily that in the ""spots"" — see below."," A naive algebraic $\alpha$ -quenching nonlinearity is assumed, $\alpha=\alpha_0/(1+B^2/B_{\rm eq}^2)$, where $B_{\rm eq}$ is the strength of the equipartition field in the general disc environment, not necessarily that in the “spots” – see below." +" We appreciate that more sophisticated approaches to the saturation process exist. and that careful consideration of helicity transport processes is required to demonstrate that limitation of the large-scale field at very low levels (catastrophic quenching"") does not occur — see e.g. Vishniae Cho (2001). Kleeorin et al. ("," We appreciate that more sophisticated approaches to the saturation process exist, and that careful consideration of helicity transport processes is required to demonstrate that limitation of the large-scale field at very low levels (""catastrophic quenching"") does not occur – see e.g. Vishniac Cho (2001), Kleeorin et al. (" +2002. 2003). Sur et al. (,"2002, 2003), Sur et al. (" +2007).,2007). + However it does appear that in some cases at least. such a naive algebraic quenching can reproduce reasonably well the results from a more sophisticated treatment (e.g. Kleeorin et al.," However it does appear that in some cases at least, such a naive algebraic quenching can reproduce reasonably well the results from a more sophisticated treatment (e.g. Kleeorin et al." + 2002)., 2002). + Of course. more sophisticated forms of algebraic alpha-quenching are also possible. such as forms that are non-local in space or time.," Of course, more sophisticated forms of algebraic alpha-quenching are also possible, such as forms that are non-local in space or time." + We choose to use the simplest possible approach., We choose to use the simplest possible approach. + In order to implement boundary conditions that B.—0 at the dise boundary (as used in earlier versionsof the code written in polar coordinates). the disc region A+Y€| was embedded in a larger computational region [av]€Αρ.)1 outside of the dise the field satisfies the diffusion equation without dynamo terms., In the region $x^2+y^2> 1$ outside of the disc the field satisfies the diffusion equation without dynamo terms. + This was found to give solutions that were small at the dise boundary. and rapidly became negligible outside of the dise.," This was found to give solutions that were small at the disc boundary, and rapidly became negligible outside of the disc." +" The standard implementation used a uniform grid of 229x points over 1.€x.»+1. with appropriate additional points in. the surrounding ""buffer zone""."," The standard implementation used a uniform grid of $229\times 229$ points over $-1 \le x,y \le +1$, with appropriate additional points in the surrounding ""buffer zone""." + With a nominal galaxy radius of 1Okkpe. this gives a resolution of about 88 pe.," With a nominal galaxy radius of kpc, this gives a resolution of about 88 pc." + With R=lOkkpe. the assumed dise. semi-thickness of /;/=500 ppe gives Ut=0.05. and the unit of time is then approximately GGyr.," With $R=10$ kpc, the assumed disc semi-thickness of $h=500$ pc gives $\lambda=0.05$, and the unit of time is then approximately Gyr." +" Subsequently. all fields are in units of the equipartition field B, (i.e. energy equipartition with turbulence). unless explicitly stated."," Subsequently, all fields are in units of the equipartition field $B_{\rm eq}$ (i.e. energy equipartition with turbulence), unless explicitly stated." + The coefhcient αρ is assumed to be uniform in the work described in this paper., The coefficient $\alpha_0$ is assumed to be uniform in the work described in this paper. + We performed tests with a radially varying coefficient ag=aU). but this did not change our results significantly.," We performed tests with a radially varying coefficient $\alpha_0=\alpha_0(r)$, but this did not change our results significantly." +" Taking typical galactic values. we can estimate R,=O(1). R,,=O(IO) (Le. D=10)."," Taking typical galactic values, we can estimate $R_\alpha=O(1)$, $R_\omega=O(10)$ (i.e. $D\approx 10$ )." + However. a considerable degree of uncertainty is attached to the conventional estimate 77=1079 cnr ss7!. and correspondingly to Αι and Αι.," However, a considerable degree of uncertainty is attached to the conventional estimate $\eta=10^{26}$ $^2$ $^{-1}$, and correspondingly to $R_\alpha$ and $R_\omega$." +" (From experiments with an arbitrary seed field. the marginal values are R,«0.6 with RX,=8. so the critical dynamo number for this no-z model is Dy=5."," >From experiments with an arbitrary seed field, the marginal values are $R_\alpha\approx 0.6$ with $R_\omega=8$, so the critical dynamo number for this $z$ model is $D_{\rm cr} \approx 5$." + This value can be compared with the critical dynamo number Di=7 which comes from the local dise dynamo problem (Ruzmaikin et al.," This value can be compared with the critical dynamo number $D_{\rm cr} +\approx 7$ which comes from the local disc dynamo problem (Ruzmaikin et al." + 1988) and illustrates the degree of consistency between the local and no-z models., 1988) and illustrates the degree of consistency between the local and $z$ models. +" In any case. the above estimates of RX, and R,, correspond to a somewhat supercritical dynamo."," In any case, the above estimates of $R_\alpha$ and $R_\omega$ correspond to a somewhat supercritical dynamo." + Of course these estimates apply to conditions im contemporary spiral galaxies and may need revision for very young objects — we will return to this later in Sect. 5.., Of course these estimates apply to conditions in contemporary spiral galaxies and may need revision for very young objects – we will return to this later in Sect. \ref{sec:discussion}. + Note again that we use z as a cartesian coordinate. and not as redshift (except in one instance. where explicitly stated.)," Note again that we use $z$ as a cartesian coordinate, and not as redshift (except in one instance, where explicitly stated.)" +" In our attempt to describe the generatior of small-seale fields in star-forming regions. i, spot centres (vs.v) are generated at random positions within the dise (7X 1."," In our attempt to describe the generation of small-scale fields in star-forming regions, $n_{\rm sp}$ spot centres $(x_{\rm sp}, +y_{\rm sp})$ are generated at random positions within the disc $r\le 1$ )." + These rotate with the local angular velocity., These rotate with the local angular velocity. +" At time intervals dfjj a random field B,s.By.p Is assigned to each of these positions Cy.Y)."," At time intervals $dt_{\rm inj}$ a random field $B_{\rm x,sp}, B_{\rm y,sp}$ is assigned to each of these positions $(x_{\rm sp}, y_{\rm sp})$." + We. slightly arbitrarily. take dfi to be about 10 million years.," We, slightly arbitrarily, take $dt_{\rm inj}$ to be about 10 million years." +" The neighbouring points. out to a radius 374. are assigned non-zero magnetic field by assuming a Gaussian distribution of components By.B, with half-width r, and central values Bysp.sp."," The neighbouring points, out to a radius $3\,r_{\rm sp}$, are assigned non-zero magnetic field by assuming a Gaussian distribution of components $B_{\rm x}, +B_{\rm y}$ with half-width $r_{\rm sp}$ and central values $B_{\rm +x,sp}, B_{\rm y,sp}$." + These spots are assumed to live for a time dfyj., These spots are assumed to live for a time $dt_{\rm sp}>> dt_{\rm inj}$ . + After this time. the old spots disappear. and a new set of Ay Spots is generated using the above algorithm.," After this time, the old spots disappear, and a new set of $n_{\rm sp}$ spots is generated using the above algorithm." + The central field strength in each spot. (Boo+Bia. Is taken from a Gaussian distribution with central value Bijj.," The central field strength in each spot, $(B_{\rm x,sp}^2+B_{\rm y,sp}^2)^{-1}$, is taken from a Gaussian distribution with central value $B_{\rm inj}$ ." + Note that after injection. these fields undergo evolution and take part in the large-scale dynamo action: thus they are a sort of continually renewed seed field.," Note that after injection, these fields undergo evolution and take part in the large-scale dynamo action: thus they are a sort of continually renewed seed field." + Thus the process is not equivalent to evolving a conventional mean-field dynamo. giving à smooth. large-scale field. and ther adding a random field component.," Thus the process is not equivalent to evolving a conventional mean-field dynamo, giving a smooth, large-scale field, and then adding a random field component." + For simplicity. all spots die. and are born. simultaneously.," For simplicity, all spots die, and are born, simultaneously." + A typical configuration of the initial field is shown in Fig. |.., A typical configuration of the initial field is shown in Fig. \ref{initfield}. . + For clarity. this figure plots vectors at only the central point of each spot.," For clarity, this figure plots vectors at only the central point of each spot." + Note that we consider here magnetic field generation from a small-scale seed field and use a small-scale initial field that is random. and distributed in discrete patches.," Note that we consider here magnetic field generation from a small-scale seed field and use a small-scale initial field that is random, and distributed in discrete patches." + This seed is supplemented continuallyby the injection process., This seed is supplemented continuallyby the injection process. +ellipsoidal light. curves.,ellipsoidal light curves. + In (he IR reeime. Chere is a smaller chance of contamination from other sources of light in the svstem.," In the IR regime, there is a smaller chance of contamination from other sources of light in the system." + While modeling several light curves [rom one wavelength reeime helps to constrain model parameters. simultaneously modeling light curves (hat span more (han one wavelength regime provides Geller constraints (han modeling I. light curves alone.," While modeling several light curves from one wavelength regime helps to constrain model parameters, simultaneously modeling light curves that span more than one wavelength regime provides tighter constraints than modeling IR light curves alone." + Previous inclination estimates for NTE J11182-450 have come Irom modeling optical ellipsoidal variations as the svstem approached quiescence (MeClintocketetal.2001:Zuritaοἱ 2002a).," Previous inclination estimates for XTE J1118+480 have come from modeling optical ellipsoidal variations as the system approached quiescence \citep{mcc01, wag01, zur02}." +. These inclination angles range from 55° citepricc0Tl to 83° citepwag01.. and correspond (o primary masses of 10 M. and 6.0 AL. respectively.," These inclination angles range from $^{\circ}$ \\citep{mcc01} to $^{\circ}$ \\citep{wag01}, , and correspond to primary masses of 10 $_{\odot}$ and 6.0 $_{\odot}$, respectively." + Since this svslem has been known to exhibit optical superhumps from the precession of an eccentric accretion disk on ils wav to quiescence (Zuritaetal.2002a).. it is important to determine the orbital inclination angle while NTE J1118-4480 is in a truly quiescent state.," Since this system has been known to exhibit optical superhumps from the precession of an eccentric accretion disk on its way to quiescence \citep{zur02}, it is important to determine the orbital inclination angle while XTE J1118+480 is in a truly quiescent state." + In order to determine an accurate orbital inclination angle for NTE J1118-4-480. we have obtained B-. V-. H-. J-. H-. and K.-band light curves of the svstem while in quiescence. ancl simultaneously model them here with the WD98 light curve modeling code (Wilson1993).," In order to determine an accurate orbital inclination angle for XTE J1118+480, we have obtained $B$ -, $V$ -, $R$ -, $J$ -, $H$ -, and $K_s$ -band light curves of the system while in quiescence, and simultaneously model them here with the WD98 light curve modeling code \citep{wil98}." +. To date. (his is (he most comprehensive ellipsoidal variation data set published for this system.," To date, this is the most comprehensive ellipsoidal variation data set published for this system." + The modeled inclination angle is combined with recently published orbital parameters {ο determine a highly constrained mass of the black hole in this X-ray binary., The modeled inclination angle is combined with recently published orbital parameters to determine a highly constrained mass of the black hole in this X-ray binary. + We observed the NTE J1118+480 field in the optical and IR wavelength regimes., We observed the XTE J1118+480 field in the optical and IR wavelength regimes. + Table summarizes our observations. while we describe them in detail below.," Table \ref{obstab} summarizes our observations, while we describe them in detail below." + We obtained optical observations of NTE J11182-480 over three nights in 2003 and [our niehtis in 2004 using standard Johnson D. V. and. H filters with the 1.5 m telescope at the TUÜDBDITTAN National Observatory in Antalya. Turkey.," We obtained optical observations of XTE J1118+480 over three nights in 2003 and four nights in 2004 using standard Johnson $B$, $V$, and $R$ filters with the 1.5 m telescope at the TÜBBİTTAK National Observatory in Antalya, Turkey." + The data were obtained with the imaging on 2003 June 4-6 and the ANDOR on 2004 March18-19 and 2004 April 23-24., The data were obtained with the imaging on 2003 June 4-6 and the ANDOR on 2004 March18-19 and 2004 April 23-24. + A total of 31. 84. and 83 images were obtained in the B-. V- and [- ," A total of 31, 84, and 83 images were obtained in the $B$ -, $V$ - and $R$ " +AcademiaSection.Sinica.FacultyInstituteofHumanitiesAstronomyandSocialAstrophysics.Sciences. It has been observed that galaxy properties change as a function of galaxy environment: the morphology-density relation reports that fraction of elliptical galaxies is larger at higher galaxy density (Gotoetal..2003):: the star formation rate (SFR) is higher in lower galaxy density (Gómezetal..2003:Tanakaetal..2004) .,"Academia\tikzmark{mainBodyEnd24} \tikzmark{mainBodyStart25}Sinica,\tikzmark{mainBodyEnd25} \tikzmark{mainBodyStart26}Institute\tikzmark{mainBodyEnd26} \tikzmark{mainBodyStart27}of\tikzmark{mainBodyEnd27} \tikzmark{mainBodyStart28}Astronomy\tikzmark{mainBodyEnd28} \tikzmark{mainBodyStart29}and\tikzmark{mainBodyEnd29} \tikzmark{mainBodyStart30}Astrophysics,\tikzmark{mainBodyEnd30} \tikzmark{mainBodyStart31}Taiwan\tikzmark{mainBodyEnd31} +\and \tikzmark{mainBodyStart32}Physics\tikzmark{mainBodyEnd32} \tikzmark{mainBodyStart33}Section,\tikzmark{mainBodyEnd33} \tikzmark{mainBodyStart34}Faculty\tikzmark{mainBodyEnd34} \tikzmark{mainBodyStart35}of\tikzmark{mainBodyEnd35} \tikzmark{mainBodyStart36}Humanities\tikzmark{mainBodyEnd36} \tikzmark{mainBodyStart37}and\tikzmark{mainBodyEnd37} \tikzmark{mainBodyStart38}Social\tikzmark{mainBodyEnd38} \tikzmark{mainBodyStart39}Sciences,\tikzmark{mainBodyEnd39} \tikzmark{mainBodyStart40}Iwate\tikzmark{mainBodyEnd40} \tikzmark{mainBodyStart41}University,\tikzmark{mainBodyEnd41} \tikzmark{mainBodyStart42}Morioka,\tikzmark{mainBodyEnd42} \tikzmark{mainBodyStart43}020-8550\tikzmark{mainBodyEnd43} +\and \tikzmark{mainBodyStart44}TOME\tikzmark{mainBodyEnd44} R\&D\tikzmark{mainBodyStart45}D\tikzmark{mainBodyEnd45} \tikzmark{mainBodyStart46}Inc.\tikzmark{mainBodyEnd46} \tikzmark{mainBodyStart47}Kawasaki,\tikzmark{mainBodyEnd47} \tikzmark{mainBodyStart48}Kanagawa\tikzmark{mainBodyEnd48} \tikzmark{mainBodyStart49}213\tikzmark{mainBodyEnd49} \tikzmark{mainBodyStart50}0012,\tikzmark{mainBodyEnd50} \tikzmark{mainBodyStart51}Japan\tikzmark{mainBodyEnd51} +\and \tikzmark{mainBodyStart52}Asahikawa\tikzmark{mainBodyEnd52} \tikzmark{mainBodyStart53}National\tikzmark{mainBodyEnd53} \tikzmark{mainBodyStart54}College\tikzmark{mainBodyEnd54} \tikzmark{mainBodyStart55}of\tikzmark{mainBodyEnd55} \tikzmark{mainBodyStart56}Technology,\tikzmark{mainBodyEnd56} \tikzmark{mainBodyStart57}2-1-6\tikzmark{mainBodyEnd57} \tikzmark{mainBodyStart58}2-jo\tikzmark{mainBodyEnd58} \tikzmark{mainBodyStart59}Shunkohdai,\tikzmark{mainBodyEnd59} \tikzmark{mainBodyStart60}Asahikawa-shi,\tikzmark{mainBodyEnd60} \tikzmark{mainBodyStart61}Hokkaido\tikzmark{mainBodyEnd61} \tikzmark{mainBodyStart62}071-8142\tikzmark{mainBodyEnd62} +%\and Astrophysics Group, Department of Physics, The Open University, Milton Keynes, MK7 6AA, UK +\tikzmark{mainBodyStart63} \tikzmark{mainBodyEnd63} \tikzmark{mainBodyStart64}}\tikzmark{mainBodyEnd64} + \date{Received September 15, 2009; accepted December 16, 2009} + + \authorrunning{Goto et al.} + + + + +% \abstract{}{}{}{}{} +% 5 {} token are mandatory + + \abstract + % con\tikzmark{mainBodyStart65}ntext\tikzmark{mainBodyEnd65} \tikzmark{mainBodyStart66}heading\tikzmark{mainBodyEnd66} \tikzmark{mainBodyStart67}(optional)\tikzmark{mainBodyEnd67} + % {} leave it empty if necessary +{}\tikzmark{mainBodyStart68}}\tikzmark{mainBodyEnd68} + % aims heading (mandatory) + { + We aim to reveal environmental dependence of infrared luminosity functions (IR LFs) of galaxies at z$\sim$0.8 using the AKARI satellite. AKARI's wide field of view and unique mid-IR filters help us to construct restframe 8$\mu$m LFs directly without relying on SED models. + }\tikzmark{mainBodyStart69}}\tikzmark{mainBodyEnd69} + % methods heading (mandatory) + { +We construct restframe 8$\mu$m IR LFs in the cluster region RXJ1716.4$+$6708 at z=0.81, and compare them with a blank field using the AKARI North Ecliptic Pole deep field data at the same redshift. +AKARI's wide field of view (10'$\times$10') is suitable to investigate wide range of galaxy environments. AKARI's 15$\mu$m filter is advantageous here since it directly probes restframe 8$\mu$m at $z\sim$0.8, without relying on a large extrapolation based on a SED fit, which was the largest uncertainty in previous work. +}\tikzmark{mainBodyStart70}}\tikzmark{mainBodyEnd70} + % results heading (mandatory) + { +We have found that cluster IR LFs at restframe 8$\mu$m have a factor of 2.4 smaller $L^*$ and a steeper faint-end slope than that of the field. %, suggesting the cluster has relatively less IR luminous galaxies. %has a relative increase of LIRG population. + Confirming this trend, we also found that faint-end slopes of the cluster LFs becomes flatter and flatter with decreasing local galaxy density. + These changes in LFs cannot be explained by a simple infall of field galaxy population into a cluster. + Physics that can pre\tikzmark{mainBodyStart71}eferentially\tikzmark{mainBodyEnd71} \tikzmark{mainBodyStart72}suppress\tikzmark{mainBodyEnd72} \tikzmark{mainBodyStart73}IR\tikzmark{mainBodyEnd73} \tikzmark{mainBodyStart74}luminous\tikzmark{mainBodyEnd74} \tikzmark{mainBodyStart75}galaxies\tikzmark{mainBodyEnd75} \tikzmark{mainBodyStart76}in\tikzmark{mainBodyEnd76} \tikzmark{mainBodyStart77}high\tikzmark{mainBodyEnd77} \tikzmark{mainBodyStart78}density\tikzmark{mainBodyEnd78} \tikzmark{mainBodyStart79}regions\tikzmark{mainBodyEnd79} \tikzmark{mainBodyStart80}is\tikzmark{mainBodyEnd80} \tikzmark{mainBodyStart81}required\tikzmark{mainBodyEnd81} \tikzmark{mainBodyStart82}to\tikzmark{mainBodyEnd82} \tikzmark{mainBodyStart83}explain\tikzmark{mainBodyEnd83} \tikzmark{mainBodyStart84}the\tikzmark{mainBodyEnd84} \tikzmark{mainBodyStart85}observed\tikzmark{mainBodyEnd85} \tikzmark{mainBodyStart86}results.\tikzmark{mainBodyEnd86} +%Environmental dependent physical mechanism cannot explain the results unless there exists a mechanism that can preferentially enhance star-formation of faint galaxies, whereas galaxy downsizing can readily explain the observed difference in LFs. +\tikzmark{mainBodyStart87}}\tikzmark{mainBodyEnd87} + % conclusions heading (optional), leave it empty if necessary + {}\tikzmark{mainBodyStart88}} It has been observed that galaxy properties change as a function of galaxy environment; the morphology-density relation reports that fraction of elliptical galaxies is larger at higher galaxy density \citep{2003MNRAS.346..601G}; the star formation rate (SFR) is higher in lower galaxy density \citep{2003ApJ...584..210G,2004AJ....128.2677T} ." + However. despite accumulating observational evidence. we still do not fully understand the underlying physics governing. environmental-dependent evolution of galaxies.," However, despite accumulating observational evidence, we still do not fully understand the underlying physics governing environmental-dependent evolution of galaxies." + Infrared (IR) emission of galaxies is an important probe of galaxy activity since at higher redshift. a significant fraction of star formation is obscured by dust (Takeuchi.Buat.& 2010)..," Infrared (IR) emission of galaxies is an important probe of galaxy activity since at higher redshift, a significant fraction of star formation is obscured by dust \citep{2005A&A...440L..17T,GOTO_NEP_LF}." + Although there exist cluster studies (Baiοἱal..2006:Shimet2010;Tranal. 2010).. not much attention has been paid to the infrared properties of high redshift cluster galaxies. mainly due to the lack of sensitivity in previous IR satellites such as ISO and IRAS.," Although there exist low-z cluster studies \citep{2006ApJ...639..827B,Shim2010,Tran2010}, not much attention has been paid to the infrared properties of high redshift cluster galaxies, mainly due to the lack of sensitivity in previous IR satellites such as ISO and IRAS." + Superb sensitivity of recently launched Spitzer and AKARI satellites can revolutionize the infrared view of environmental dependence of galaxy evolution., Superb sensitivity of recently launched Spitzer and AKARI satellites can revolutionize the infrared view of environmental dependence of galaxy evolution. + In this work. we compare restframe 8j/m LFs between cluster and fieldregions at z=0.8 using data from the AKARI.," In this work, we compare restframe $\mu$ m LFs between cluster and fieldregions at z=0.8 using data from the AKARI." +" Monochromatic restframe 87m luminosity (Ly,,,,.) 18 important since it is known to correlate well with the total IR luminosity (Babbedgeetal..2006:Huang2007).. and hence. with the SER of galaxies (Kennicutt.1998)."," Monochromatic restframe $\mu$ m luminosity $L_{8\mu m}$ ) is important since it is known to correlate well with the total IR luminosity \citep{2006MNRAS.370.1159B,2007ApJ...664..840H}, and hence, with the SFR of galaxies \citep{1998ARA&A..36..189K}." +. This is especially true for star-forming galaxies because the rest-frame 8j/m flux are dominated by prominent PAH features such as at 6.2. 7.7 and 8.6 ym (Desert.Boulanger.&Puget.1990).," This is especially true for star-forming galaxies because the rest-frame $\mu$ m flux are dominated by prominent PAH features such as at 6.2, 7.7 and 8.6 $\mu$ m \citep{1990A&A...237..215D}." +". Important advantages brought by the AKARI are as follows: (1) At z=0.8. AKARIUS I5jim filter (£15) covers the redshifted restframe 8,575. thus we can estimate ὅμπι LFs without using a large extrapolation based on SED models. which were the largest uncertainty in previous work. ("," Important advantages brought by the AKARI are as follows: (i) At z=0.8, AKARI's $\mu$ m filter $L15$ ) covers the redshifted restframe $\mu m$, thus we can estimate $\mu$ m LFs without using a large extrapolation based on SED models, which were the largest uncertainty in previous work. (" +11) Large field of view of the AKARI’s mid-IR camera (IRC. < 10°) allows us to study wider area including clusteroutskirts. where important evolutionary mechanisms are suggested to be at work (Gotoetal..2004:Kodama 2004)..,"ii) Large field of view of the AKARI's mid-IR camera (IRC, $\times$ 10') allows us to study wider area including clusteroutskirts, where important evolutionary mechanisms are suggested to be at work \citep{2004MNRAS.348..515G,2004MNRAS.354.1103K}. ." + For example. passive spiral galaxies have been observed m such an environment (Gotoetal. 2003)... ," For example, passive spiral galaxies have been observed in such an environment \citep{2003PASJ...55..757G}. ." +"Unless otherwise stated. we adopt a cosmology with (77.O,,.Q4)=(0.7.0.3.0.7) ).."," Unless otherwise stated, we adopt a cosmology with $(h,\Omega_m,\Omega_\Lambda) = (0.7,0.3,0.7)$ \citep{2009ApJS..180..330K}. ." +X-ray. observations. of ⋅↴⋅Seyfert 1. galaxies. made with. ASCAAs have shown that the iron. emission2. lines. discovered.. with. GINGA (Poundset al.,X-ray observations of Seyfert 1 galaxies made with ASCA have shown that the iron emission lines discovered with GINGA (Pounds et al. + 1990: Matsuoka et al., 1990; Matsuoka et al. + 1990) are broad (Fabian et al., 1990) are broad (Fabian et al. + 1994: Alushotzky et al., 1994; Mushotzky et al. + 1995: Hevnolds 1997 Nancdra et al., 1995; Reynolds 1997; Nandra et al. + 1997)., 1997). + In particular. the line in ALCC6-30-15 was found to be both broad and skew from a 4.5 clay long observation in 1994. CLanaka et al.," In particular, the line in MCG–6-30-15 was found to be both broad and skew from a 4.5 day long observation in 1994 (Tanaka et al." + 1995)., 1995). + The line extends about 2 keV belowthe rest [rame energy of the line (6.4 keV) and only 0.3 keV above., The line extends about 2 keV below the rest frame energy of the line (6.4 keV) and only 0.3 keV above. + The line profile is well fitted. by that expected from. [uorescence of matter on the surface of an accretion disk less than 20 gravitational radii (i.c. hn=BOCA c) from a black hole of mass Al (Tanaka et al., The line profile is well fitted by that expected from fluorescence of matter on the surface of an accretion disk less than 20 gravitational radii (i.e. $20r_{\rm g}=20GM/c^2$ ) from a black hole of mass $M$ (Tanaka et al. + 1995: Fabian οἱ al., 1995; Fabian et al. + 1995)., 1995). + Much of the skewness of the line is explained. by gravitational redshift. ancl is the first clear| evidence for the elfects of strong nagravity.," Much of the skewness of the line is explained by gravitational redshift, and is the first clear evidence for the effects of strong gravity." +" ]tecent workl Dortexamining ⋅variability| in the| |line relevantprofile"" during the 4.5 dav observation has revealed that it broadened still further during a deep minimum in the light curve (lwasawa∖ et al.", Recent work examining variability in the line profile during the 4.5 day observation has revealed that it broadened still further during a deep minimum in the light curve (Iwasawa et al. + 1996)., 1996). + The red (ie.∖ low⋟ energy)pee wing of the line extended further to the red ‘and the blue (i.c.' high? energv)or wing5 disappeared., The red (i.e. low energy) wing of the line extended further to the red and the blue (i.e. high energy) wing disappeared. +CISADDCs This behaviour‘ can‘ be explained if much. of the emission originates from. within Gre (Iwasawa ct al., This behaviour can be explained if much of the emission originates from within $6r_{\rm g}$ (Iwasawa et al. + 1996)., 1996). + Since a disk. around. a non-spinning.um Schwarzschilel. black hole does not extend: withinE this region. it was concluded that the black hole must. be spinning rapidlv.," Since a disk around a non-spinning, Schwarzschild black hole does not extend within this region, it was concluded that the black hole must be spinning rapidly." + In this case the νου metric applies anc frame ciraggingaoὃν causes the disk to extend inward of 67.E , In this case the Kerr metric applies and frame dragging causes the disk to extend inward of $6r_{\rm g}$. +Light bending ellects. in particular the return of some isk radiation to the disk itself. can then become significant (sec eg. Cunningham 1976).," Light bending effects, in particular the return of some disk radiation to the disk itself, can then become significant (see e.g. Cunningham 1976)." + In. hwasawa et al. (, In Iwasawa et al. ( +1996) -- was proposed (without detailed: calculation) that these fleets could enhance the strength (equivalent width) of the —uorescent line relative to to the continuum. emitted above 10 disk. as required by the observations.,"1996) it was proposed (without detailed calculation) that these effects could enhance the strength (equivalent width) of the fluorescent line relative to to the continuum, emitted above the disk, as required by the observations." + In this Letter we examine the line emission. [rom a isk around a lxerr black hole. from the point of. view of. profile.⋅ and of⋅ equivalent. width.. for⋅ the parameters to ALCG 6-30-15.," In this Letter we examine the line emission from a disk around a Kerr black hole, from the point of view of profile and of equivalent width, for the parameters relevant to MCG–6-30-15." +PEDEPreviously only. the line profile. ⋅ of either a Schwarzschilel black hole (Fabian et al., Previously only the line profile of either a Schwarzschild black hole (Fabian et al. + 1989) or a maximal Ixerr. black hole (Laor 1991: Wojima 1991) have been available. for ⋅⋅⊀fitting., 1989) or a maximal Kerr black hole (Laor 1991; Kojima 1991) have been available for fitting. + Here we explicithy↔ fit ⋅⋅for the angular momentum parameter of the black hole. as well as the inclination⊀⊀∢ angle of the normal to the disk. to the line. of sight.," Here we explicitly fit for the angular momentum parameter of the black hole, as well as the inclination angle of the normal to the disk to the line of sight." + Lo addition. results of a free-form: fit to the radial cnussivity profile of the disk in the D'uorescent line are given. again for the first tine.," In addition, results of a free-form fit to the radial emissivity profile of the disk in the fluorescent line are given, again for the first time." +Using the more accurate WEPC2 photometry. were-estimated. Ale for the 6 galaxies with known redshifts.,"Using the more accurate WFPC2 photometry, were-estimated $M_B$ for the 6 galaxies with known redshifts." + For cach galaxy. the correction (14οHua)z) is derived from the same interpolated model SED as used by. IRLINO2. and then used to derive Ag from the WEPC2 £ magnitude (Table 3).," For each galaxy, the correction $(B_{rest}-I_{814})(z)$ is derived from the same interpolated model SED as used by RLK02, and then used to derive $M_B$ from the WFPC2 $I$ magnitude (Table 3)." + The surface brightnesses and luminosities of our racdio-selected galaxies. are compared with those of normal opticallv-selected. field. galaxies., The surface brightnesses and luminosities of our radio-selected galaxies are compared with those of normal optically-selected field galaxies. +" The half-light radius ry, is equal to or. for bulges and. 1.679.rm.) for disks.", The half-light radius $r_{hl}$ is equal to $r_{e}$ for bulges and $1.679~r_{exp}$ for disks. +" Dinggeli.o Sandage and Tarenghi (1984) lind that for nearby LE/SOs with Ade90 (for 44,=50 km s*\Ipe 1j and for the less luminous (Ale 950) E/SOs For spirals. the Freeman (1970) central SD. is pig21.65 mag aresec7 at all luminosities. which corresponds lo llowever. more recently. Cross and Driver (2002) determined. a bivarate brightness function. for 435000. disk galaxies in the 2dEGIU. and found evidence of a positive correlation between 5D. and. luminosity."," Binggeli, Sandage and Tarenghi (1984) find that for nearby E/S0s with $M_B\leq -20$ (for $H_0=50$ km $\rm s^{-1}Mpc^{-1}$ ) and for the less luminous $M_B> -20$ ) E/S0s For spirals, the Freeman (1970) central SB is $\mu_B=21.65$ mag $\rm arcsec^{-2}$ at all luminosities, which corresponds to However, more recently, Cross and Driver (2002) determined a bivarate brightness function for 45000 disk galaxies in the 2dFGRS, and found evidence of a positive correlation between SB and luminosity." + Their. best-fit relation corresponds to with scatter σοςrjj)= 0.103. or to a central SB," Their best-fit relation corresponds to with scatter $\sigma({\rm log}~r_{hl})=0.103$ , or to a central SB" +We will concentrate in this analysis on the behaviour of the temperature anisotropy power spectrum given. by the covariance of the temperature [uctuation expanded in spherical harmonics C= ,We will concentrate in this analysis on the behaviour of the temperature anisotropy power spectrum given by the covariance of the temperature fluctuation expanded in spherical harmonics C_l = . +ACgo. gives the transfer function for each {ἐν P is the initial powerp) spectrum ancl go is the conformal time todas.," $\Delta_l(k,\eta_0,\mu)$ gives the transfer function for each $\ell$, ${\cal P}_\chi$ is the initial power spectrum and $\eta_0$ is the conformal time today." + On Large scales the transfer functions are of the form aim where AP are the contributions from the last scattering surface given by the ordinary Sachs-Wolfe elfect and the temperature anisotropy. and AES(k) is the contribution due to the change in the potential ó alone the line of sight and is called the integrated Sachs-Wolle (ISW) ellect.," On large scales the transfer functions are of the form _0) = +, where $\Delta_l^{\rm LSS}(k)$ are the contributions from the last scattering surface given by the ordinary Sachs-Wolfe effect and the temperature anisotropy, and $\Delta_l^{\rm ISW}(k)$ is the contribution due to the change in the potential $\phi$ along the line of sight and is called the integrated Sachs-Wolfe (ISW) effect." + The ISW contribution can be written 1967:Llu&Sugivama1995) eerie for an overview of the covariant perturbation formalism. we use here).," The ISW contribution can be written \citep{Sachs:67,Hu95} = 2 for an overview of the covariant perturbation formalism we use here)." + The Poisson equation relates the potential to. the density perturbations via kro = Axa? where dp is the total comoving clensity perturbation.," The Poisson equation relates the potential to the density perturbations via k^2 = - G a^2, where $\overline{\delta\rho}$ is the total comoving density perturbation." +" Thus the source term for the [SW contribution assuming only matter and dark energy is given by dai On, ]. where the perturbations are evaluated in the rest frame of the total energy."," Thus the source term for the ISW contribution assuming only matter and dark energy is given by k^2 = -4 G _m ], where the perturbations are evaluated in the rest frame of the total energy." + The magnitude of the ISW contribution therefore depends on theevolution of the total density. perturbation., The magnitude of the ISW contribution therefore depends on the of the total density perturbation. + In general the fractional perturbations 0;=opip; of a non-interacting [uid evolve as where H is the conformal Hubble parameter. e; is the velocity. w;—τρ. and bh’=(afa). where the local scale [actor α is defined by integrating the Hubble expansion.," In general the fractional perturbations $\delta_i \equiv \delta\rho_i/\rho_i$ of a non-interacting fluid evolve as _i' + _i + (1+w_i)kv_i =, where $\H$ is the conformal Hubble parameter, $v_i$ is the velocity, $w_i\equiv p_i/\rho_i$, and $h' = (\delta a/a)'$, where the local scale factor $a$ is defined by integrating the Hubble expansion." + The sound speed ez is frame-dependent. ancl defined. as ος=pip.," The sound speed $c_s^2$ is frame-dependent, and defined as $ c_s^2 \equiv \delta p/\delta \rho$ ." + Neelectingὃνo anisotropic stress the potential ὁ evolves as where the RIS is a frame invariant combination.," Neglecting anisotropic stress the potential $\phi$ evolves as + + ^2 + = G p - ), where the RHS is a frame invariant combination." +" For a constant total equation of state parameter wy, this becomes o"" = πένα dp.", For a constant total equation of state parameter $\wt$ this becomes ' + = G a^2. + In matter or cosmological constant(11) domination the comoving pressure perturbation is zero on scales where the barvon pressure is negligible., In matter or cosmological constant domination the comoving pressure perturbation is zero on scales where the baryon pressure is negligible. + In this case the growing mocde is the solution ©=const. and there is no contribution to the ISW elfect.," In this case the growing mode is the solution $\phi=\rm{const}$, and there is no contribution to the ISW effect." + Lowever for varying typ. as between matter and dark energy domination. or when there are dark energy perturbations. the potential will not be constant.," However for varying $\wt$, as between matter and dark energy domination, or when there are dark energy perturbations, the potential will not be constant." + In general the evolution. of the perturbations can be computed. numericallv., In general the evolution of the perturbations can be computed numerically. +". For a non-interacting [uid with constant qw. defining the frame invariant quantity ὃςd (the Iluid sound speed in the frame comoving with the Iuid) we have the evolution equations y (Liwhe 2 BOLpwiAt vi | | m AAκ Oy, where cl is the acceleration. (cL=0 in the Cay=0 frame (svnchronous gauge). ef=V in the zero shear frame (Newtonian gauge))"," For a non-interacting fluid with constant $w_i$, defining the frame invariant quantity $\hat{c}_{s,i}^2$ (the fluid sound speed in the frame comoving with the fluid) we have the evolution equations _i' + _i (1+w_i)kv_i = -3(1+w_i)h' v_i' + + kA = k _i/(1+w_i), where $A$ is the acceleration $A=0$ in the $v_m=0$ frame (synchronous gauge), $A=-\Psi$ in the zero shear frame (Newtonian gauge))." + We have assumed zero anisotropic stress. which is the case for matter and simple dark energy models.," We have assumed zero anisotropic stress, which is the case for matter and simple dark energy models." + Also note that a varying equation of state factor will lead to extra contributions to the ISW effect etal. 2003)., Also note that a varying equation of state factor will lead to extra contributions to the ISW effect \citep{Corasaniti:03}. +. In order to study the full evolution of the dark energy uid including Huctuations we need to specify the speed of sound and hence its density and. pressure perturbations., In order to study the full evolution of the dark energy fluid including fluctuations we need to specify the speed of sound and hence its density and pressure perturbations. + A simple way to achieve this. is by relating the dark energy to a scalar field.," A simple way to achieve this, is by relating the dark energy to a scalar field." + In order to be able to analyse models with an equation, In order to be able to analyse models with an equation +NIL; (3.3) maser has never been seen stronger than 0.5.J.]v.,"$_3$ (3,3) maser has never been seen stronger than Jy." + Our observations of the suspected maser in €:23.33-0.30 give a peak Εαν density of τν above the NIL; (3.3) thermal emission. which would make itthe brightest NIL; (3.3) maser known by over an order of magnitude.," Our observations of the suspected maser in G23.33-0.30 give a peak flux density of Jy above the $_3$ (3,3) thermal emission, which would make itthe brightest $_3$ (3,3) maser known by over an order of magnitude." + 123.33-0.30 is associated with an infrared dark cloud (Porettero&Fuller2009) and cold dust continuum. source (DiFrancescoοἱal.2008)., G23.33-0.30 is associated with an infrared dark cloud \citep{peretto09} and cold dust continuum source \citep{difrancesco08}. +. Lt is also associated with a Class IL CLI;OLI maser (Szvmczak.Heynek&Ixus2000).. however. he CLI5OLL maser enission is seen over a velocity range that covers between 63 and and does not overlap with the suspected NIL;(3.3) maser.," It is also associated with a Class II $_3$ OH maser \citep{szymczak00}, however, the $_3$ OH maser emission is seen over a velocity range that covers between 63 and and does not overlap with the suspected $_3$(3,3) maser." + Dased on the possible associations. the suspected dla (3.3) maser is likely to arise [rom a high mass star forming region. although the exact nature of any associations will almost certainly require higher spatial resolution observations to investigate the spatial coincidence of the NIL; (3.3) emission and other features in this region.," Based on the possible associations, the suspected $_3$ (3,3) maser is likely to arise from a high mass star forming region, although the exact nature of any associations will almost certainly require higher spatial resolution observations to investigate the spatial coincidence of the $_3$ (3,3) emission and other features in this region." + Figure 12 shows the Galactic latitude clistribution for water masers detected in LOPS., Figure \ref{glat} shows the Galactic latitude distribution for water masers detected in HOPS. +" The dashed line in Figure 12 shows a fitted Gaussian to the distribution. which has a peak at 0.062"" ancl EWLLM of 0.607."," The dashed line in Figure \ref{glat} shows a fitted Gaussian to the distribution, which has a peak at $-0.062^\circ$ and FWHM of $^\circ$." + Phe PWIAL corresponds to a scale height of 0.5°. which is slightly smaller than the scale height for regions of 0.67 (Wood&Churchwell1989b) and sliehtly larger than the scale height found for Class LE CLL;OLL masers of 0.4° (Walshetal.1997).," The FWHM corresponds to a scale height of $^\circ$, which is slightly smaller than the scale height for regions of $^\circ$ \citep{wood89b} and slightly larger than the scale height found for Class II $_3$ OH masers of $^\circ$ \citep{walsh97}." +. Both regions and Class LL ΟΙ masers are reliable tracers of high mass star formation and their scale height appears to be the smallest known for any class of Galactic object., Both regions and Class II $_3$ OH masers are reliable tracers of high mass star formation and their scale height appears to be the smallest known for any class of Galactic object. + Since the masers appear to be as tightly constrained as the regions and the CIE;OLL masers. we surmise that the majority of detected masers are likely drawn from the same population as regions/— of high mass star formation.," Since the masers appear to be as tightly constrained as the regions and the $_3$ OH masers, we surmise that the majority of detected masers are likely drawn from the same population as regions of high mass star formation." + Given the fitted: Gaussian. to the Galactic latitucle distribution. we can estimate the number of water mascrs that are detectable. but lic at Galactic latitucles outsicle the survey area. between Galactic longitudes of 290° ancl 30°," Given the fitted Gaussian to the Galactic latitude distribution, we can estimate the number of water masers that are detectable, but lie at Galactic latitudes outside the survey area, between Galactic longitudes of $^\circ$ and $^\circ$." +" ‘This is done by integrating under the entire Gaussian curve and comparing this number to the 540 detected masers in he area under the curve between 0.5"" ancl 10.57.", This is done by integrating under the entire Gaussian curve and comparing this number to the 540 detected masers in the area under the curve between $-0.5^\circ$ and $+0.5^\circ$. + We find hat this analysis vieles about 32 undetected maser sites. or.," We find that this analysis yields about 32 undetected maser sites, or." +. We expect this number of undetected masers is a lower imit., We expect this number of undetected masers is a lower limit. + This is because. as mentioned. above. the Gaussian is dominated by. maser sites associated with high mass star ormation.," This is because, as mentioned above, the Gaussian is dominated by maser sites associated with high mass star formation." + But masers are known to also be associated with evolved stars. which have a larger scale height. about he Galactic plane.," But masers are known to also be associated with evolved stars, which have a larger scale height about the Galactic plane." + Based on a MMIETz OLL maser survey owirds evolved stars (Sevensterοἱal.1997)... we estimate he scale height of evolved stars is 1.5.," Based on a MHz OH maser survey towards evolved stars \citep{sevenster97}, we estimate the scale height of evolved stars is $^\circ$." + Therefore. we expect more detections of water masers at higher Galactic latitudes rom evolved. stars.," Therefore, we expect more detections of water masers at higher Galactic latitudes from evolved stars." + Only 15 maser sites in our survey have »een associated with evolved stars. with possibly some other maser sites vet to be associated.," Only 15 maser sites in our survey have been associated with evolved stars, with possibly some other maser sites yet to be associated." + We estimate that probably no more than of all detected masers will be associated with evolved. stars. making them a minor contribution to the total number of masers.," We estimate that probably no more than of all detected masers will be associated with evolved stars, making them a minor contribution to the total number of masers." + Assuming up to of masers are associated with evolved stars. which have a scale height of 1.5. we estimate that no more than about τὸ detectable masers lie in this region.," Assuming up to of masers are associated with evolved stars, which have a scale height of $^\circ$, we estimate that no more than about 73 detectable masers lie in this region." + Note that we have only considered the regions at greater Galactic latitudes. but within the same Galactic longitude range. as the survey area.," Note that we have only considered the regions at greater Galactic latitudes, but within the same Galactic longitude range, as the survey area." + This covers approximately of all Galactic loneituces., This covers approximately of all Galactic longitudes. +" I£ we assume the clistribution of masers is svmmetrical about the Galactic centre in Galactic longitude. then given there are 339 masers between |—290 and (0. we estimate there at least GSO masers between /=290° and/=το and [bf<0.5""."," If we assume the distribution of masers is symmetrical about the Galactic centre in Galactic longitude, then given there are 339 masers between $l=290^\circ$ and $^\circ$, we estimate there at least 680 masers between $l=290^\circ$ and $l=70^\circ$ and $|b|<0.5^\circ$." + Based on the scale. heights given. above. we estimate that there are about SOO detectable masers at all Galactic [atitudes. within this Galactic longitucle range.," Based on the scale heights given above, we estimate that there are about 800 detectable masers at all Galactic latitudes, within this Galactic longitude range." + Without knowing the true distribution of masers in the outer Galaxy. we cannot reliably extrapolate to the number of detectable masers in the entire Galaxy.," Without knowing the true distribution of masers in the outer Galaxy, we cannot reliably extrapolate to the number of detectable masers in the entire Galaxy." + However. we expect that the remaining of the Galaxy will not contain as many detectable masers as the inner Galaxy. so we place an approximate upper limit of 1500 in the entire Galaxy.," However, we expect that the remaining of the Galaxy will not contain as many detectable masers as the inner Galaxy, so we place an approximate upper limit of 1500 in the entire Galaxy." + 1n conclusion. we estimate that there are between SOO and 1500 masers in the Galaxy that are detectable with a survey sensitivity comparable to LOPS.," In conclusion, we estimate that there are between 800 and 1500 masers in the Galaxy that are detectable with a survey sensitivity comparable to HOPS." + Figure 13. shows the distribution of mascrs in Galactic longitude., Figure \ref{glon} shows the distribution of masers in Galactic longitude. + There are. three prominent concentrations of masers at. approximately 3107. 335 and 25°.," There are three prominent concentrations of masers at approximately $^\circ$ , $^\circ$ and $^\circ$ ." + These positions— in the Galaxy. correspond to tangent points of Calactic spiral arms., These positions in the Galaxy correspond to tangent points of Galactic spiral arms. + Towards the Galactic centre. we do not find anv peak in the number of masers. compared. to other longitudes within 20° ," Towards the Galactic centre, we do not find any peak in the number of masers, compared to other longitudes within $^\circ$ " +as (he sum total of the error propagation reports in Table 5..,as the sum total of the error propagation reports in Table \ref{K-[12]}. + If there is a universal mass loss rate (hat varies linearly with the number of stars in a population. then galaxies. observed mass loss rates should scale with Iuminosity (0 a common value.," If there is a universal mass loss rate that varies linearly with the number of stars in a population, then galaxies' observed mass loss rates should scale with luminosity to a common value." + When we propogate the observed errors [rom the various mass loss determinations aud scale by the luminosity of the galaxies (Table 1)). the range of values over the nine galaxies varies by a [actor of ten.," When we propogate the observed errors from the various mass loss determinations and scale by the luminosity of the galaxies (Table \ref{Galaxy Properties Table}) ), the range of values over the nine galaxies varies by a factor of ten." + Meanwhile. the propogatecd errors of observational uncertainties predict a scatter of approximately one-half.," Meanwhile, the propogated errors of observational uncertainties predict a scatter of approximately one-half." + We could justifiably throw out NGC 1344 and/or NGC 5102 [rom our sample. however (hese removals do not change the results.," We could justifiably throw out NGC 1344 and/or NGC 5102 from our sample, however these removals do not change the results." + Because the range of luminosity scaled mass loss rates is much larger than the observational uncertainties. the data suggests Chat we are detecting physical dillerences between these populations and not observing the same phenomena over clilferent sized populations.," Because the range of luminosity scaled mass loss rates is much larger than the observational uncertainties, the data suggests that we are detecting physical differences between these populations and not observing the same phenomena over different sized populations." + The most likely plivsical differences are age and metallicity., The most likely physical differences are age and metallicity. + It is also possible to address the global mass loss rate [rom theoretical stellar evolutionary models for a stellar population., It is also possible to address the global mass loss rate from theoretical stellar evolutionary models for a stellar population. + Because elliptical galaxies consist of an old coeval population and all (hese stars have similar end states. it is possible to construct arguments and/or models predicting the result from a collection of these stars moving through their AGB phase.," Because elliptical galaxies consist of an old coeval population and all these stars have similar end states, it is possible to construct arguments and/or models predicting the result from a collection of these stars moving through their AGB phase." + The first task in such a theoretical line of reasoning is (o determine the fractional number of stars in a given old stellar population that is currently in the AGB phase., The first task in such a theoretical line of reasoning is to determine the fractional number of stars in a given old stellar population that is currently in the AGB phase. + One method for determining (his critical input parameter is (o use observations of supernovae (SNe) and planetary. nebulae (DN)., One method for determining this critical input parameter is to use observations of supernovae (SNe) and planetary nebulae (PN). + These stellar evolutionary phases are short lived. but over a large enough population such as a galaxy. there are enough of these seen al any given lime {ο eive an idea of the relative numbers of stars in these post-AGD phases.," These stellar evolutionary phases are short lived, but over a large enough population such as a galaxy, there are enough of these seen at any given time to give an idea of the relative numbers of stars in these post-AGB phases." + If the number of these observables are extrapolated to include the entire AGB phase. then an estimate can be obtained of the Traction of stars of a population that are currently losing mass.," If the number of these observables are extrapolated to include the entire AGB phase, then an estimate can be obtained of the fraction of stars of a population that are currently losing mass." + From stellar modeling and stellar remnant observations. it is known that stars with masses around lose approximately in (he AGB phase.," From stellar modeling and stellar remnant observations, it is known that stars with masses around lose approximately in the AGB phase." + Also. from stellar modeling applied to observations of clusters of stars it is known that the approximate time spent in the AGB phase is on the order of vears.," Also, from stellar modeling applied to observations of clusters of stars it is known that the approximate time spent in the AGB phase is on the order of years." + Combining the fraction of a population in the AGB phase with the total mass loss for 1.0 stars and the time taken to lose this mass. itis possible to derive estimates of galaxyv-wide mass loss rates.," Combining the fraction of a population in the AGB phase with the total mass loss for 1.0 stars and the time taken to lose this mass, it is possible to derive estimates of galaxy-wide mass loss rates." + Faber&Gallagher(1976) made such arguments based on the observations at the time, \citet{Faber & Gallagher} made such arguments based on the observations at the time +two clillerent regimes. for low (roughly lower than one solar mass). and hiei masses.,"two different regimes, for low (roughly lower than one solar mass), and high masses." + The IME at low masses is essential. but in many «uses in the literature the value of the index adopted in chemical evolution. models seems. unrealistic.," The IMF at low masses is essential, but in many cases in the literature the value of the index adopted in chemical evolution models seems unrealistic." + For instance. Portinari Chiosi (1999) adopt. x—1.35 for M< 2 ιν wule others Gratton et al. (," For instance, Portinari Chiosi (1999) adopt x=1.35 for $<$ 2 $_{\odot}$, while others Gratton et al. (" +2000) use Scalo (1986). which is also too steep at low masses.,"2000) use Scalo (1986), which is also too steep at low masses." + Other works utilise a singlο index for calculating the vield. such as ilvugin Ecmunes (1996).," Other works utilise a single index for calculating the yield, such as Pilyugin Edmunds (1996)." + Recent measurements of the IME from the solar neighbourhood luminosity function have ooved that the EME index at low masses is much shallower han the Salpeter value. at x=0.05 (Reidctal.1996)..," Recent measurements of the IMF from the solar neighbourhood luminosity function have proved that the IMF index at low masses is much shallower than the Salpeter value, at x=0.05 \cite{96REI_EA}." +. At ueher masses. the IAL is much more uncertain (see Scalo (1998). Laywood et al. (," At higher masses, the IMF is much more uncertain (see Scalo (1998), Haywood et al. (" +1997b) for a review).,1997b) for a review). + We consider hat values between x=1 and 2 are reasonable. and. values oetween 2 and 3 are not unrealistic.," We consider that values between x=1 and 2 are reasonable, and values between 2 and 3 are not unrealistic." + Fig., Fig. + 12) shows that for values of the high mass IME index less than = 1.9. the vield is larger than 0.01.," \ref{yieldfig1} shows that for values of the high mass IMF index less than $\approx$ 1.9, the yield is larger than 0.01." + For Salpeter EME index. values of the vield as high as 0.05 are possible.," For Salpeter IMF index, values of the yield as high as 0.05 are possible." +" Assuming that (he present ratio S44:0)/94,.00) is around 0.10.3 and that the abundance of the interstellar mecium is of the order 0.020.03. this value is in the range of possible viclds."," Assuming that the present ratio $_{gas}$ $_{gas}$ (0) is around 0.1–0.3 and that the abundance of the interstellar medium is of the order 0.02–0.03, this value is in the range of possible yields." + An important issue when ciscussing the distribution of metallicities is the surface densities of the stellar and gas components in the solar neighbourhood., An important issue when discussing the distribution of metallicities is the surface densities of the stellar and gas components in the solar neighbourhood. + According to (Jahreiss&Wiclen.1997).. the local stellar density is 10TAL. I.," According to \shortcite{97JAH_EA}, the local stellar density is $\times$ $^{-2}$ $_{\odot}$ $^{-3}$." + The projection to distance outside the galactic plane can be mace assuming exponential density for the thin disc and the thick disc., The projection to distance outside the galactic plane can be made assuming exponential density for the thin disc and the thick disc. + Assuming the thick disce is responsible for 2 per cent of the local stellar mass. and has a scale height of 1400 pe (Reid&Majewski.1993).. the thin disc with 325 pe. then the relative amount of thick disc is of the order of 89 per cent.," Assuming the thick disc is responsible for 2 per cent of the local stellar mass, and has a scale height of 1400 pc \shortcite{93REI_EA}, the thin disc with 325 pc, then the relative amount of thick disc is of the order of 8–9 per cent." + The total surface density of visible stars (i.e no stellar remnants) is of the order of 27 AL. 2, The total surface density of visible stars (i.e no stellar remnants) is of the order of 27 $_{\odot}$ $^{-2}$. + ‘Taking into account the gas surface density and allowing for some stellar remnant. the total surface density is of the order of 4050 M..pe 7.," Taking into account the gas surface density and allowing for some stellar remnant, the total surface density is of the order of 40–50 $_{\odot}$ $^{-2}$." + Assuming disce characteristics as those proposed by (Llavwoodetal.LOOT) and (Robinet1996).. one finds that the thick disc represents 15 per cent of the local stellar surface censitv.," Assuming disc characteristics as those proposed by \shortcite{97HAY_EA2} and \shortcite{96ROB_EA}, one finds that the thick disc represents 15 per cent of the local stellar surface density." + A correlated. problem is the correction one has to apply in order to convert volume densities to surface densities. and vice versa.," A correlated problem is the correction one has to apply in order to convert volume densities to surface densities, and vice versa." + This is a dillicult problem. because the scale heights of the (thin and thick) disces are a function of age. which is not a quantity that can be derived for stars in the sample.," This is a difficult problem, because the scale heights of the (thin and thick) discs are a function of age, which is not a quantity that can be derived for stars in the sample." + Various attempts have been mace. see in particular Sommer-Larsen (1991) and. Wyse Gilmore (1995).," Various attempts have been made, see in particular Sommer-Larsen (1991) and Wyse Gilmore (1995)." + Wyse Gilmore (1995) estimated a correction function. of the metallicity., Wyse Gilmore (1995) estimated a correction function of the metallicity. + One problem with their solution is that they use the same correction for stars in the interval be/l]=-0.3.|12].," One problem with their solution is that they use the same correction for stars in the interval [Fe/H]=[-0.3,+0.3]." + llowever. even though this may seem a rather narrow range. there is a significant age trend over this interval (sce the age-metallicity relation below).," However, even though this may seem a rather narrow range, there is a significant age trend over this interval (see the age-metallicity relation below)." + It. implies that such stars may have quite cdillerent ages. hence quite dilferent correction should be applied.," It implies that such stars may have quite different ages, hence quite different correction should be applied." +" We choose to ""correct the predicted distribution instead (that is. we convert mocel surface density to volume density). since metallicity is an explicit function of age in the mocdel."," We choose to `correct' the predicted distribution instead (that is, we convert model surface density to volume density), since metallicity is an explicit function of age in the model." + This solution has the advantage of being consistent with the fact that the vertical velocity dispersion is also à known function of age., This solution has the advantage of being consistent with the fact that the vertical velocity dispersion is also a known function of age. +" Quantitative estimates o ""the corrections as a function of age have been derived using the oscillation period given in Wyse Gilmore (1995).", Quantitative estimates of the corrections as a function of age have been derived using the oscillation period given in Wyse Gilmore (1995). + We combine this relative oscillation period with the age-vertical velocity dispersion. relation eiven in CGómmoez et al. (, We combine this relative oscillation period with the age-vertical velocity dispersion relation given in Gómmez et al. ( +2001).,2001). + Phe combination of these two factors gives a relative correction of the order of 13 for ‘thick disc. stars. and 5 for the oldest disc stars.," The combination of these two factors gives a relative correction of the order of 13 for 'thick disc' stars, and 5 for the oldest disc stars." + Note that these values are. much larger than that. applied. by Wovse Cilmore (1995). and partly explains why we succeed in eiving a reasonable [fit to the data.," Note that these values are much larger than that applied by Wyse Gilmore (1995), and partly explains why we succeed in giving a reasonable fit to the data." + Note also that. these values are compatible with scale height variations within the (thick and thin) disc., Note also that these values are compatible with scale height variations within the (thick and thin) disc. + Since the previous section shows the uncertainty introduced bv converting Fe/H] to ΟΠΗ]. we preferentially work with the iron distribution.," Since the previous section shows the uncertainty introduced by converting [Fe/H] to [O/H], we preferentially work with the iron distribution." + Phis means that we have to drop the IRA and caleulate numerically the metallicity distribution., This means that we have to drop the IRA and calculate numerically the metallicity distribution. +there are 50 fringes during an observation of a primordial ficlel.),there are 50 fringes during an observation of a primordial field.) + All of the current CMD experiments thus have different calibration and svstematic problems. markedly so in the case of the interferometers versus the balloons. and therefore agreement between them is essential {ο establish. the reliability of the power spectrum measurements.," All of the current CMB experiments thus have different calibration and systematic problems, markedly so in the case of the interferometers versus the balloons, and therefore agreement between them is essential to establish the reliability of the power spectrum measurements." + Absolute Εαν calibration of VSA observations. is. based on the Hux scale of ?.., Absolute flux calibration of VSA observations is based on the flux scale of \citet{mason_casscal}. + Our primary Bux calibrator is Jupiter. for which the brightness tempcrature is taken to be 154.5 Woat our observing frequency of 34 1.," Our primary flux calibrator is Jupiter, for which the brightness temperature is taken to be 154.5 K at our observing frequency of 34 GHz." + The solid angle of the planet is caleulated at the epoch of each calibration observation. and the flux determined., The solid angle of the planet is calculated at the epoch of each calibration observation and the flux determined. + Jupiter is unresolved. on all VSA baselines (including the source subtractor baseline) so no further correction is mace for the angular size., Jupiter is unresolved on all VSA baselines (including the source subtractor baseline) so no further correction is made for the angular size. + We also observe Tau A and Cas A. whose Iluxes are determined via our primary calibration of Jupiter.," We also observe Tau A and Cas A, whose fluxes are determined via our primary calibration of Jupiter." + ‘Translerringe our calibration scale to both Cas A ancl Tau A ensures that an alternative bright. calibrator source is always available should. a Jupiter observation be lost. due to. for example. back weather. or obscured by the Sun or Aloon.," Transferring our calibration scale to both Cas A and Tau A ensures that an alternative bright calibrator source is always available should a Jupiter observation be lost due to, for example, bad weather, or obscured by the Sun or Moon." + Care has to be taken. however. when transferring our Hus calibration to Tau A. since it is known to be polarized (approximately S percent at 34 αν. (2))). and hence the ας as observed by the VSA changes with the hour angle of observation.," Care has to be taken, however, when transferring our flux calibration to Tau A, since it is known to be polarized (approximately 8 percent at 34 GHz, \citep{polarization}) ), and hence the flux as observed by the VSA changes with the hour angle of observation." + To ensure that this does not introduce any systematic error. our calibration observations of Tau A are short and are made at the same hour angle cach day.," To ensure that this does not introduce any systematic error, our calibration observations of Tau A are short and are made at the same hour angle each day." + We also make cailv observations of two fainter sources. 3C48 and NCGCTO27. allowing us to check the quality of observations throughout the observing dav.," We also make daily observations of two fainter sources, 3C48 and NGC7027, allowing us to check the quality of observations throughout the observing day." + The measured Hux ratios of these sources to our primary calibrators agree well with those reported. by. Mason ct αἱ.," The measured flux ratios of these sources to our primary calibrators agree well with those reported by Mason et al.," + suggesting that the accuracy of our Lux calibration is dominated by the error estimate of the absolute temperature of Jupiter. which is approximately 3.5 percent.," suggesting that the accuracy of our flux calibration is dominated by the error estimate of the absolute temperature of Jupiter, which is approximately 3.5 percent." + Further to. this. we have cross-checkec our calibration with that used by the CDI instrument (?)..," Further to this, we have cross-checked our calibration with that used by the CBI instrument \citep{cbi}." + CBI also uses Jupiter as one of its primary calibrators and. since they have a bancdwidth of 10. ο] centred on 31 Cillz. this has enabled them to estimate the spectral index of Jupiter and Saturn over the frecqucney range 26-36 Gllz and hence cross-check our calibration at 34 CGllz.," CBI also uses Jupiter as one of its primary calibrators and, since they have a bandwidth of 10 GHz centred on 31 GHz, this has enabled them to estimate the spectral index of Jupiter and Saturn over the frequency range 26-36 GHz and hence cross-check our calibration at 34 GHz." + We have cross-calibrations based on Jupiter and Saturn which agree to 1 percent., We have cross-calibrations based on Jupiter and Saturn which agree to 1 percent. + Phase calibration of the VSA is also applied on a daily basis using the same three calibrators. Cas A. Tau A and Jupiter.," Phase calibration of the VSA is also applied on a daily basis using the same three calibrators, Cas A, Tau A and Jupiter." + The telescope is sullicienthy phase stable that a single phase calibration made within +12 hours of a CMD observation is adequate to calibrate the phases to «10, The telescope is sufficiently phase stable that a single phase calibration made within $\pm 12$ hours of a CMB observation is adequate to calibrate the phases to $<10^{\circ}$. + In the same process. errors in the quadrature of up to 15° between the real and imaginary parts of each visibility are corrected. for.," In the same process, errors in the quadrature of up to $15^{\circ}$ between the real and imaginary parts of each visibility are corrected for." + These quadrature errors. arise due to path dillerences in the cables going to the correlator boards., These quadrature errors arise due to path differences in the cables going to the correlator boards. + Consider two measured components of a visibility R and 7 αἱ angles 6 and c respectively from the theoretical fringe-rotated. components R” and Z., Consider two measured components of a visibility $\mathcal{R}$ and $\mathcal{I}$ at angles $\phi$ and $\psi$ respectively from the theoretical fringe-rotated components $\mathcal{R}''$ and $\mathcal{I}''$. + Phe quadrature error. is vc 6., The quadrature error is $\chi = \psi-\phi$ . + DComponents BRoi and ZoE which. are orthogonal to each other can be svnthesised by rotating by 7=\/2 in opposite directions., Components $\mathcal{R}'$ and $\mathcal{I}'$ which are orthogonal to each other can be synthesised by rotating by $\beta=\chi/2$ in opposite directions. + These can then be rotated by à=o|3 to give visibilities corresponding to the appropriate phase centre., These can then be rotated by $\alpha=\phi+\beta$ to give visibilities corresponding to the appropriate phase centre. + Thus: Figure 2. shows this scheme., Thus: Figure \ref{quadrature} shows this scheme. + Correcting for quadrature errors necessarily results in a loss of signal to noise bv a factor cosy. and the cata must be. cown-weighted appropriately., Correcting for quadrature errors necessarily results in a loss of signal to noise by a factor $\cos{\chi}$ and the data must be down-weighted appropriately. + Figure 3 shows a tvpical CLIZANed map of a calibrator. in this case Jupiter.," Figure \ref{fig:x-calib} shows a typical CLEANed map of a calibrator, in this case Jupiter." + Such maps are made claily to check the performance and stability. of the telescope: the amplitude and phase stability are such that any un-CLIZANed artefacts are below the thermal noise level., Such maps are made daily to check the performance and stability of the telescope; the amplitude and phase stability are such that any un-CLEANed artefacts are below the thermal noise level. + Since this observation has a higher signal-to-noise ratio than anv CMD measurement. we can be confident that our CMD. measurements are unallected by dynamic range limitations.," Since this observation has a higher signal-to-noise ratio than any CMB measurement, we can be confident that our CMB measurements are unaffected by dynamic range limitations." + The pointing accuracy of the VSA is primarily determined by mechanical alignment tolerances. but we frequentIy make long observations of unresolved calibrators in order to check both the pointing ancl geometry of the array.," The pointing accuracy of the VSA is primarily determined by mechanical alignment tolerances, but we frequently make long observations of unresolved calibrators in order to check both the pointing and geometry of the array." + Pointing is checked. with two sets of observations., Pointing is checked with two sets of observations. + Firstly. the antennas in turn are offset in the antenna tracking co-ordinate on either side of the calibration source: secondly. the whole table is olfset in the table tracking co-ordinate.," Firstly, the antennas in turn are offset in the antenna tracking co-ordinate on either side of the calibration source; secondly, the whole table is offset in the table tracking co-ordinate." + Phese allow us to fit for olfsets in the table and antenna encoders. and to check the co-alignment of the antennas.," These allow us to fit for offsets in the table and antenna encoders, and to check the co-alignment of the antennas." + Alignment is better than 5 aremin. about 1.5 percent of the beannividth.," Alignment is better than 5 arcmin, about 1.5 percent of the beamwidth." + Geometry is. checked using lone observations of two or more calibrators at. dilferent declinations., Geometry is checked using long observations of two or more calibrators at different declinations. + In conjunction with a model of the telescope.we employ a maximum-likelihood technique to fit simultaneously. for," In conjunction with a model of the telescope,we employ a maximum-likelihood technique to fit simultaneously for" +The inner radii set the initial excitation temperature. which is a function of the distance from the central star.,"The inner radii set the initial excitation temperature, which is a function of the distance from the central star." + As a result. changing the inner radius etfects both the temperature in the dise and the rotational broadening of the bandhead.," As a result, changing the inner radius effects both the temperature in the disc and the rotational broadening of the bandhead." + To consistently determine the temperature structure of the disc. and thus more stringent constraints. a detailed radiative transfer model of the dise is required.," To consistently determine the temperature structure of the disc, and thus more stringent constraints, a detailed radiative transfer model of the disc is required." + However. even if the gas dise were modelled in detail. the properties of the central star are essentially unknown.," However, even if the gas disc were modelled in detail, the properties of the central star are essentially unknown." + For example the star may swell to several times its main sequence size as a consequence of high accretion rates (2)... which will reduce its effective temperature.," For example the star may swell to several times its main sequence size as a consequence of high accretion rates \citep{Hosokawa2009}, which will reduce its effective temperature." + Therefore. even a sophisticated disc model wold be subject to several unknowns.," Therefore, even a sophisticated disc model wold be subject to several unknowns." + The best-titting line-widths are generally greater than the value of ~4kms! determined by ?.. who fit the CO l| overtone emission of the Be star 31 Oph with a circumstellar dise model.," The best-fitting line-widths are generally greater than the value of $\mathrm{\sim 4\,km\,s^{-1}}$ determined by \citet{Berthoud2007}, who fit the CO $\mathrm{1^{st}}$ overtone emission of the Be star 51 Oph with a circumstellar disc model." + The line widths are also approximately ten times the thermal broadening due to motion of the CO molecules., The line widths are also approximately ten times the thermal broadening due to motion of the CO molecules. + Therefore. the dominant contribution must be due to turbulence.," Therefore, the dominant contribution must be due to turbulence." + However. we do not consider shear broadening in the model.," However, we do not consider shear broadening in the model." + If this were taken into account. the turbulent velocity may well be less than the best-fitting values presented in Table 3..," If this were taken into account, the turbulent velocity may well be less than the best-fitting values presented in Table \ref{fit}." + The properties of accretion discs around MYSOs has only recently begun to be examined in detail (2). and incorporating vertical dise structure to the dise model (whichisrequiredtoassessshearbroadening??) is beyond the scope of this paper.," The properties of accretion discs around MYSOs has only recently begun to be examined in detail \citep{Vaidya2009}, and incorporating vertical disc structure to the disc model \citep[which +is required to assess shear broadening][]{Horne1986,Hummel2000} is beyond the scope of this paper." + Therefore. we neglect shear velocity.," Therefore, we neglect shear velocity." + However. it is important to note that neglecting vertical structure may artificially limit the extent of the CO emitting region.," However, it is important to note that neglecting vertical structure may artificially limit the extent of the CO emitting region." + In a dise with a vertical extent the upper regions of the dise may be hot enough to excite CO emission at radii where the mid-plane temperature has dropped below the required ~2000K., In a disc with a vertical extent the upper regions of the disc may be hot enough to excite CO emission at radii where the mid-plane temperature has dropped below the required $\mathrm{\sim2000~K}$. + Therefore. incorporating vertical structure in the model may allow CO emission from a wider range of radii than the thin dise model.," Therefore, incorporating vertical structure in the model may allow CO emission from a wider range of radii than the thin disc model." + This would have the effect of increasing the resulting spectro-astrometric signatures. and thus the predictions presented here may be lower limits.," This would have the effect of increasing the resulting spectro-astrometric signatures, and thus the predictions presented here may be lower limits." + Little is known about the circumstellar environments of the RMS objects., Little is known about the circumstellar environments of the RMS objects. + In particular. there are no previous high resolution studies with which to compare the best-fitting model parameters.," In particular, there are no previous high resolution studies with which to compare the best-fitting model parameters." + However. the two non-RMS objects in the sample. M8 E and IRAS 08576—4334 have been both been studied previously.," However, the two non-RMS objects in the sample, M8 E and IRAS $-$ 4334 have been both been studied previously." + Here. we assess whether the best-titting models for these objects are consistent with otYr observations.," Here, we assess whether the best-fitting models for these objects are consistent with other observations." + ? determine he inclination of IRAS 08576—4334 to be 27u based on fitting ye CO I overtone bandhead., \citet{Bik2004} determine the inclination of IRAS $-$ 4334 to be $\mathrm{27^{{\circ}+2}_{-14}}$ based on fitting the CO $\mathrm{1^{st}}$ overtone bandhead. + The best-fitting value of ~[8° deermined here is thus consistent with the previous value., The best-fitting value of $\mathrm{\sim18^{\circ}}$ determined here is thus consistent with the previous value. + This might be expected as we apply the same methodology. none the less. this provides an important check that the results are consistent Wi) previous work.," This might be expected as we apply the same methodology, none the less, this provides an important check that the results are consistent with previous work." + Turning to MSE. ? postulate hat this object possesses an edge on dise: contrary to our best-fitting inclination of ~167.," Turning to M8E, \citet{Simon1985} postulate that this object possesses an edge on disc; contrary to our best-fitting inclination of $\mathrm{\sim16^{\circ}}$." + However. ?. find an inclination <30 is required to fit 1e SED of MSE. These authors suggest that the interpretation of ye lunar occultation data of ?. is complicated by he presence of scattered light and outflow cavities.," However, \citet{Linz2009} find an inclination $\mathrm{<30^{\circ}}$ is required to fit the SED of M8E. These authors suggest that the interpretation of the lunar occultation data of \citet{Simon1985} is complicated by the presence of scattered light and outflow cavities." + Given that the conclusion of ?. is based on the SED of M8 E from the visible to mid infrared. in ziddition to the grid of models of 2.. we suggest he inclination determined by ? is currently the best estimate. which is in agreement with the best-fitting value.," Given that the conclusion of \citet{Linz2009} is based on the SED of M8 E from the visible to mid infrared, in addition to the grid of models of \citet{Robitaille2007}, we suggest the inclination determined by \citet{Linz2009} is currently the best estimate, which is in agreement with the best-fitting value." + Therefore. we conclude that the best-fitting models are consistent with results in he literature. although only a few are available. indicating that the best-titting model parameters are representative of the circumstellar environments of the sample.," Therefore, we conclude that the best-fitting models are consistent with results in the literature, although only a few are available, indicating that the best-fitting model parameters are representative of the circumstellar environments of the sample." + In all but one case. the dise model not only provided a good fit to the data (as measured with (7). but was also consisten with the observed flux densities. and where they existed. previous observations.," In all but one case, the disc model not only provided a good fit to the data (as measured with $\chi^2$ ), but was also consistent with the observed flux densities, and where they existed, previous observations." +Therefore. it would appear that small scale disces are present around the majority. of the sample.,"Therefore, it would appear that small scale discs are present around the majority of the sample." +" However. i was not possible to fit the CO I"". overtone bandhead of G287.3716+00.6444 with the circumstellar dise model used to Π the other profiles."," However, it was not possible to fit the CO $\mathrm{1^{st}}$ overtone bandhead of G287.3716+00.6444 with the circumstellar disc model used to fit the other profiles." + As shown in Fig., As shown in Fig. + 2 ye disc model could no fit observed the bandhead shoulder. nor the slope red-wards of the peak.," \ref{co_spec} the disc model could not fit observed the bandhead shoulder, nor the slope red-wards of the peak." + Furthermore. the bandhead could not be fit with emission from an isothermal. non-rotating body of CO.," Furthermore, the bandhead could not be fit with emission from an isothermal, non-rotating body of CO." + Therefore. we are led to consider alternative scenarios to explain the emission and its profile.," Therefore, we are led to consider alternative scenarios to explain the emission and its profile." + Besides hot. dense discs there are other viable sources of CO I overtone bandhead emission.," Besides hot, dense discs there are other viable sources of CO $\mathrm{1^{st}}$ overtone bandhead emission." + One such scenario is a dense. neutral wind.," One such scenario is a dense, neutral wind." +" 2? were able to fit the CO I“ overtone bandheads of several YSOs with models of neutral winds. but note that the mass loss rates required were relatively high. up to 10M.yr1,"," \citet{Chandler1995} were able to fit the CO $\mathrm{1^{st}}$ overtone bandheads of several YSOs with models of neutral winds, but note that the mass loss rates required were relatively high, up to $\mathrm{10^{-6}\,M_{\odot}yr^{-1}}$." +" ? consider it unlikely CO I"" overtone emission originates in a wind as such mass loss rates are much higher than observed for solar mass YSOs.", \citet{Chandler1995} consider it unlikely CO $\mathrm{1^{st}}$ overtone emission originates in a wind as such mass loss rates are much higher than observed for solar mass YSOs. + However. the winds of MYSOs may well lead to mass loss rates of 10M.yr! (2).," However, the winds of MYSOs may well lead to mass loss rates of $\mathrm{10^{-6}\,M_{\odot}yr^{-1}}$ \citep{Drew1993}." + Consequently. CO. 1“ overtone emission from a dense wind should perhaps be re-considered in this case.," Consequently, CO $\mathrm{1^{st}}$ overtone emission from a dense wind should perhaps be re-considered in this case." + Alternatively. ?. propose that the CO I“ overtone bandhead emission of the Becklin-Neugebauer object is created in shocks (as the observed velocity dispersion and estimated emitting area are both small.," Alternatively, \citet{Scoville1983} + propose that the CO $\mathrm{1^{st}}$ overtone bandhead emission of the Becklin-Neugebauer object is created in shocks (as the observed velocity dispersion and estimated emitting area are both small)." + We note that ? also report that the CO [| overtone bandhead of one of their sample tof four YSOs) was ditheult to fit with a model of CO emission from a cireumstellar dise., We note that \citet{Blum2004} also report that the CO $\mathrm{1^{st}}$ overtone bandhead of one of their sample (of four YSOs) was difficult to fit with a model of CO emission from a circumstellar disc. + Following the example of ?.. they suggest that this may be due to the circumstellar dise exhibiting an outer bulge. which shields the inner regions of the disc.," Following the example of \citet{Kraus2000}, they suggest that this may be due to the circumstellar disc exhibiting an outer bulge, which shields the inner regions of the disc." + The etfect ofthis would be to limit the visible CO emitting region to low velocity regions. resulting in a narrow profile.," The effect of this would be to limit the visible CO emitting region to low velocity regions, resulting in a narrow profile." + In this case. however. it is not the width of the profile we cannot fit. but rather the slope of the profile red-wards of the bandhead peak.," In this case, however, it is not the width of the profile we cannot fit, but rather the slope of the profile red-wards of the bandhead peak." + Most formation scenarios. such as winds and disces. result in excess blue-shifted emission. therefore this bandhead protile is ditficult to explain.," Most formation scenarios, such as winds and discs, result in excess blue-shifted emission, therefore this bandhead profile is difficult to explain." + It is conceivable that the emission from several. discrete regions in a shock. will have ditterent excitation temperatures. and when superimposed. will result in a ditferent slope to the bandhead than the dise model.," It is conceivable that the emission from several, discrete regions in a shock, will have different excitation temperatures, and when superimposed, will result in a different slope to the bandhead than the disc model." + If such shocks exist. the shocked region must be located close to the central star. within a few au. as we do not see a positional excursion in the spectroastrometrie data.," If such shocks exist, the shocked region must be located close to the central star, within a few au, as we do not see a positional excursion in the spectroastrometric data." + However. it is difficult to envisage a scenario in which the shock emission is predominately red-shifted.," However, it is difficult to envisage a scenario in which the shock emission is predominately red-shifted." + As an alternative it may be that the emission does originate in a disc. but the receding part of the dise is significantly brighter than the approaching side. similar to the V/R variations exhibited by Be stars (e.g. 2)..," As an alternative it may be that the emission does originate in a disc, but the receding part of the disc is significantly brighter than the approaching side, similar to the V/R variations exhibited by Be stars \citep[e.g.][]{Hanuschik1995}." + Regardless. it is apparent that while the majority of MYSO CO bandheads are well tit by models of circumstellar discs. the circumstellar environments of MYSOs are not yet completely understood.," Regardless, it is apparent that while the majority of MYSO CO bandheads are well fit by models of circumstellar discs, the circumstellar environments of MYSOs are not yet completely understood." +"The huninosity in soft and lard photons can then be fouud I=wo osni The critical y-ray compactuess is giveu by Figure 2. shows PH, as odd fuuction. of e. foy two values of the maeucetic field.",The luminosity in soft and hard photons can then be found = = The critical $\gamma$ -ray compactness is given by Figure \ref{lcr2} shows $\lcr$ as a function of $\eg$ for two values of the magnetic field. + When the threshold euergv for absorption 2/e. is much lower than the maximal enerey of the soft svuclrotron photons be?/L. the critical conpactuess as a function of e. behaves as for the 6- cross section.," When the threshold energy for absorption $2/\eg$ is much lower than the maximum energy of the soft synchrotron photons $b\eg^2/4$, the critical compactness as a function of $\eg$ behaves as for the $\delta$ -function cross section." +" Towever. when the two euergies become comparable, {δα abruptly duereasess because the nuuber of soft photons serving as tarects for the absorption siguificautly decreases."," However, when the two energies become comparable, $\lcr$ abruptly increases, because the number of soft photons serving as targets for the absorption significantly decreases." + This effect can be secu in Fie., This effect can be seen in Fig. + 2 as a change in the curvature of the curves., \ref{lcr2} as a change in the curvature of the curves. + To umuerically investigate the properties of quenchinga. oue needs to solve again the system of equs (5)-(7) augmented to include more plysical processes.," To numerically investigate the properties of quenching, one needs to solve again the system of eqns (5)-(7) augmented to include more physical processes." + As iu the mmuerical code. there is no need to treat the tinie-evolution of soft photous and 5ravs through separate equations. the svstem eun be written: — aud IQ where i. and s. are the differential electron aud photon uuuboer deusity. respectively. normalized as im 822.," As in the numerical code, there is no need to treat the time-evolution of soft photons and $\gamma-$ rays through separate equations, the system can be written: + = and + =, where $\nelec$ and $\nphot$ are the differential electron and photon number density, respectively, normalized as in 2." + Uere we cousidered the following processes: (i) Photon-photon pair production. which acts as a source term for electrous (QU.) aud a sink term forphotous (£7. ): (1) svuchrotron radiation. which acts as a loss term for electrons (C54) and a source term for photons (Ωω):TUM Gil) svuchrotron sclfabsorption. which acts as a loss term or photons (C:pana j and (v) inverse Compton scatteriug. which acts as a loss term for clectrous GC;ο) aud a source enu for photons (QU.," Here we considered the following processes: (i) Photon-photon pair production, which acts as a source term for electrons $\cal{Q}^{\rm e}_{\gamma\gamma}$ ) and a sink term forphotons $\cal{L}_{\gamma\gamma}^\gamma$ ); (ii) synchrotron radiation, which acts as a loss term for electrons $\cal{L}^{\rm e}_{\rm syn}$ ) and a source term for photons $\cal{Q}_{\rm syn}^\gamma$ ); (iii) synchrotron self-absorption, which acts as a loss term for photons ${\cal{L}}^{\gamma}_{\rm ssa}$ ) and (iv) inverse Compton scattering, which acts as a loss term for electrons $\cal{L}^{\rm e}_{\rm ics}$ ) and a source term for photons $\cal{Q}_{\rm ics}^\gamma$ )." + Iu addition to the above. we assunie that > rays are injected into the source through he term (Q7—-uj j ," In addition to the above, we assume that $\gamma-$ rays are injected into the source through the term $\cal{Q}_{\rm inj}^\gamma$ )." +The functional forms of the various rates ive been presented elsewhere — 7 aud 7., The functional forms of the various rates have been presented elsewhere – \cite{mastkirk97} and \cite{petromast09} . + The photons are assunied to escape the source iu oue crossing time. herefore f.44=Rc.," The photons are assumed to escape the source in one crossing time, therefore $\tgesc=R/c$." + The paraincters of the problem are completely specified once the values of radius & aud of the magnetic field D are set aud the jection rate Qu Ix specified., The parameters of the problem are completely specified once the values of radius $R$ and of the magnetic field $B$ are set and the injection rate $\cal{Q}_{\rm inj}^\gamma$ is specified. + [2DocauscTERIvay Qu; is readily related to the injected. luminosity LU through the relation «2)?V fds xxcalQsrinj- where V ds the volume of the source. the injection rate is specified. once he injection coumpactuess 09. and the uuctional depeudence of Qj.nj ou e. is set.," Because $\cal{Q}_{\rm inj}^\gamma$ is readily related to the injected luminosity $L_\gamma^{\rm inj}$ through the relation c^2)^2 V dx x, where $V$ is the volume of the source, the injection rate is specified once the injection compactness $\lginj$ and the functional dependence of $\cal{Q}_{\rm inj}^\gamma$ on $\eg$ is set." + The electron oivesical escape timescale from he source £2; Is another ree paranneter which. however. is not important in our case.," The electron physical escape timescale from the source $\teesc$ is another free parameter which, however, is not important in our case." +" Thus. we wil fix it at value f,=τνοΠο."," Thus, we will fix it at value $\teesc=\tgesc=R/c$." + The final settings are the initial conditions or the electron audphoton muuber densities., The final settings are the initial conditions for the electron andphoton number densities. + Because we are investigating the spontancous erowth of pairs and svuchrotron photons. we asstune that at £—0 there are 10 electrons or photons iu he source. so we set in(5.0)27.66.0)Ξ 0.," Because we are investigating the spontaneous growth of pairs and synchrotron photons, we assume that at $t=0$ there are no electrons or photons in the source, so we set $\nelec(\gamma,0)=\nphot(x,0)=0$ ." + As a first example we study the case where the > rays injected are 1nonoenergetie at an cuerev ε., As a first example we study the case where the $\gamma-$ rays injected are monoenergetic at an energy $\eg$ . +", The expected trivial solution of the kinetic equations is that because", The expected trivial solution of the kinetic equations is that because +conlidence.,confidence. + Stricter limits will follow from dark energv program., Stricter limits will follow from dark energy program. +" Third. O522.—0.20, [or Q4<< I."," Third, $\Omega_2 ~\approx~ -0.2\Omega_1$ for $\Omega_1~ <<$ 1." + IL Qs.=€ (sav. °) due to inflation. O4.<0.018/C/4—fu)=0.06.," If $\Omega_2~ = ~\epsilon$ (say, $^{-6}$ ) due to inflation, $\Omega_1~<~0.018/(f_1-f_0)~=~0.06$." +" ] acknowledge verv helpful discussions with Brian Schmidt and Chris Blake,", I acknowledge very helpful discussions with Brian Schmidt and Chris Blake. + Thanks eo to Ixul Glazebrook. Lucas Macri: and. Paul Sehechter for reading a draft and to Ned Wright for compiling the observational data and making Chem available on his web page.," Thanks go to Karl Glazebrook, Lucas Macri, and Paul Schechter for reading a draft and to Ned Wright for compiling the observational data and making them available on his web page." + This research is part of the Dark Universe scientific program of CAASTRO http://eaastro.org and supported by ARC., This research is part of the Dark Universe scientific program of CAASTRO http://caastro.org and supported by ARC. + (Linde&Mukhanov1997:Lath. (SalopekVerdeetal.2000:Itomatsi&Spergel2001) where ᾧ denotes Dardeeu's eauge-variant potential. which. on sub-IIubble scales reduces to the usual Newtoman peculiar gravitational potential. up to a uinus sign and o denotes a Gaussian random field.," \citet{BKMR04} \citep{linde/mukhanov:1997,lyth/ungarelli/wands:2003, BabichCreminelli04,chen/etal:2007,holman/tolley:2008,chen/easther/lim:2007,langlois/etal:2008, Meerburgetal09} \citep{SalopekBond90, Ganguietal94,VWHK00, KS01} + where $\Phi$ denotes Bardeen's gauge-invariant potential, which, on sub-Hubble scales reduces to the usual Newtonian peculiar gravitational potential, up to a minus sign and $\phi$ denotes a Gaussian random field." + The nou-Caussianity parameter fxp is often considered o be constant. in which case this is called local ron-Caussiawity and its bispectimm is maximized for squeezed configurations Gvliere one wave vector is mach sunaller than the other two).," The non-Gaussianity parameter $f_{\rm NL}$ is often considered to be constant, in which case this is called local non-Gaussianity and its bispectrum is maximized for squeezed configurations (where one wave vector is much smaller than the other two)." + Nou-Caussianity of the ocal type is generated in standard inflation (in this case νι is expected to be of the same order of the slow-roll paraincters) aud for miulti-field models., Non-Gaussianity of the local type is generated in standard inflation (in this case $f_{\rm NL}$ is expected to be of the same order of the slow-roll parameters) and for multi-field models. + Note. rowever. that an expression like Eq.(1)) is not general and there are neu inflationary models which predict different types of deviations from Caussianity.," Note, however, that an expression like \ref{eq:fnl}) ) is not general and there are many inflationary models which predict different types of deviations from Gaussianity." + In general. heir non-CGaussiauitv is specified by their bispectim.," In general, their non-Gaussianity is specified by their bispectrum." + There are some cases where the trispectrmm iav be inuportaut Gvhen. for example. the bispectrmm is zero) mt in general oue expects the trispectruui coutribution ο be sub-cominant compared to the bispectruii onc.," There are some cases where the trispectrum may be important (when, for example, the bispectrum is zero) but in general one expects the trispectrum contribution to be sub-dominant compared to the bispectrum one." + While CAMB and large-scale structure can neasure he bispectzruni shape-cdependenuce auc thus can iu xinciple discriminate the shape of nou-Cioussiauity (6.9.. Foreusson&Shellard(2008). and references therein) here are also other powerful| probes.," While CMB and large-scale structure can measure the bispectrum shape-dependence and thus can in principle discriminate the shape of non-Gaussianity (e.g., \cite{FergussonShellard08} and references therein) there are also other powerful probes." + One technique is sed on the abundance (Robinson&Baker2000:Robiu-&Verde2009) of rare events such as dark matter density peaks as they trace the tail of the uuderlving distribution.," One technique is based on the abundance \citep{RB00, RGS00,MVJ00, VJKM01, Loverdeetal07,KVJ09,JV09} of rare events such as dark matter density peaks as they trace the tail of the underlying distribution." + This probe is seusitive to the primorcial skewness: beiug the skewness an integral over all bispectrmm shapes. this probe cannot easily discriminate amone ditfereut shapes of non-Cuussimuitv.," This probe is sensitive to the primordial skewness: being the skewness an integral over all bispectrum shapes, this probe cannot easily discriminate among different shapes of non-Gaussianity." + Receutly. Dalaletal.(2007). and Matarrese&Verde (2008)(Chereatter ALTVO0s) have shown that primordial nuon-Cuonssimnitv affects the clustering of dark matter halos inducing Gu the case of local uou-Caussiautv) a scale-dependent bias on large scales.," Recently, \cite{DDHS07} and \cite{MV08}( (hereafter MV08) have shown that primordial non-Gaussianity affects the clustering of dark matter halos inducing (in the case of local non-Gaussianty) a scale-dependent bias on large scales." + Thiseffect. which gocs uuder the name of non-Caussiau halo bias. isparticularly promising. viclding already striugeut," Thiseffect, which goes under the name of non-Gaussian halo bias, isparticularly promising, yielding already stringent" +TNormenudy Saucers (1992) compared the stellar and molecular gas mass densities and velocity dispersious of a few ULICs with the stellar mass densities aud velocity dispersions of elliptical galaxy cores in an attempt to establish an evolutionary connection between the two ealaxy types.,Kormendy Sanders (1992) compared the stellar and molecular gas mass densities and velocity dispersions of a few ULIGs with the stellar mass densities and velocity dispersions of elliptical galaxy cores in an attempt to establish an evolutionary connection between the two galaxy types. + As a follow-up to their work. molecular gas lass densities have been calculated for cach nucleus using both CO size estimations. and the results are compiled iu Table 8.," As a follow-up to their work, molecular gas mass densities have been calculated for each nucleus using both CO size estimations, and the results are compiled in Table 8." + The latter two size determinations give lass densities primarily iu the range p~10?+ M. ? and are plotted along with the line-ofsieht CO velocity dispersions. c. in Figure 5 (ie. the cooling diagrams).," The latter two size determinations give mass densities primarily in the range $\rho \sim 10^{2-4}$ $_\odot$ $^{-3}$ and are plotted along with the line-of-sight CO velocity dispersions, $\sigma$, in Figure 5 (i.e., the cooling diagram)." + Given the obvious uucertaiuties in determining p aud σ. the area of Figure 5 occupied by the ULICs should be treated as the general range of deusitv aud dispersion values that intermediate stage mergers nav possess.," Given the obvious uncertainties in determining $\rho$ and $\sigma$, the area of Figure 5 occupied by the ULIGs should be treated as the general range of density and dispersion values that intermediate stage mergers may possess." + The stellar mass deusitv and diuc-ofsight velocity dispersious of nearby elliptical galaxies. obtained from Faber et al. (," The stellar mass density and line-of-sight velocity dispersions of nearby elliptical galaxies, obtained from Faber et al. (" +1997). are also plotted.,"1997), are also plotted." + The sas ass densities and velocity dispersious of the ULICs are consistent with the stellar nass densities aud dispersion of elliptical ealaxics with absolute visual magnitudes ALκ19., The gas mass densities and velocity dispersions of the ULIGs are consistent with the stellar mass densities and dispersion of elliptical galaxies with absolute visual magnitudes $M_{\rm V} < -19$. + The ULIG data poiuts overlap the regious occupied by both rapidly rotating elliptical galaxies with disky isophotes aud power-law light profiles. which Faber et al. (," The ULIG data points overlap the regions occupied by both rapidly rotating elliptical galaxies with disky isophotes and power-law light profiles, which Faber et al. (" +1997) speculate may be the end-products of gaseous merger eveuts. auc slow rotating elliptical galaxies with boxy isophotes aud cores.,"1997) speculate may be the end-products of gaseous merger events, and slow rotating elliptical galaxies with boxy isophotes and cores." + From the data plotted in Figure 5. it cau be coucluded that the phase-space density of star-forming molecular gas is sufficient to form the stars in the nuclear regious of huninous elliptical galaxies.," From the data plotted in Figure 5, it can be concluded that the phase-space density of star-forming molecular gas is sufficient to form the stars in the nuclear regions of luminous elliptical galaxies." + Molecular gas observations of a sample of double-uucleus ultralunimous infrared ealaxics (ULIGs) were preseuted., Molecular gas observations of a sample of double-nucleus ultraluminous infrared galaxies (ULIGs) were presented. + This observations were motivated by the dearth of CO(L 0) data for ULICs at intermediate stages of evolution (i.c.. with nuclear separations of 3/5 kpc).," This observations were motivated by the dearth of $1\to0$ ) data for ULIGs at intermediate stages of evolution (i.e., with nuclear separations of 3–5 kpc)." + The following conclusions have been reached: Three observed double-uucleus objects with wari far-infrared dust temperatures have detected. CO cussion associated only with one of the two uucleà — the nucleus hat is reddest aud has the highest radio continu cluission., The following conclusions have been reached: Three observed double-nucleus objects with warm far-infrared dust temperatures have detected CO emission associated only with one of the two nuclei – the nucleus that is reddest and has the highest radio continuum emission. + Two observed objects with cool £u-iufrared dust cluperatures have detected CO emission associated with th. uuclei;, Two observed objects with cool far-infrared dust temperatures have detected CO emission associated with both nuclei. + Molecular gas masses for the detected uuclci are estimated to be in the rauge 0.1.1.2«1029 ML., Molecular gas masses for the detected nuclei are estimated to be in the range $0.1-1.2\times10^{10}$ $_\odot$. + The relative amount of molecular gas iu cach galaxy xür appears to be correlated with the relative levels of activity as imeasured by both optical/ucar-iufrared recolubination liue enüssiou and radio flux deusitv., The relative amount of molecular gas in each galaxy pair appears to be correlated with the relative levels of activity as measured by both optical/near-infrared recombination line emission and radio flux density. + The xeseuce of LINER aud Sevtert unclei combined with the veh central concentration of CO provides evidence that nolecular gas is an important component in ficling ACN and vigorous. massive star formation.," The presence of LINER and Seyfert nuclei combined with the high central concentration of CO provides evidence that molecular gas is an important component in fueling AGN and vigorous, massive star formation." + Where possible. star formation rates have been computed for cach uncleus using four ciffereut techniques.," Where possible, star formation rates have been computed for each nucleus using four different techniques." +" Star formation rates estimated to be 20290 AL. ! nucleusο, with correspouding eas cousuuptiou timescales of l7«10' vears."," Star formation rates estimated to be 20–290 $_\odot$ $^{-1}$ $^{-1}$, with corresponding gas consumption timescales of $1-7\times10^7$ years." + The star formation rates may be considerably lower (aud the gas constuption timescales considerable longer) if ACN contribute significantly to the infrared and radio enission observed in these galaxy pairs., The star formation rates may be considerably lower (and the gas consumption timescales considerable longer) if AGN contribute significantly to the infrared and radio emission observed in these galaxy pairs. + The πιο. with associated molecular gas appear to have significantly redder infrared colors than their colupanions that lack CO detections. sugeestive of clusticr environments in the C'O-luminous nuclei.," The nuclei with associated molecular gas appear to have significantly redder infrared colors than their companions that lack CO detections, suggestive of dustier environments in the CO-luminous nuclei." + Coluun densities for the nuclei of the ULICs were estimated to be ~10252? cur2. which corresponds. to ercater than 1000 magnitudes of visual extinction.," Column densities for the nuclei of the ULIGs were estimated to be $\sim 10^{24-25}$ $^{-2}$, which corresponds to greater than 1000 magnitudes of visual extinction." + Where possible. molecular gas iuass densities were estimated for cach nucleus.," Where possible, molecular gas mass densities were estimated for each nucleus." +" A reasonable estimate for the range of molecular gas densities is 10?1 AL. ο,", A reasonable estimate for the range of molecular gas densities is $10^{2-4}$ $_\odot$ $^{-3}$. + Such values. combined with measured line-ofsight CO(L>0) velocity dispersions. are equivaleut to the stellar mass densities aud velocity dispersions of elliptical galaxies with AMc19 aud indicate that the molecular gas has a sufficieutlv high phase-space deusity to formi the stars in elliptical galaxy cores.," Such values, combined with measured line-of-sight $1\to0$ ) velocity dispersions, are equivalent to the stellar mass densities and velocity dispersions of elliptical galaxies with $M_V < -19$ and indicate that the molecular gas has a sufficiently high phase-space density to form the stars in elliptical galaxy cores." + The present sample is small (5 ealaxies). but the analysis presented here shows compcling results that may be solidified or refuted with a lavecr. more statistically sienificant sample of ULICs in their intermediate phases of evolution.," The present sample is small (5 galaxies), but the analysis presented here shows compelling results that may be solidified or refuted with a larger, more statistically significant sample of ULIGs in their intermediate phases of evolution." + A σος»0) survev is presently underway to observe all of the intermediate stage ULIC in the TRAS 2 Jv sample., A $1\to0$ ) survey is presently underway to observe all of the intermediate stage ULIGs in the IRAS 2 Jy sample. + These data will be combined with multiwavelength data iu a manner similar to what has been prescuted for the five ULICs iu this paper., These data will be combined with multiwavelength data in a manner similar to what has been presented for the five ULIGs in this paper. + Further Huprovement of the preseut dataset will also be possible with high-resolution CO observations with the soou-to-he colmlussioned Sinithsoman SubMillieter Array (SALA) and the upcoming Combined Array for Research in A\Gillimeter Astronomy (CARAIA): these interferometers will make if possible to obtain CO resolutions approaching that of the 2:12 UST data. thus removing the ambiguity in the true extent of the molecular gas.," Further improvement of the present dataset will also be possible with high-resolution CO observations with the soon-to-be commissioned Smithsonian SubMillimeter Array (SMA) and the upcoming Combined Array for Research in Millimeter Astronomy (CARMA); these interferometers will make it possible to obtain CO resolutions approaching that of the $\micron$ HST data, thus removing the ambiguity in the true extent of the molecular gas." + We thank the staff aud postdoctoral scholars of the Owens Valley Millimeter array for their support both durig and after the observations were obtained., We thank the staff and postdoctoral scholars of the Owens Valley Millimeter array for their support both during and after the observations were obtained. + The NICMOS images of ALK 163 were provided to us courtesy of D. C. Ilues., The NICMOS images of Mrk 463 were provided to us courtesy of D. C. Hines. + We also thank the referee for readius the manuscript carefully aud providing detailec conuneuts that ereatly muproved several sections of he iuanuscript., We also thank the referee for reading the manuscript carefully and providing detailed comments that greatly improved several sections of the manuscript. + ASE was supported by NSF eran AST O0-508S81. RE9736D. aud the 2002 NASA/ASEE Faculty Fellowship.," ASE was supported by NSF grant AST 00-80881, RF9736D, and the 2002 NASA/ASEE Faculty Fellowship." + JAIN aud JAS were supported by he Jet Propulsion Laboratory. California Iustitute of Technology. wider coutract with NASA.," JMM and JAS were supported by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA." + D.B.S. eratefullv acknowledges the hospitality of the Max-Plauk. Iustitu ur Extraterrestrische Plowsik aud the Alexander vou Thunboldt Stiftung for a Ihuuboldt senior award. aud xwtial financial support from NASA eraut. GO-8190.01-OTA.," D.B.S. gratefully acknowledges the hospitality of the Max-Plank Institut fur Extraterrestrische Physik and the Alexander von Humboldt Stiftung for a Humboldt senior award, and partial financial support from NASA grant GO-8190.01-97A." + The Owens Vallev Millineter Array is ai radio clescope facility. operated by the California. Institute of Technology aud is supported by NSF erauts AST 99-S1516., The Owens Valley Millimeter Array is a radio telescope facility operated by the California Institute of Technology and is supported by NSF grants AST 99-81546. + The NASA/ESA IIibble Space Telescope is operated by the Space Telescope Science Tustitute managed by the Association of Universities for research iu Astronomy Ine. uuder NASA coutract NAS5-26555., The NASA/ESA Hubble Space Telescope is operated by the Space Telescope Science Institute managed by the Association of Universities for research in Astronomy Inc. under NASA contract NAS5-26555. + This research has made use of the NASA/TPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under" +in the field.,in the field. +" We find no evidence of any extended emission associated with the PWN in any of the images, but due to uncertainties in the extent of the PWN and the quality of point source subtraction we are unable to put flux limit on possible emission."," We find no evidence of any extended emission associated with the PWN in any of the images, but due to uncertainties in the extent of the PWN and the quality of point source subtraction we are unable to put a flux limit on possible emission." + Point source upper limits are aapproximated from the dimmest observable object in the field., Point source upper limits are approximated from the dimmest observable object in the field. +" We find no evidence of any extended emission associated with the PWN in any of the images, even after the PSF subtraction of point sources in the field."," We find no evidence of any extended emission associated with the PWN in any of the images, even after the PSF subtraction of point sources in the field." +" Neither do we find any nIR counterparts to the X-ray point sources, except to confirm the K, magnitude of the previously identified counterpart of citepRatti2010:MNRAS.408.."," Neither do we find any nIR counterparts to the X-ray point sources, except to confirm the $K_s$ magnitude of the previously identified counterpart of \\citep{Ratti2010:MNRAS.408}." +" Based on sspectra, Tomsicketal.(2009) confirm that citepKeek2006:ATel.810 is an SNR with a PWN, while Renaudetal.(2010) discovereda 31.18mms X-ray/radio pulsar at its centre."," Based on spectra, \cite{Tomsick2009:ApJ701} confirm that \\citep{Keek2006:ATel.810} is an SNR with a PWN, while \cite{Renaud2010:ApJ.716} discovereda ms X-ray/radio pulsar at its centre." +" Tomsicketal. do not find any higher energy (TeV, GeV) counterparts to the source but Renaudetal. obtain radio observations which reveal counterparts to both the point source and the PWN."," \citeauthor{Tomsick2009:ApJ701} do not find any higher energy (TeV, GeV) counterparts to the source but \citeauthor{Renaud2010:ApJ.716} obtain radio observations which reveal counterparts to both the point source and the PWN." +" We find no source within 3σ of the ppoition ofJ14003—6326,, down to the magnitudes given in reftable:observations.."," We find no source within $3\sigma$ of the poition of, down to the magnitudes given in \\ref{table:observations}. ." +" However there is a dim source detected at J=18.6+0.2 and marginally at i=20.90+0.15, at RA, Dec = 14:00:45.45, —63:25:41.8 (+0.3”)) or ~5σ from the pposition."," However there is a dim source detected at $J = 18.6 \pm 0.2$ and marginally at $i = 20.90 \pm 0.15$, at RA, Dec = 14:00:45.45, $-$ 63:25:41.8 $\pm 0.3$ ) or $\sim 5\sigma$ from the position." + We are unable to discern if this is a point or extended source due to its faintness but it is likely unrelated to the X-ray source given the distance discrepancy., We are unable to discern if this is a point or extended source due to its faintness but it is likely unrelated to the X-ray source given the distance discrepancy. +" wwas initially suggested to be associated with JJ16320-4751 (Aharonianetal.,2006) though this was subsequently rejected after deep observations of the source (Balboetal,2010).", was initially suggested to be associated with J16320-4751 \citep{Aharonian2006:ApJ.636} though this was subsequently rejected after deep observations of the source \citep{Balbo2010:A&A.520}. + It was instead associated with an independent X-ray point source with diffuse emission., It was instead associated with an independent X-ray point source with diffuse emission. +" These authors also obtained data from radio and high energy archives or catalogs to describe the nature of the source, which they suggest is an energetic PWN with a, yet to be confirmed, central pulsar."," These authors also obtained data from radio and high energy archives or catalogs to describe the nature of the source, which they suggest is an energetic PWN with a, yet to be confirmed, central pulsar." +" We find no source within the XMM error circle of J1632—478,,down to a limiting magnitude of K,> 17.7."," We find no source within the XMM error circle of ,down to a limiting magnitude of $K_s > 17.7$ ." +" However, there is a dim source 2.6”2.60 to the East (source"," However, there is a dim source $\sim 2.6 \sigma$ to the East (source" +for the damping time as a function of the density contrast in the radial direction is shown in Figure 3bb. Finally. the most important parameter that determines the damping of transverse thread oscillations is the width of the non-uniform transitional layer in the radial direction.,"for the damping time as a function of the density contrast in the radial direction is shown in Figure \ref{check}b b. Finally, the most important parameter that determines the damping of transverse thread oscillations is the width of the non-uniform transitional layer in the radial direction." + The damping time strongly decreases when this parameter is increased. as can be seen in Figure 3ec. which again shows a very good agreement between the values computed in 2D and the previous ID computations.," The damping time strongly decreases when this parameter is increased, as can be seen in Figure \ref{check}c c, which again shows a very good agreement between the values computed in 2D and the previous 1D computations." + These results were in agreement with previous works in the context of the damping of coronal loop transverse oscillations (e.g.Goossensetal..1992;Ruderman&Roberts.2002:Goossensetal..2002) Once we are confident about the goodness of the code. we consider the new ingredients introduced by the two-dimensional nature of the prominence thread models considered in this work.," These results were in agreement with previous works in the context of the damping of coronal loop transverse oscillations \citep[e.g.][]{goossens92,RR02,GAA02} + Once we are confident about the goodness of the code, we consider the new ingredients introduced by the two-dimensional nature of the prominence thread models considered in this work." + These new ingredients are the length of the thread. £4. re. the length of the part of the magnetic flux tube filled with dense absorbing plasma. and the density in the evacuated part of the tube. o4.," These new ingredients are the length of the thread, $L_{\rm thread}$, i.e., the length of the part of the magnetic flux tube filled with dense absorbing plasma, and the density in the evacuated part of the tube, $\rho_{\rm ev}$." +" The non-uniform transitional layer in density between both regions along the tube. /,. has an irrelevant effect on the oscillatory period for low harmonics in the longitudinal direction, as show by Díazetal.(2008)."," The non-uniform transitional layer in density between both regions along the tube, $l_{\rm z}$, has an irrelevant effect on the oscillatory period for low harmonics in the longitudinal direction, as shown by \citet{diazmargarita08}." +. Our computations (not shown here) cofirm the finding by Díazetal.(2008) on the negligible importance of this parameter for the oscillatory period and show a similar irrelevance concerning the damping time by resoant absorption., Our computations (not shown here) confirm the finding by \citet{diazmargarita08} on the negligible importance of this parameter for the oscillatory period and show a similar irrelevance concerning the damping time by resonant absorption. + For this reason. we have concentrated our analysis on the remaining two parameters. μοι and pa.," For this reason, we have concentrated our analysis on the remaining two parameters, $L_{\rm thread}$ and $\rho_{\rm ev}$." + We first consider the influence of the length of the thread on the period and damping of resonantly damped transverse thread oscillations., We first consider the influence of the length of the thread on the period and damping of resonantly damped transverse thread oscillations. + An initial analysis on this subject was presented by Soleretal.(2010).. who considered the thin tube and thin boundary approximations (TTTB) in a two-dimensional thread model with transverse inhomogeneity only in. the dense part of the tube.," An initial analysis on this subject was presented by \cite{soler102dthread}, who considered the thin tube and thin boundary approximations (TTTB) in a two-dimensional thread model with transverse inhomogeneity only in the dense part of the tube." + Our analysis goes beyond the TTTB approximations by considering a fully Inhomogeneous two-dimensional density distribution and combining its influence with that of the density in the evacuated part of the tube. p.," Our analysis goes beyond the TTTB approximations by considering a fully inhomogeneous two-dimensional density distribution and combining its influence with that of the density in the evacuated part of the tube, $\rho_{\rm ev}$." +" We have first analysed the variation of period. damping time. and damping ratio. Ty/P. by setting pa.=p,. so that we mimic the case studied by Soleretal.(2010) analytically."," We have first analysed the variation of period, damping time, and damping ratio, $\tau_d/P$, by setting $\rho_{\rm ev}=\rho_c$, so that we mimic the case studied by \citet{soler102dthread} analytically." + We start with a fully filled tube and gradually decrease the length of the thread., We start with a fully filled tube and gradually decrease the length of the thread. + The obtained results. for two values of the density contrast between the filament and coronal plasma. are shown in Figures 4aa-c. The period is strongly dependent on the length of the thread.," The obtained results, for two values of the density contrast between the filament and coronal plasma, are shown in Figures \ref{figlthread}a a-c. The period is strongly dependent on the length of the thread." + It decreases by almost a factor of two when going from La=£ to Lg=O.1L., It decreases by almost a factor of two when going from $L_{\rm thread}=L$ to $L_{\rm thread}=0.1L$. + Figure daa also shows that the oscillatory period is almost independent of the density contrast. once this parameter ts large enough.," Figure \ref{figlthread}a a also shows that the oscillatory period is almost independent of the density contrast, once this parameter is large enough." + As for standing kink waves in one-dimensional thread models (Arregui 2008).. the kink frequency is a weighted mean of the internal and external Alfvénn frequencies.," As for standing kink waves in one-dimensional thread models \citep{Arregui08thread}, the kink frequency is a weighted mean of the internal and external Alfvénn frequencies." + Regardless of the density contrast. the period is allowed to vary in a a narrow range determined by a factor that goes from v2 to I. when going from pr/pe=1 to pr/p;—co.," Regardless of the density contrast, the period is allowed to vary in a a narrow range determined by a factor that goes from $\sqrt{2}$ to $1$, when going from $\rho_{\rm f}/\rho_{\rm c}=1$ to $\rho_{\rm f}/\rho_{\rm c}\rightarrow\infty$." + For typical density contrasts in prominence plasmas. the period can be considered independent of the density contrast.," For typical density contrasts in prominence plasmas, the period can be considered independent of the density contrast." + The damping time produced by resonant absorption (Fig., The damping time produced by resonant absorption (Fig. + 4bb) also decreases remarkably whenthe length of the cool and dense part of the tube is decreased., \ref{figlthread}b b) also decreases remarkably whenthe length of the cool and dense part of the tube is decreased. + The decrease is also around a factor of two in the considered range of values for Lg. Sole, The decrease is also around a factor of two in the considered range of values for $L_{\rm thread}$. +retal.(2010). find that in the TTTB limit the dependence of the period and the damping time with the length of the thread is exactly the same. hence any influence on the damping ratio. τα/P. is cancelled out.," \citet{soler102dthread} find that in the TTTB limit the dependence of the period and the damping time with the length of the thread is exactly the same, hence any influence on the damping ratio, $\tau_{\rm d}/P$, is cancelled out." + Outside the TTTB approximations. we find that this is not the case (see Fig.," Outside the TTTB approximations, we find that this is not the case (see Fig." + dec). although the damping ratio is almost independent of the length of thread and only for very short threads a slight increase in the damping ratio is found when further decreasing this parameter.," \ref{figlthread}c c), although the damping ratio is almost independent of the length of thread and only for very short threads a slight increase in the damping ratio is found when further decreasing this parameter." + In Figure 4. we overplot results obtained by Soleretal.(2010) by solving their dispersion relation., In Figure \ref{figlthread} we overplot results obtained by \citet{soler102dthread} by solving their dispersion relation. + We see that there is a very good agreement and the differences. that are due to the simplifying assumptions of the analytical treatment. are rather small.," We see that there is a very good agreement and the differences, that are due to the simplifying assumptions of the analytical treatment, are rather small." + One can observe an anomalous behaviour on the damping time computed by Soleretal.(2010).. for small values of μα.," One can observe an anomalous behaviour on the damping time computed by \cite{soler102dthread}, for small values of $L_{\rm thread}$." + This ts due to the simplifying assumptions considered to obtain the semi-analytic solution. that might not be entirely valid outside the long-wavelength limit.," This is due to the simplifying assumptions considered to obtain the semi-analytic solution, that might not be entirely valid outside the long-wavelength limit." + Overall. our results confirm the validity of the analytical approximations obtained by Soleretal.(2010) concerning the influence of the length of the thread on periods and damping times.," Overall, our results confirm the validity of the analytical approximations obtained by \cite{soler102dthread} concerning the influence of the length of the thread on periods and damping times." + In physical terms. the shortening of the length of the thread produces shorter period oscillations. since the physical system ts equivalent to a fully filled tube. with the wavelength of oscillations replaced by a shorter effective wavelength.," In physical terms, the shortening of the length of the thread produces shorter period oscillations, since the physical system is equivalent to a fully filled tube, with the wavelength of oscillations replaced by a shorter effective wavelength." + A physical explanation of the damping time dependence on the length of the thread is provided. by using energy arguments. in Sect. ??..," A physical explanation of the damping time dependence on the length of the thread is provided, by using energy arguments, in Sect. \ref{energyanal}." + Similar conclusions can be extracted from the computations we have performed by fixing the density contrast and for three different values of the width of the inhomogeneous layer., Similar conclusions can be extracted from the computations we have performed by fixing the density contrast and for three different values of the width of the inhomogeneous layer. + Figures 4dd-f show the obtained results., Figures \ref{figlthread}d d-f show the obtained results. + They clearly show how strongly the damping time and the damping ratio are influenced by the width of the transitional layer. also in 2D models. while the period of the oscillations is almost unaffected by the value of //a.," They clearly show how strongly the damping time and the damping ratio are influenced by the width of the transitional layer, also in 2D models, while the period of the oscillations is almost unaffected by the value of $l/a$." + In view of the results displayed in Figure 4.. we conclude that the length of the thread is a very important parameter.," In view of the results displayed in Figure \ref{figlthread}, we conclude that the length of the thread is a very important parameter." + When allowing to vary from the limit of fully filled tube to filled tube. periods and damping times are decreased as much as percent.," When allowing to vary from the limit of fully filled tube to filled tube, periods and damping times are decreased as much as percent." + This is very relevant in connection to prominence seismology., This is very relevant in connection to prominence seismology. + We must note that. in principle. the length of the thread can be estimated directly from observations.," We must note that, in principle, the length of the thread can be estimated directly from observations." + However. the length of the supporting magnetic flux tube is. much more difficult to estimate. since its end points are usually unobservable.," However, the length of the supporting magnetic flux tube is much more difficult to estimate, since its end points are usually unobservable." + Our general density model enable us to analyse the etfect of the density in the evacuated part of the tube on the oscillatory properties. as well.," Our general density model enable us to analyse the effect of the density in the evacuated part of the tube on the oscillatory properties, as well." + The study of the influence of this parameter was not undertaken by Soleretal. (2010).. and requires a fully numerical approach.," The study of the influence of this parameter was not undertaken by \citet{soler102dthread}, , and requires a fully numerical approach." + We allow for ps. to be different, We allow for $\rho_{\rm ev}$ to be different +indices span the full range between disk- to bulge-dominated values (2~| to 2~ 4) and the inferred dispersions range from =150 to !400kms..,"indices span the full range between disk- to bulge-dominated values $n\sim 1$ to $n\sim 4$ ) and the inferred dispersions range from $\lesssim 150$ to $\gtrsim +400$." + We have shown that the 3D-HST Treasury program i$. providing high quality near-IR spectroscopy and accompanying imaging for galaxies in the crucial. epoch ]<2<3. when the cosmic star formation rate peaked (e.g.. 2007).," We have shown that the 3D-HST Treasury program is providing high quality near-IR spectroscopy and accompanying imaging for galaxies in the crucial epoch $1I.," This is the first study of the $\alpha$ emission and rest-frame optical morphologies of a complete, mass-limited galaxy sample at $z>1$." + The most striking result of our study is the diversity of the spectra and structure of massive galaxies at z>I: a large fraction has strong Ha emission. whereas others have absorption features characteristic of relatively old. stellar populations.," The most striking result of our study is the diversity of the spectra and structure of massive galaxies at $z>1$: a large fraction has strong $\alpha$ emission, whereas others have absorption features characteristic of relatively old stellar populations." + Similarly. the morphologies. Sersic indices. and implied. velocity dispersions show a large range.," Similarly, the morphologies, Sersic indices, and implied velocity dispersions show a large range." + These results are broadly consistent with previous studies that were based on photometric redshifts. the SED shapes of galaxies. and/or imaging of lower quality (e.g.. 2005: 2010: 2011b: Weinzirl 2011).," These results are broadly consistent with previous studies that were based on photometric redshifts, the SED shapes of galaxies, and/or imaging of lower quality (e.g., 2008; 2010; 2011b; Weinzirl 2011)." + The simplest interpretation is that at z>| we are entering the epoch when massive galaxies were undergoing rapid evolution., The simplest interpretation is that at $z>1$ we are entering the epoch when massive galaxies were undergoing rapid evolution. + Specifically. the star-forming disks may be progenitors of some of today's most massive SO and Sa galaxies.Noeske (," Specifically, the star-forming disks may be progenitors of some of today's most massive S0 and Sa galaxies. (" +"2007) suggested that the star formation rates of galaxies are tightly coupled to their mass and redshift. and it is Interesting to compare the range in iin our sample to the scatter in their ""star formation main sequence"".","2007) suggested that the star formation rates of galaxies are tightly coupled to their mass and redshift, and it is interesting to compare the range in in our sample to the scatter in their “star formation main sequence”." + At fixed massNoeske (2007) find a of a factor of —4 (among galaxies with clear signs of star formation); if we limit the sample to the central distribution of galaxies with >10 wire findalargerrangeo faufactoro f six., At fixed mass (2007) find a of a factor of $\sim 4$ (among galaxies with clear signs of star formation); if we limit the sample to the central distribution of galaxies with $>10$ we find a larger range of a factor of six. + Moretothe point. withinoursam ple ccan be significantly reduced by considering the structure of the galaxies.," More to the point, within our sample the scatter in can be significantly reduced by considering the structure of the galaxies." + The range in aamong the 11 galaxies with inferred 0<200 iis only a factor of 1.7., The range in among the 11 galaxies with inferred $\sigma<200$ is only a factor of 1.7. + We therefore follow earlier work in suggesting that velocity dispersion (or surface density) is a more fundamental parameter than mass in determining the properties of galaxies (see. e.g.. 2003b; 2008: 2011).," We therefore follow earlier work in suggesting that velocity dispersion (or surface density) is a more fundamental parameter than mass in determining the properties of galaxies (see, e.g., 2003b; 2008; 2011)." + The growth rate of the star-forming galaxies is substantial: using standard prescriptions to correct for extinction toward regions 2000: 2011a). we find a median stellar mass increase due to star formation of ~50 An important question is in the galaxies the. star formation is occurring. that is. which structural component of massive galaxies is in the process of formation at ||., A key open question is what drives the diversity of massive galaxies at $z>1$. + At fixed stellar mass. we see large. star forming spiral galaxies and very compact galaxies in which star formation has apparently ceased.," At fixed stellar mass, we see large, star forming spiral galaxies and very compact galaxies in which star formation has apparently ceased." + If AGN feedback is responsible for shutting off star formation in massive galaxies it is clearly more effective in some galaxies than in others., If AGN feedback is responsible for shutting off star formation in massive galaxies it is clearly more effective in some galaxies than in others. + It may be that AGN feedback correlates with black hole mass. which correlates better with velocity dispersion than with stellar mass (e.g.. 1998).," It may be that AGN feedback correlates with black hole mass, which correlates better with velocity dispersion than with stellar mass (e.g., 1998)." + It will also be interesting to study correlations with other parameters. such as the environment. at fixed stellar mass and at fixed (inferred) velocity dispersion.," It will also be interesting to study correlations with other parameters, such as the environment, at fixed stellar mass and at fixed (inferred) velocity dispersion." + Finally. itwill be important to extend this study to lower masses and to higher redshifts.," Finally, itwill be important to extend this study to lower masses and to higher redshifts." + Star forming galaxies that have been studied at z>2 tend to have higher aand also more irregular morphologies than the galaxies studied here (e.g.. 2006; 2009b:," Star forming galaxies that have been studied at $z\gtrsim 2$ tend to have higher and also more irregular morphologies than the galaxies studied here (e.g., 2006; 2009b;" +"evroradius p; for anti-parallel reconnection is the ion inertial scale d; (Cassaketal.2005).. where O,; is the ion evclotron frequency. vy; is the ion plasma Lrequency. and € is the ion charge.","gyroradius $\rho_{i}$ for anti-parallel reconnection is the ion inertial scale $d_{i}$ \citep{Cassak05}, where $\Omega_{ci}$ is the ion cyclotron frequency, $\omega_{pi}$ is the ion plasma frequency, and $e$ is the ion charge." +" For reconnection with a (guide) magnetic field along the current sheet. the relevant evroradius becomes p,=C./ος25ep. where c, is the sound speed (Cassaketal.2007a)."," For reconnection with a (guide) magnetic field along the current sheet, the relevant gyroradius becomes $\rho_{s} = c_{s} / \Omega_{ci}$, where $c_{s}$ is the sound speed \citep{Cassak07a}." +. To see how magnetic reconnection sell-organizes the corona. consider an active region.," To see how magnetic reconnection self-organizes the corona, consider an active region." + Belore an eruption. the plasma cannot be collisionless: if it were. (he stored magnetic energy would be rapidly released by Hall reconnection.," Before an eruption, the plasma cannot be collisionless: if it were, the stored magnetic energy would be rapidly released by Hall reconnection." + Therefore. the pre-IIare active region mist be collisional.," Therefore, the pre-flare active region must be collisional." + Since (collisional) Sweet-Parker reconnection is exceedinglv slow. magnetic energy can be stored. [," Since (collisional) Sweet-Parker reconnection is exceedingly slow, magnetic energy can be stored. [" +By “collisional”. we mean ógp> d;. which. using eqs. )),"By “collisional”, we mean $\delta_{SP} > d_{i}$ , which, using eqs. \ref{deltaspdef}) )" +" and (2)). is equivalent to mj.>οLap. where pj;=ane?/im, is the ion-electron collision frequency."," and \ref{didef}) ), is equivalent to $\nu_{ie} > c_{A} / L_{SP},$ where $\nu_{ie} = \eta n e^{2} / m_{i}$ is the ion-electron collision frequency." + Therefore. reconnection is collisional when the ion transit lime along the Sweet-Parker diffusion region is longer than the ion-electron collision time.," Therefore, reconnection is collisional when the ion transit time along the Sweet-Parker diffusion region is longer than the ion-electron collision time." + See also Uzdensky.(2007h)..|, See also \citet{Uzdensky07b}. .] + When Sweet-Parker reconnection begins in (he corona. as a result of two coronal flux tubes coming together. the reconnecting magnetic field 2 is initially much weaker than the strong asvinplolic magnetic field in the core of the flix tube. the reconnection is embedded within a wider current sheet.," When Sweet-Parker reconnection begins in the corona, as a result of two coronal flux tubes coming together, the reconnecting magnetic field $B$ is initially much weaker than the strong asymptotic magnetic field in the core of the flux tube, the reconnection is embedded within a wider current sheet." + From equation (1)). the thickness of the diffusion region will be relatively wide. so that dsp29p.," From equation \ref{deltaspdef}) ), the thickness of the diffusion region will be relatively wide, so that $\delta_{SP} \gg \rho_{i}$." + It was shown (Cassaketal.2006) that embedded: Sweet-Parker reconnection spontaneously sell-drives the current sheet (o {hinner scales. even without external forcing.," It was shown \citep{Cassak06} that embedded Sweet-Parker reconnection spontaneously self-drives the current sheet to thinner scales, even without external forcing." + This is because the reconnection inflow convects stronger magnetic fields into the diffusion region. which causes dyp to decrease [see eq. (1))].," This is because the reconnection inflow convects stronger magnetic fields into the diffusion region, which causes $\delta_{SP}$ to decrease [see eq. \ref{deltaspdef}) )]." + Thus. the reconnectjon process itself sell-drives Che svstem (toward lower collisionality.," Thus, the reconnection process itself self-drives the system toward lower collisionality." + If the asymptotic field is strong enough so that dgpcpj. the svstem becomes mareinally collisioness. (hen a bifurcation causes Hall reconnection to beein. eruptivelv releasing the stored energy. [," If the asymptotic field is strong enough so that $\delta_{SP} \sim +\rho_{i}$, the system becomes marginally collisionless, then a bifurcation causes Hall reconnection to begin, eruptively releasing the stored energy. [" +We note in passing that if 2 in an active region is not strong enough to ever salisV Osp~d; lor a given density and temperature (hen no eruption occurs. potentially providing an observational constraint on which active regions erupt and which cdo not.],"We note in passing that if $B$ in an active region is not strong enough to ever satisfy $\delta_{SP} \sim +d_{i}$ for a given density and temperature then no eruption occurs, potentially providing an observational constraint on which active regions erupt and which do not.]" + After (he eruption. the corona retums to a collisional state. and the process begins again.," After the eruption, the corona returns to a collisional state, and the process begins again." + The continual sel-driving of the corona toward lower collisionality keeps coronal parameters near the critical condition where the bifurcation occurs (sp~ p;)., The continual self-driving of the corona toward lower collisionality keeps coronal parameters near the critical condition where the bifurcation occurs $\delta_{SP} \sim \rho_{i}$ ). + We propose that (this process regulates the temperature of (he corona., We propose that this process regulates the temperature of the corona. + Η (he temperature T of the corona is larger than the critical value. the Spitzer resisUivily 7 is smaller. (since jxT 77).," If the temperature $T$ of the corona is larger than the critical value, the Spitzer resistivity $\eta$ is smaller (since $\eta \propto +T^{-3/2}$ )." + From equation (1)). a smaller jjallows asmaller. B to initiate an eruption.," From equation \ref{deltaspdef}) ), a smaller $\eta$allows asmaller $B$ to initiate an eruption." + As such. less magnetic οποιον is stored. and released. and the corona cools.," As such, less magnetic energy is stored and released, and the corona cools." + Alternately.," Alternately," +slope at Miniκ ΝΤ.,slope at $_{\rm init}$$\simgreat$ $_{\odot}$. +However. the data in Miiz:3.3M .. regime appear to sit slightly above (a few hundreths of a solar mass) both this and the initial mass-core mass at first thermal pulse relation which may indicate that third dredge-up may not be quite as efficient here as assumed in the Padova models.," However, the data in $_{\rm init}$$\simgreat$ $_{\odot}$ regime appear to sit slightly above (a few hundreths of a solar mass) both this and the initial mass-core mass at first thermal pulse relation which may indicate that third dredge-up may not be quite as efficient here as assumed in the Padova models." + Nevertheless. the similarities between the forms of the theoretical relations and the trends delineated by the bulk of white dwarfs from solar metalicity open clusters lend some assurance to the results of modern stellar evolutionary calculations.," Nevertheless, the similarities between the forms of the theoretical relations and the trends delineated by the bulk of white dwarfs from solar metalicity open clusters lend some assurance to the results of modern stellar evolutionary calculations." + We have obtained high signal-to-noise low resolution optical spectroscopy of the nine candidate white dwarfs members of NGC3532 and NGC?287 with FORSI and the VLT., We have obtained high signal-to-noise low resolution optical spectroscopy of the nine candidate white dwarfs members of NGC3532 and NGC2287 with FORS1 and the VLT. + The analysis of these data and of new \ band photometry indicate that only six of these objects are probably members of the clusters., The analysis of these data and of new $V$ band photometry indicate that only six of these objects are probably members of the clusters. + These six objects. in particular the four members of NGC3532. do not substantiate any claim that there is substantial scatter in the IFMR.," These six objects, in particular the four members of NGC3532, do not substantiate any claim that there is substantial scatter in the IFMR." + While a simple linear fit to these data could still be deemed acceptable. there are now clear hints that the IFMR is steeper in the initial mass range 3M. Mini S4M. than at progenitor masses immediately lower and higher than this.," While a simple linear fit to these data could still be deemed acceptable, there are now clear hints that the IFMR is steeper in the initial mass range $_{\odot}$$\simless$ $_{\rm init}$$ +\simless$ $_{\odot}$ than at progenitor masses immediately lower and higher than this." + This result is consistent with the predictions of stellar evolutionary models., This result is consistent with the predictions of stellar evolutionary models. + Moreover. it can help explain the relatively sharp drop in the number density of white dwarfs on the high mass side of the main peak in the white dwarf mass distribution.," Moreover, it can help explain the relatively sharp drop in the number density of white dwarfs on the high mass side of the main peak in the white dwarf mass distribution." + Unfortunately. the IFMR remains rather poorly constrained at Mii; zZ3M.. where there is particular interest in its form.," Unfortunately, the IFMR remains rather poorly constrained at $_{\rm init}$$\simgreat$ $_{\odot}$, where there is particular interest in its form." + Additional white dwarts and improved spectroscopy on exisiting data points are urgently required in this progenitor mass range., Additional white dwarfs and improved spectroscopy on exisiting data points are urgently required in this progenitor mass range. + MBU and RN are supported by STFC advanced fellowships., MBU and RN are supported by STFC advanced fellowships. + We thank Paola Marigo for forwarding to us in tabular form the latest Padova theoretical IFMR., We thank Paola Marigo for forwarding to us in tabular form the latest Padova theoretical IFMR. + We thank the referee. Andre Maeder. for a prompt and helpful report.," We thank the referee, Andre Maeder, for a prompt and helpful report." +Support for program GO-9490 was provided by NASA through a grant from the Space Telescope Science Institute. which is operated bv the Association of Universities for Research in Astronomy. Inc.. under NASA contract NAS 5-26555.,"Support for program GO-9490 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555." +This analysis shows that a) about half of the YSOs in LC348 exhibits low-level variability in. near-inlrarect bancs. typically on the level of a few percent. and b) the level of variations is slightly enhanced in objects with clisks.,"This analysis shows that a) about half of the YSOs in IC348 exhibits low-level variability in near-infrared bands, typically on the level of a few percent, and b) the level of variations is slightly enhanced in objects with disks." + Νάς19939 is an extremely voung cluster with an age of | MMsr and a distance of ~300 ppc., NGC1333 is an extremely young cluster with an age of $\sim 1$ Myr and a distance of $\sim 300$ pc. + As IC348. NGC1333 is located in the Perseus star forming region.," As IC348, NGC1333 is located in the Perseus star forming region." + We use the sample of 137 Class L| and 1 sources identified by 7 based. on Spitzer data. which should. be essentially free from contamination.," We use the sample of 137 Class I and II sources identified by \citet{2008ApJ...674..336G} based on Spitzer data, which should be essentially free from contamination." + As these objects are identified [rom the infrared excess. all are considered to have a disk (or at least circumstellar materia," As these objects are identified from the infrared excess, all are considered to have a disk (or at least circumstellar material)." + The cluster has been observed by 2ALASS from ovember 1999 to October 2000 and by UIKIDSS/GPS carly 2007. i.c. the average epoch dillerence is Tver.," The cluster has been observed by 2MASS from November 1999 to October 2000 and by UKIDSS/GPS early 2007, i.e. the average epoch difference is $\sim 7$ yr." + From the initial sample. 96 have Ike and. H-band yhotometry in the two surveys. S82 of them unallected o» saturation.," From the initial sample, 96 have K- and H-band photometry in the two surveys, 82 of them unaffected by saturation." + SJ have I|x- and J-hancd photometry. 72 unalfIected by saturation.," 84 have K- and J-band photometry, 72 unaffected by saturation." + In Fig., In Fig. + 5 the usual plots are shown. or the ffdy colour (right panel) and the JA colour (left uel).," \ref{f6} the usual plots are shown, for the $H-K$ colour (right panel) and the $J-K$ colour (left panel)." + Three objects appear in the plots at diy70.5. one of hem in both panels.," Three objects appear in the plots at $dK>0.5$, one of them in both panels." + All three have z0.5 mmag amplitudes in one more band., All three have $>0.5$ mag amplitudes in one more band. + These three are contained in Table 1.., These three are contained in Table \ref{var}. + As indicated. all of them are considered: to have disks.," As indicated, all of them are considered to have disks." + Compared with the other regions. the upper limit of the amplitudes is somewhat higher in λές09 (1.6 in [x. instead of 1.0). possibly due to the extreme vouth and early evolutionary stage of the cluster.," Compared with the other regions, the upper limit of the amplitudes is somewhat higher in NGC1333 (1.6 in K, instead of 1.0), possibly due to the extreme youth and early evolutionary stage of the cluster." + Ehe frequeney. of highly variable objects is 3/82 or4%., The frequency of highly variable objects is 3/82 or. + Some more objects have large variations in the J-band up to dd. but are much less variable in the other mands.," Some more objects have large variations in the J-band up to $dJ>1$, but are much less variable in the other bands." + Ho turns out that they are close to the sensitivity imit of 2ALASS in the J-band and in some cases alfected by neighbouring brighter stars., It turns out that they are close to the sensitivity limit of 2MASS in the J-band and in some cases affected by neighbouring brighter stars. + Although they need. verification with additional epochs. at this point they are not considered o be variable.," Although they need verification with additional epochs, at this point they are not considered to be variable." + Similar to IC348. 1 determine the level of variability in he entire sample.," Similar to IC348, I determine the level of variability in the entire sample." + The median dilference in the three bands J. HL. and Ix is 0.09. 0.09. mmag.," The median difference in the three bands J, H, and K is 0.09, 0.09, mag." + The fraction of objects with 2e variability is 47. 40. and.," The fraction of objects with $\sigma$ variability is 47, 40, and." +". ""ποσο fractions have vpical binomial lo errors of6%.", These fractions have typical binomial $\sigma$ errors of. +.. For the variable objects. he median dillerence between 23LASS and. UIKKIDSS after subtracting 2NLASS errors is 0.20. 0.12. mmaeg in the hree bands J. HH. Ix. As noted above. all objects analysed in NGC1333 show evidence for the presence of a disk.," For the variable objects, the median difference between 2MASS and UKIDSS after subtracting 2MASS errors is 0.20, 0.14, mag in the three bands J, H, K. As noted above, all objects analysed in NGC1333 show evidence for the presence of a disk." + The raction of variable objects is similar to 1€528. but. the vpical level of variations is higher in NCIO'1333 by a factor of ~2. maybe because the cluster is vounger than 10348.," The fraction of variable objects is similar to IC348, but the typical level of variations is higher in NGC1333 by a factor of $\sim 2$, maybe because the cluster is younger than IC348." + For comparison. variable stars in the ONC. a cluster similar in age to NGC1333. show median peak-to-peak amplitudes of 0.15. 0.12. and mamas in the three bands J. H. and Ix on timescales of about one month (?)..," For comparison, variable stars in the ONC, a cluster similar in age to NGC1333, show median peak-to-peak amplitudes of 0.15, 0.12, and mag in the three bands J, H, and K on timescales of about one month \citep{2001AJ....121.3160C}." + This is consistent with the values in NCCT332. indicating that the low-level variability mostlyoccurs on timescales of davs to weeks. not. vears.," This is consistent with the values in NGC1333, indicating that the low-level variability mostlyoccurs on timescales of days to weeks, not years." + For the open cluster & OOri. age ~3MNMyr. ο recently published a comparison between 2ALASS and UINIDSS data.," For the open cluster $\sigma$ Ori, age $\sim 3$ Myr, \citet{2009A&A...505.1115L} recently published a comparison between 2MASS and UKIDSS data." + Thev look at 263 sources with J-band magnitudes between 12 and 16., They look at 263 sources with J-band magnitudes between 12 and 16. + Two of them show J-band variability by d~1.0. three more with d0.5.," Two of them show J-band variability by $dJ \sim 1.0$, three more with $dJ>0.5$." +" ""Phus the frequeney of highly variable objects is in the range of for the total sample Or. assuming a clisk fraction of830%.. for the objects with clisks."," Thus the frequency of highly variable objects is in the range of for the total sample or, assuming a disk fraction of, for the objects with disks." + These numbers are derived for the J-band. whereas the Ix-band is used in the other regions. but they confirm that highly variable objects are rare (well below 104)) in star forming regions.," These numbers are derived for the J-band, whereas the K-band is used in the other regions, but they confirm that highly variable objects are rare (well below ) in star forming regions." + The main result from the analysis in Sect., The main result from the analysis in Sect. + 3. is that strongly variable objects on timescales of several vears are rare among Class LE YSOs., \ref{s2} is that strongly variable objects on timescales of several years are rare among Class II YSOs. + Adding p-Oph. ONC. 10348. and NGCOC1333. here are 11 sources with ο0.5 mamag variations in two near-infrared. bands on timescales vvr. out of ~620. YSOs. rom which ~320 have disks (here L assume a clisk frequency of for the ONC).," Adding $\rho$ -Oph, ONC, IC348, and NGC1333, there are 11 sources with $>0.5$ mag variations in two near-infrared bands on timescales yr, out of $\sim 620$ YSOs, from which $\sim 320$ have disks (here I assume a disk frequency of for the ONC)." + Ehe fraction of such variable objects is thus for the full sample and for YSOs with disks (Class Ll or Class HD)., The fraction of such variable objects is thus for the full sample and for YSOs with disks (Class I or Class II). + These low fractions are confirmed w the independent study in c OOri (2)..., These low fractions are confirmed by the independent study in $\sigma$ Ori \citep{2009A&A...505.1115L}. + Phev are much ower than the number reported in 2.20-254..., They are much lower than the number reported in \citet[][20-25\%]{2009MNRAS.398..873S}. + Fhis may be due to the much smaller sample size in the previous study (only about 20 accretors) or due to an overestimate in the assumed contamination for their sample of photometrically selected: YSO candidates., This may be due to the much smaller sample size in the previous study (only about 20 accretors) or due to an overestimate in the assumed contamination for their sample of photometrically selected YSO candidates. + In the current study. only hieh-confidence members of star forming regions are considered. which should. provide a more reliable result.," In the current study, only high-confidence members of star forming regions are considered, which should provide a more reliable result." + These results have implications for the interpretation ofthe μαoead in LX diagrams that is ubiquitously observed in star forming regions., These results have implications for the interpretation of the spread in HR diagrams that is ubiquitously observed in star forming regions. + Variability in the optical ancl near-infrared bands will to some extent contribute to this spread. as the luminosities are routinely estimated from LI- or J-band photometry which is considered to give the best estimate of the photospheric Dux.," Variability in the optical and near-infrared bands will to some extent contribute to this spread, as the luminosities are routinely estimated from I- or J-band photometry which is considered to give the best estimate of the photospheric flux." + In luminosity. the spread. in. Hi diagrams for very voung regions is often as much as 1 order of magnitude (e.g.?)..," In luminosity, the spread in HR diagrams for very young regions is often as much as 1 order of magnitude \citep[e.g.][]{2003ApJ...593.1093L}." + The results in this study indicate that the variability in the J-band is less than mimag for the overwhelming majority of YSOs. Le. a factor of «1.6 in luminosity. which is only a minor part of the observed. spread. in the LL diagrams.," The results in this study indicate that the variability in the J-band is less than mag for the overwhelming majority of YSOs, i.e. a factor of $<1.6$ in luminosity, which is only a minor part of the observed spread in the HR diagrams." + Moreover. thefypicad level of variability in the J-band is much lower than that.," Moreover, the level of variability in the J-band is much lower than that." + About half the objects show variations of.. depending on the disk. fraction ancl possibly age. the other half is not variable within a few percent. consistent with previous results by ?..," About half the objects show variations of, depending on the disk fraction and possibly age, the other half is not variable within a few percent, consistent with previous results by \citet{2001AJ....121.3160C}." + Variability on timescales up to vvr can definitely cause outliers in HI diagrams and has to be taken into account when deriving fundamental parameters for individual sources. as argued in ?.. ," Variability on timescales up to yr can definitely cause outliers in HR diagrams and has to be taken into account when deriving fundamental parameters for individual sources, as argued in \citet{2009MNRAS.398..873S}. ." +For the analysis of the stellar properties of large samples. however. it is insignificant.," For the analysis of the stellar properties of large samples, however, it is insignificant." + This finding is similar to the conclusions drawn by ? and. ?.., This finding is similar to the conclusions drawn by \citet{2001AJ....121.3160C} and \citet{2005MNRAS.363.1389B}. . +Μαν 1.J.. 1984. 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(" +Cambridge University Press). p. 87 Wills D.J.. Brotherton M.S.. 1995. ApJ. 448. LSI Wills D.J.. et al..,"Cambridge University Press), p. 87 Wills B.J., Brotherton M.S., 1995, ApJ, 448, L81 Wills B.J., et al.," + 1983. ApJ. 274. 62 Wills D.J.. Brotherton M.S.. Fang D.. Steidel CC... Sargent WLLAV.. 1993. ApJ. 415. 563 Wills D.J.. et al. 1995. ApJ. 447. 139 Wilson AS... 1993. in. Astrophysical Jets. Burgarclla D.. Livio AL. ODea ο. eds. (," 1983, ApJ, 274, 62 Wills B.J., Brotherton M.S., Fang D., Steidel C.C., Sargent W.L.W., 1993, ApJ, 415, 563 Wills B.J., et al, 1995, ApJ, 447, 139 Wilson A.S., 1993, in Astrophysical Jets, Burgarella D., Livio M., O'Dea C., eds. (" +Cambridge University Press). p. 121 Yee LINC... 1980. ApJ. 241. 894 Zheng W.. Ixriss GAL. Veller IC... Crimes J.P... Davidsen AGE. 1996. ApJ. in press The kinetic luminosity of pescale jets. as estimated rom the SSC) theory. is plotted against. the estimated uminositv in broad lines. for different classes of racio:Loud sources. namely Core Dominated High Polarization Quasars cireles). Core Dominated Low Polarization Quasars circles). Lobe Dominated Quasars squares). and DL Lac objects (erosses).,"Cambridge University Press), p. 121 Yee H.K.C., 1980, ApJ, 241, 894 Zheng W., Kriss G.A., Telfer R.C., Grimes J.P., Davidsen A.F., 1996, ApJ, in press The kinetic luminosity of pc–scale jets, as estimated from the SSC theory, is plotted against the estimated luminosity in broad lines, for different classes of radio–loud sources, namely Core Dominated High Polarization Quasars ), Core Dominated Low Polarization Quasars ), Lobe Dominated Quasars ), and BL Lac objects )." + The underlined svmbols refer to sources for which the derived Doppler Factor is less than one (sce text)., The underlined symbols refer to sources for which the derived Doppler factor is less than one (see text). +" The clashed line corresponds to Li,=Lair.", The dashed line corresponds to $\lk = \ll$. + 0.5 trucem Ehe core radio Iuminosityv. tyLycore VS he luminosity in broad lines. for the same objects of Fig.," 0.5 truecm The core radio luminosity, $\nu_{\rm r} L_{\rm r,core}$ vs the luminosity in broad lines, for the same objects of Fig." + 1., 1. + The dashed line corresponds to £L;c=Lair.," The dashed line corresponds to $\nu_{\rm r} +L_{\rm r,core} = \ll$." +" While the correlation between the two luminosities is larecly due to the common redshift dependence. it still suggests that the large spread in the correlation Ly, vs Leon is due to uncertainties in the estimate of Li."," While the correlation between the two luminosities is largely due to the common redshift dependence, it still suggests that the large spread in the correlation $\lk$ vs $\ll$ is due to uncertainties in the estimate of $\lk$." + 0.5 truecm The distribution of logCLyu/Lppn) [or the various classes of sources. that is (from top to bottom): Core Dominated High Polarization Quasars. Core Dominatec Low Polarization Quasars. Lobe Dominated Quasars. all Quasars. and BL Lac objects.," 0.5 truecm The distribution of $\log +(\lk/\ll)$ for the various classes of sources, that is (from top to bottom): Core Dominated High Polarization Quasars, Core Dominated Low Polarization Quasars, Lobe Dominated Quasars, all Quasars, and BL Lac objects." + Dashed areas indicate objects with an estimated ὁ<1 (see text), Dashed areas indicate objects with an estimated $\delta <1$ (see text). +is of sufficient size to measure the disk frequency across spectral type. aud as a function of age and multiplicity.,"is of sufficient size to measure the disk frequency across spectral type, and as a function of age and multiplicity." + Subinillumeter observatious have already: been pivotal in studies of debris disks. having imaged or discovered seven of the fourteen resolved disks aud coustraincd the mass and temperature and hence radial extent of many of the remainder.," Submillimeter observations have already been pivotal in studies of debris disks, having imaged or discovered seven of the fourteen resolved disks and constrained the mass and temperature and hence radial extent of many of the remainder." + The subnülliueter enüssion is both optically-thin aud scusitive to relatively large. cold eraius Which dominate the massses of these disks.," The submillimeter emission is both optically-thin and sensitive to relatively large, cold grains which dominate the massses of these disks." + Hence. our survev will provide immediate nass estimates for etected disks.," Hence, our survey will provide immediate mass estimates for detected disks." + Constraiiug the temperature of nowlv identified disks will require complementary data in the nude or far-IR., Constraining the temperature of newly identified disks will require complementary data in the mid- or far-IR. + This will be particularly critical for warm isks. since the two potential subuullimeter wavelengths observable through our survey (850 and 150 j24)) will both lie longward of the peak of the spectral energv distribution (SED) aud provide little coustraiut on the teniperature.," This will be particularly critical for warm disks, since the two potential submillimeter wavelengths observable through our survey (850 and 450 ) will both lie longward of the peak of the spectral energy distribution (SED) and provide little constraint on the temperature." + The study of these disks is revolutionizing our ucderstanding of plauct formation., The study of these disks is revolutionizing our understanding of planet formation. + For the fourteen disks which have been resolved. observed structures have eve con used to infer the location of uuseen planets (6.9..Wratt 2003).," For the fourteen disks which have been resolved, observed structures have even been used to infer the location of unseen planets \citep[e.g.,][]{wya03}." +. Muy more disks have been characterized w their SEDs. showing that they are the extrasolar equivalents of the Nuiper and asteroid belts of the Solar System.," Many more disks have been characterized by their SEDs, showing that they are the extrasolar equivalents of the Kuiper and asteroid belts of the Solar System." + The racial positions aud masses of these belts. xwtieularlv when this iuformation can be compared for stars of different ages. spectral types. imuultiplicitv or shown planetary companions. provide vital constraiuts on planet formation processes and on how the resulting dlanctary svstenis subsequently evolve.," The radial positions and masses of these belts, particularly when this information can be compared for stars of different ages, spectral types, multiplicity or known planetary companions, provide vital constraints on planet formation processes and on how the resulting planetary systems subsequently evolve." + SCUDA-2 (IIollaudetal.2006) is a new submillimeter caniera arriving at the James Clerk Maxwell Telescope (JOXMT) in late 2007., SCUBA-2 \citep{hol06} is a new submillimeter camera arriving at the James Clerk Maxwell Telescope (JCMT) in late 2007. + SCUDA-2 is expected to be. per pixel five times as scusitive as its predecessor SCUBA (SubiuillnuieterCommonUserBoloueteretal.1999) at 850piu.," SCUBA-2 is expected to be, per pixel, five times as sensitive as its predecessor SCUBA \citep[Submillimeter Common User Bolometer Array,][]{hol99} at 850." + Its larger « 79). fullv-uupled field of view males it a premiere survey iustrmucnt. aud seven comprehensive surveys have been planned to maximize the scicutific output frou the JOAIT over the next five vears (Ward-Thompson et al.," Its larger $\times$ ), fully-sampled field of view makes it a premiere survey instrument, and seven comprehensive surveys have been planned to maximize the scientific output from the JCMT over the next five years (Ward-Thompson et al." + 2007. in prep: SES paper (Plumeetal.2007).," 2007, in prep; SLS paper \citep{plu07}." +". Like its predecessor. it observes siuultaucouslv at 850 aud 150jau.. with resolutions of 15 aud77"".. respectively,"," Like its predecessor, it observes simultaneously at 850 and 450, with resolutions of 15 and, respectively." + Uulike its predecessor. SCUBA-2 will Nyquist sample the sky at 850pau at 150pau. the array is undersauipled by a factor of two.," Unlike its predecessor, SCUBA-2 will Nyquist sample the sky at 850; at 450, the array is undersampled by a factor of two." +" The focal plane area coverage is provided byfour ""sub-uravs at cach wavelength. where cach array is comprised of 32«10 detectors (seeTollandetal. 2006)."," The focal plane area coverage is provided byfour “sub-arrays” at each wavelength, where each sub-array is comprised of $32 \times 40$ detectors \citep[see][]{hol06}." +. The SCUBA-2 Uubiased Nearby Stars (SUNS) survey will utilize 390 hours to observe 500 nearby stars (the — yuearest AL Is. C. Ε and A stars) to the JCAIT’s extragalactic confusion lit at 850 | detect aud map circumstellar dust.," The SCUBA-2 Unbiased Nearby Stars (SUNS) survey will utilize 390 hours to observe 500 nearby stars (the 100 nearest M, K, G, F and A stars) to the JCMT's extragalactic confusion limit at 850 to detect and map circumstellar dust." + The survey is completely unbiased: no star will be rejected due to its intrinsic properties., The survey is completely unbiased; no star will be rejected due to its intrinsic properties. + The survey will determine the incidence of disks around nearby stars. coustralli lasses (and temperatures of disks detected in the far-IR). iscover disks too cold to be detected iu the far-IR. and provide limits ou the presence of dust which are vital to targeted plauet search mussious such as Darwin and the Terrestrial Plauct Finder (TPF). as well as future missions which will resolve disks in unprecedented detail. i.e. the AtacamaLarge Millienieter-subiuillimeter Array. the James Webb Space Telescope. aud tle Far-IR Tuterferometer CFIRI.Ivisou&Blain2005).," The survey will determine the incidence of disks around nearby stars, constrain masses (and temperatures of disks detected in the far-IR), discover disks too cold to be detected in the far-IR, and provide limits on the presence of dust which are vital to targeted planet search missions such as Darwin and the Terrestrial Planet Finder (TPF), as well as future missions which will resolve disks in unprecedented detail, i.e., the AtacamaLarge Milliemeter-submillimeter Array, the James Webb Space Telescope, and the Far-IR Interferometer \citep[FIRI,][]{ivi05}." +". The ass sensitivity of the survey is a strong function of both distance and disk temperature,", The mass sensitivity of the survey is a strong function of both distance and disk temperature. + For disks of TO Ix. the seusitivitv ranges from 0.003L.μμ (Minna—1/81M4 for the nearest (2 pe) aud furthest (15 pe) stars.," For disks of 70 K, the sensitivity ranges from $0.003 - 1.4 M_{\rm lunar}$ $M_{\rm lunar} = 1/81 \ +M_\oplus$ ) for the nearest (2 pc) and furthest (45 pc) stars." + For lower disk temperatures of LO Ix. the range is 0005—2.7Mas.," For lower disk temperatures of 40 K, the range is $0.005 - 2.7 M_{\rm +lunar}$." + At the mean distance of the survey stars (15 pe). we will be sensitive to dust masses typically ~200 times the dust mass of the wiper Belt (mLO°AL). which is the mass of the disk around € Eridani.," At the mean distance of the survey stars (15 pc), we will be sensitive to dust masses typically $\sim 200$ times the dust mass of the Kuiper Belt $\approx 10^{-5} M_\oplus$ ), which is the mass of the disk around $\epsilon$ Eridani." + Thus. while it will not be sensitive to prescut dav Solar System analogues. it will detect such svstenis which are in a period of unusually hieh dust mass.," Thus, while it will not be sensitive to present day Solar System analogues, it will detect such systems which are in a period of unusually high dust mass." + We know that the wiper Belt is a factor of zz100 tines less massive than expected from the distribution of solids in the Solar System (Morbidelhi2001)., We know that the Kuiper Belt is a factor of $\approx 100$ times less massive than expected from the distribution of solids in the Solar System \citep{mor04}. +. Thus the πηρα: Belt used to be more massive., Thus the Kuiper Belt used to be more massive. + Equally. au episodic mode of dust creation could render the I&uiper Belt detectable in the future.," Equally, an episodic mode of dust creation could render the Kuiper Belt detectable in the future." + The mass limit for uudetected svsteimis will also be useful for future planet search missions., The mass limit for undetected systems will also be useful for future planet search missions. + Missions such as Darwin/TPF require a dust free svstei. typically below 10 times that of the Solar System. to linüt the inteeration time required to detect Earth-like plaucts (Beichinanetal.2001).," Missions such as Darwin/TPF require a dust free system, typically below 10 times that of the Solar System, to limit the integration time required to detect Earth-like planets \citep{bei04}." + The SUNS survey will provide a significant legacy for he field) of extrasolar planetary svstem research., The SUNS survey will provide a significant legacy for the field of extrasolar planetary system research. + This Ποια is rapidly evolving. aud a varicty of techniques are cine developed to characterize the planetary svstenis of rearby stars.," This field is rapidly evolving, and a variety of techniques are being developed to characterize the planetary systems of nearby stars." + This survey will determine the dust aud dlanetesimal content of these systems aud so provide vital complementary information on the outcome of auet formation in them: for some techniques. the dust content even provides the limiting factor determining whether such techuiques are going to work (¢.¢..TPF.Beichinanctal. 2006)).," This survey will determine the dust and planetesimal content of these systems and so provide vital complementary information on the outcome of planet formation in them; for some techniques, the dust content even provides the limiting factor determining whether such techniques are going to work \citep[e.g., +TPF,][]{bei06b}." +. Tn this paper. we provide details about the SUNS survey. including the motivation for the survey in the contest of our current understanding of debris disk systems (5 2)). advantages of the submillimeter compared to shorter wavelengths (5 2.2)). aud the mass seusitivitv of our survey (5 2.3)).," In this paper, we provide details about the SUNS survey, including the motivation for the survey in the context of our current understanding of debris disk systems $\S$ \ref{motivation}) ), advantages of the submillimeter compared to shorter wavelengths $\S$ \ref{adsubmm}) ), and the mass sensitivity of our survey $\S$ \ref{masssen}) )." + Our science goals are described in 58 D. and we describe the details of our target List in 5 L. meludiug ancillary targets. subset populations and statistics.," Our science goals are described in $\S$ \ref{science}, and we describe the details of our target list in $\S$ \ref{targets}, including ancillary targets, subset populations and statistics." + Plaus for complementary data to the SUNS survey are described iu 8 5.., Plans for complementary data to the SUNS survey are described in $\S$ \ref{complementary}. + We describe the data products in 5 6 and sumunarize the survey in © 7.., We describe the data products in $\S$ \ref{dataproducts} and summarize the survey in $\S$ \ref{summary}. + All of the approximately 200 known candidate debris disks were first discovered by their thermal emission. which is brighter than the photospleric cussion oftheir host stars at far-IR aud longer waveleneths (c.e..Mauimines&Barlow 1998).," All of the approximately 200 known candidate debris disks were first discovered by their thermal emission, which is brighter than the photospheric emission of their host stars at far-IR and longer wavelengths \citep[e.g.,][]{man98}." +". The majority of these disks aud disk candidates were discovered byLRAS. which provided the first ancl only large unbiased survey of nearby stars for excess thermal eiission at 12-100 (with resolutions tto 9/1),"," The majority of these disks and disk candidates were discovered by, which provided the first and only large unbiased survey of nearby stars for excess thermal emission at 12-100 (with resolutions to )." + This strvey showed that ~15% of ncarby stars exhibit detectable excess cussion (Backinan&Paresce 1993).. and the JRAS disk cauclidates lave heen the subject of intense follow-up observations from the στο," This survey showed that $\sim 15$ of nearby stars exhibit detectable excess emission \citep{bp93}, , and the disk candidates have been the subject of intense follow-up observations from the ground" +Thus for the limit of large 7 i.e. ignoring shot noise only keeping the cosmic variance term where V is the volume of the survey.,Thus for the limit of large $\bar{n}$ i.e. ignoring shot noise only keeping the cosmic variance term where V is the volume of the survey. +" We will however always include shot noise in our calculations, assuming a constant number density of tracers n=5x10-*(h~*Mpc)~3."," We will however always include shot noise in our calculations, assuming a constant number density of tracers $\bar{n} = 5\times10^{-4} (h^{-1} {\rm Mpc})^{-3}$ ." + For a more detailed explanation see ?.. (, For a more detailed explanation see \cite{1998ApJ...499..555T}. ( +There is the implicit assumption that uncertainties in the measurement of the power spectrum are independent of cosmology.,There is the implicit assumption that uncertainties in the measurement of the power spectrum are independent of cosmology. + This assumption is incorrect since knowledge of the Hubble function and angular diameter distance are needed to convert redshifts to galaxy positions and derive a power spectrum from observational data.), This assumption is incorrect since knowledge of the Hubble function and angular diameter distance are needed to convert redshifts to galaxy positions and derive a power spectrum from observational data.) +" We then put this into equation 17,, (6P)?= c?, using 0P/P=OlnP and recognising that because the effects on the power spectrum that we are interested in are anisotropic we require the full two dimensional anisotropic Fisher matrix, we get: The logarithmic derivatives of the toy model power spectrum can be found in the appendix."," We then put this into equation \ref{fish_pk}, $(\delta P)^2 = \sigma^2$ , using $\partial P/ P = \partial \ln P$ and recognising that because the effects on the power spectrum that we are interested in are anisotropic we require the full two dimensional anisotropic Fisher matrix, we get: The logarithmic derivatives of the toy model power spectrum can be found in the appendix." + We have assumed here that the different k-modes of the power spectrum are uncorrelated., We have assumed here that the different k-modes of the power spectrum are uncorrelated. + In reality a given galaxy redshift survey will only cover part of the sky and may vary in depth., In reality a given galaxy redshift survey will only cover part of the sky and may vary in depth. + Thus different k-modes of the power spectrum are correlated by a window function and are not independant., Thus different k-modes of the power spectrum are correlated by a window function and are not independant. +" The assumption of uncorrelated modes is valid if the k-bin Ak>>1/L, where L is the smallest linear dimension of the survey, in our case this is ~1(h"," The assumption of uncorrelated modes is valid if the $k$ -bin $\Delta k >> 1/L$, where L is the smallest linear dimension of the survey, in our case this is $\sim 1 (h^{-1}Gpc)^3$." + We used a k-bin size of Ak=1.9x107?hMpc which !Gpc)..satisfies this criterion., We used a $k$ -bin size of $\Delta k = 1.9 \times 10^{-3} h {\rm Mpc}$ which satisfies this criterion. + In order to reduce the size of our parameter set we have two options., In order to reduce the size of our parameter set we have two options. +" Either “fix” the parameters we are uninterested in, i.e. assume that we know their values completely."," Either “fix"" the parameters we are uninterested in, i.e. assume that we know their values completely." + If we think we know the value of a parameter completely then we can just remove that row and column from the Fisher matrix., If we think we know the value of a parameter completely then we can just remove that row and column from the Fisher matrix. + This is equivalent to adding an infinite prior on that parameter., This is equivalent to adding an infinite prior on that parameter. + Or we can marginalise over that parameter., Or we can marginalise over that parameter. + Treating it as a “nuisance” parameter.," Treating it as a “nuisance"" parameter." + Constraints obtained from a marginalised Fisher matrix will always be weaker or equal to those from an unmarginalised matrix., Constraints obtained from a marginalised Fisher matrix will always be weaker or equal to those from an unmarginalised matrix. + Marginalisation will have no effect on the error on a parameter only if all other parameters are completely uncorrelated to it., Marginalisation will have no effect on the error on a parameter only if all other parameters are completely uncorrelated to it. + T'his assumption breaks down because our observed parameters hide shared cosmological information and are therefore correlated., This assumption breaks down because our observed parameters hide shared cosmological information and are therefore correlated. + For example all our parameters except A* are dependant on Qn., For example all our parameters except $A^*$ are dependant on $\Omega_{\rm m}$. + The procedure we follow to marginalise over unwanted parameters is to first invert the Fisher matrix to get the covariance matrix., The procedure we follow to marginalise over unwanted parameters is to first invert the Fisher matrix to get the covariance matrix. + Then we remove the row and column corresponding to the “nuisance” parameter and reinvert to obtain the new reduced Fisher matrix.," Then we remove the row and column corresponding to the “nuisance"" parameter and reinvert to obtain the new reduced Fisher matrix." + This is then repeated until we have marginalised over all our “nuisance” parameters.," This is then repeated until we have marginalised over all our “nuisance"" parameters." + In our toy model analysis we demonstrate calibration of LSS information to the CMB by the addition of a prior on the sound horizon scale r;., In our toy model analysis we demonstrate calibration of LSS information to the CMB by the addition of a prior on the sound horizon scale $r_{\rm s}$. + The sound horizon can be calculated using the description by ??..," The sound horizon can be calculated using the description by \citet{1996ApJ...471..542H,1998ApJ...496..605E}." +" 'The prior matrix is simply a diagonal matrix made up of Ρτ,|—1/c?, where σ is the error on parameter 0; and off diagonal components being zero."," The prior matrix is simply a diagonal matrix made up of $Pr_{i=j} = 1/\sigma^2$, where $\sigma$ is the error on parameter $\theta_i$ and off diagonal components being zero." + Adding this matrix to the original Fisher matrix then produces a matrix which includes the prior information., Adding this matrix to the original Fisher matrix then produces a matrix which includes the prior information. + In Figures 2 and 3 we have drawn error ellipses representing the constraints on pairs of parameters (marginalising over all other parameters) in our toy power spectrum from a 1(h!Gpc)? volume limited survey (blue)., In Figures \ref{fig:toy_model_error_ellipses_LRG.eps} and \ref{fig:toy_model_error_ellipses_DESpec.eps} we have drawn error ellipses representing the constraints on pairs of parameters (marginalising over all other parameters) in our toy power spectrum from a $1(h^{-1} {\rm Gpc})^3$ volume limited survey (blue). +" 'The ellipses are then redrawn including only a prior on the sound horizon of ~1%, ie. that op,=l.AMpch! is a Gaussian error bar."," The ellipses are then redrawn including only a prior on the sound horizon of $\sim 1 \%$, i.e. that $\sigma_{r_{\rm s}} = 1.4 \, {\rm Mpc} h^{-1}$ is a Gaussian error bar." + This is about the size of the error bar on the the sound horizon scale from WMAP-7., This is about the size of the error bar on the the sound horizon scale from WMAP-7. +" The shrinking on the c,—cj ellipse implies that calibrating the sound horizon from the CMB to the sound horizon in the BAO features in the galaxy power spectrum can tell us whether we have the correct value for the angular diameter distance and Hubble function.", The shrinking on the $c_\bot - c_\parallel$ ellipse implies that calibrating the sound horizon from the CMB to the sound horizon in the BAO features in the galaxy power spectrum can tell us whether we have the correct value for the angular diameter distance and Hubble function. + The affect that decreasing the strength of the prior on the sound horizon has on constraints in the οι —B and cj—β planes is illustrated in figure 4..," The affect that decreasing the strength of the prior on the sound horizon has on constraints in the $c_\bot - c_\parallel$ , $c_\bot - \beta$ and $c_\parallel - \beta$ planes is illustrated in figure \ref{fig:ellipse_size_with_sigma_rs.eps}." +" Note how --ει,ειcalibrating the sound horizon has next to no effect of our constraints on 6.", Note how calibrating the sound horizon has next to no effect of our constraints on $\beta$. +" However, within da(z) and H(z) lie all the standard cosmological parameters (the dark energy equation of state appears in the Hubble function and in the angular diameter distance)."," However, within $d_A(z)$ and $H(z)$ lie all the standard cosmological parameters (the dark energy equation of state appears in the Hubble function and in the angular diameter distance)." + In order to know how much information we have on those parameters from the original toy power spectrum we need to transform the original Fisher matrix., In order to know how much information we have on those parameters from the original toy power spectrum we need to transform the original Fisher matrix. + This isa straight forward coordinate transformation of a rank-2 tensor, This isa straight forward coordinate transformation of a rank-2 tensor +Phe Horsehead Nebula in Orion is one of the most familiar images in astronomwvy see Figure 1.,The Horsehead Nebula in Orion is one of the most familiar images in astronomy – see Figure 1. + lt appears as D33 in the catalogue of clark clouds of Barnard (1919)., It appears as B33 in the catalogue of dark clouds of Barnard (1919). + It. has been observed by many people at many wavelengths., It has been observed by many people at many wavelengths. + Recent studies bv. Pound. Reipurth Bally (2003). Abergel et al. (," Recent studies by Pound, Reipurth Bally (2003), Abergel et al. (" +2003). Tevssier et al. (,"2003), Teyssier et al. (" +2004). Pety et al. (,"2004), Pety et al. (" +2005). and Habart et al. (,"2005), and Habart et al. (" +"2005) have concentrated on the edge of the nebula that is nearest to the LUE region (the ""top. of the horse's head).",2005) have concentrated on the edge of the nebula that is nearest to the HII region (the `top' of the horse's head). + All derived. various values for the gas densities and temperatures across the photon-dominated: region (PDR) that exists along this οσο of the nebula., All derived various values for the gas densities and temperatures across the photon-dominated region (PDR) that exists along this edge of the nebula. + Abergel et al. (, Abergel et al. ( +2003) confirmed that the star & Orionis is responsible for the ionising radiation producing the PDR.,2003) confirmed that the star $\sigma$ Orionis is responsible for the ionising radiation producing the PDR. + They deduced that the PDR is ~0.01 pc in thickness and they found densities of —10! em57 immediately behind the ionisation front., They deduced that the PDR is $\sim$ 0.01 pc in thickness and they found densities of $\sim$ $^4$ $^{-3}$ immediately behind the ionisation front. + Teyssier et al. (, Teyssier et al. ( +2004) presented observations of various carbon-bearing species. and Pety et. al. (,"2004) presented observations of various carbon-bearing species, and Pety et al. (" +2005) showed interferometer observations of the PDR. from which they concluded that no current model of PDIts could explain all of their data. and that this might be explained by fragmentation of polveyclic aromatic hydrocarbon. (PALL),"2005) showed interferometer observations of the PDR from which they concluded that no current model of PDRs could explain all of their data, and that this might be explained by fragmentation of polycyclic aromatic hydrocarbon (PAH)" +"The energy density of an isotropic background of individually unresolvable GW sources is related to the spectral density in the LISA detector by Saw(f)=4G/(xc?f?)dpm/df ler 2004),, or where equations (19)) and (20)) were used.","The energy density of an isotropic background of individually unresolvable GW sources is related to the spectral density in the LISA detector by $S_{\GW}(f) = 4G/(\pi c^2 f^{2})\ d \rho_{\M}/d f$ \citep{Bar04b}, or where equations \ref{eq:espec}) ) and \ref{eq:z}) ) were used." + The integral is taken over VY representing that part of orbit space that is populated according to refsec:processes.., The integral is taken over $\mathcal{V}$ representing that part of orbit space that is populated according to \\ref{sec:processes}. . +" For our main model, the resulting EMBB (fSgw)!/? of the four species of stars is shown in figure (2))."," For our main model, the resulting EMBB $(f S_{\GW})^{1/2}$ of the four species of stars is shown in figure \ref{fig:zplota}) )." + The EMBB is dominated by contributions from BHs., The EMBB is dominated by contributions from BHs. + This is mainly due to two reasons., This is mainly due to two reasons. +" First, a single burst emitted by a BH is more energetic than a burst emitted by the other species of stars in a similar orbit."," First, a single burst emitted by a BH is more energetic than a burst emitted by the other species of stars in a similar orbit." +" Second, the BH distribution is steeper due to mass-segregation which leads to a higher burst rate, see Eq. (7))."," Second, the BH distribution is steeper due to mass-segregation which leads to a higher burst rate, see Eq. \ref{eq:gamma}) )." +" Note that the EMBB due to MSs is cut off at ~10? Hz, because tidal effects prohibit the existence of non-compact objects at small distances from the MBH."," Note that the EMBB due to MSs is cut off at $\sim 10^{-3}$ Hz, because tidal effects prohibit the existence of non-compact objects at small distances from the MBH." + The EMRI background is caused by BHs that spiral in to the MBH., The EMRI background is caused by BHs that spiral in to the MBH. +" These sources are excluded in our calculations by eliminating inspiral orbits, see refsec:insp.."," These sources are excluded in our calculations by eliminating inspiral orbits, see \\ref{sec:insp}." + The expression for the EMRI background was taken from Barack&Cutler(2004) and scales with the inspiral rate., The expression for the EMRI background was taken from \citet{Bar04b} and scales with the inspiral rate. + From Hopman&Alexander(2006b) we take an inspiral rate of 1x1077 yr! leading to a EMRI background at a level comparable to the instrumental noise of LISA.," From \citet{Hop06b} we take an inspiral rate of $1 +\times 10^{-7}$ $^{-1}$ leading to a EMRI background at a level comparable to the instrumental noise of LISA." + In our favoured model the EMBB is well below the instrumental noise of LISA., In our favoured model the EMBB is well below the instrumental noise of LISA. +" At closest approach the EMBB (fSaw)!? is a factor ~ 10 below the instrumental noise of LISA, and a factor ~ 19 lowerthan the confusion noise of Galactic WD binaries."," At closest approach the EMBB $(f S_{\GW})^{1/2}$ is a factor $\sim$ 10 below the instrumental noise of LISA, and a factor $\sim$ 19 lowerthan the confusion noise of Galactic WD binaries." + The EMBB is also lower than the EMRI background in, The EMBB is also lower than the EMRI background in +GRBs can happen.,GRBs can happen. + And finally the prospects for correlating such globular cluster passages and events of mass extinction are discussed., And finally the prospects for correlating such globular cluster passages and events of mass extinction are discussed. +" To determine the expected minimum distance to Earth of a GRB launched in a globular cluster in the last Gyr, first the rate of such events per globular cluster has to be constrained."," To determine the expected minimum distance to Earth of a GRB launched in a globular cluster in the last Gyr, first the rate of such events per globular cluster has to be constrained." +" The estimated rate of GRBs originating in globular clusters that are beamed towards the Earth ranges from Rgc~4 GGpcyr ! (Guetta&Stella,2009) to Rec~20 GGpc?yr! (Salvaterraetal.,2008).", The estimated rate of GRBs originating in globular clusters that are beamed towards the Earth ranges from $R_{GC} \sim 4$ $^{-3}$ $^{-1}$ \citep{guetta2009} to $R_{GC} \sim 20$ $^{-3}$ $^{-1}$ \citep{salvaterra2008}. +". Using now the density of globular clusters in the local of about 3 Mpc? (PortgiesZwart&McMillan,2000) this results in a GRB rate of ®~107?(Rgc/30Gpe“yr7!) per year per globular cluster."," Using now the density of globular clusters in the local of about 3 $^{-3}$ \citep{portegies2000} this results in a GRB rate of $\Phi \approx 10^{-8}\,(R_{GC}/30\, +\mathrm{Gpc}^{-3}\mathrm{yr}^{-1})$ per year per globular cluster." +" From this estimate the expected minimum distance d,j, for a GRB exploding in the last Gyr can be estimated.", From this estimate the expected minimum distance $d_{min}$ for a GRB exploding in the last Gyr can be estimated. + For an event rate of 10-? per year d; is given by the volume around the Earth where the probability to find a globular cluster is 1072/6=0.1x(Rgc/30Gpc?yr-!)!.," For an event rate of $^{-9}$ per year $d_{min}$ is given by the volume around the Earth where the probability to find a globular cluster is $10^{-9}/\Phi \approx 0.1 \times (R_{GC}/30\, +\mathrm{Gpc}^{-3}\mathrm{yr}^{-1})^{-1}$." + The resulting minimal distance is then given by: Here Bpac is the (assnumberyr-! density (25)kpc?of globular clusters around the Earth., The resulting minimal distance is then given by: Here $\rho_\mathrm{GC}$ is the number density of globular clusters around the Earth. +" Adopting a local number density of globular clusters of 0.006 kpc? (Djorgovski&Meylan,1994) this results in a minimum distance of about 1.6 kpc for a short GRB rate launched in globular clusters for Rgc=30Gpcγι]."," Adopting a local number density of globular clusters of 0.006 $^{-3}$ \citep{djorgovski1994} this results in a minimum distance of about 1.6 kpc for a short GRB rate launched in globular clusters for $R_{GC} = 30\, \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$." +" The dependence of dj, on the parameters Κας and pac is shown in Fig. 1..", The dependence of $d_{min}$ on the parameters $R_\mathrm{GC}$ and $\rho_\mathrm{GC}$ is shown in Fig. \ref{figure:dmin}. + For reasonable input parameters din falls between ~1-3.5 kpc., For reasonable input parameters $d_\mathrm{min}$ falls between $\sim1 - 3.5$ kpc. +" Potential terrestrial signatures generated by a nearby GRB could comprise the impact on the biota in-printed in the fossil record (seeGalante&Horvath,2007,foradiscussiononvari-oustothebiotahazardouseffectsconnectedanearby burst),, a glaciation event following reduced atmospheric transparency due to NO» production by the ionizing radiation of a GRB (Thomasetal.,2005),, anomalies of radioactive isotopes or fossil cosmic ray tracks (Daretal.,1998).."," Potential terrestrial signatures generated by a nearby GRB could comprise the impact on the biota in-printed in the fossil record \citep[see][for a discussion on various to the biota +hazardous effects connected to a nearby burst]{galante2007}, , a glaciation event following reduced atmospheric transparency due to $_2$ production by the ionizing radiation of a GRB \citep{thomas2005}, anomalies of radioactive isotopes or fossil cosmic ray tracks \citep{dar1998}." + From the expected minimal distance of a GRB launched in a globular cluster the strength of corresponding terrestrial signatures can be estimated., From the expected minimal distance of a GRB launched in a globular cluster the strength of corresponding terrestrial signatures can be estimated. +" Depletion of the ozone-layer has been found to be an important consequence of a nearby GRB explosion for the biota (Thorsett,1995;Thomasetal.,2005)."," Depletion of the ozone-layer has been found to be an important consequence of a nearby GRB explosion for the biota \citep{thorsett1995,thomas2005}." +. The level of depletion of the ozone-layer will depend on the fluence of X-rays and soft gamma-rays from the GRB., The level of depletion of the ozone-layer will depend on the fluence of X-rays and soft gamma-rays from the GRB. +" If the mean isotropic gamma-ray luminosity Eyjs36.5x1050 erg found for short bursts by Swift--BAT (Racusinetal.,2011) is adopted this results in a fluence of 6Χ106 erg cm” at a distance of 1 kpc."," If the mean isotropic gamma-ray luminosity $E_\mathrm{\gamma,iso} \approx 6.5 \times 10^{50}$ erg found for short bursts by -BAT \citep{racusin2011} is adopted this results in a fluence of $6 \times 10^{6}$ erg $^{-2}$ at a distance of 1 kpc." +" In comparison to that value, Galante&Horvath(2007) estimated the critical fluence of a GRB to destroy the ozone layer on a level where damages on the biota will occur to 3x106 erg cm""? and also Thomasetal.(2005) found significant ozone depletion for the case of 107 erg cm?."," In comparison to that value, \citet{galante2007} estimated the critical fluence of a GRB to destroy the ozone layer on a level where damages on the biota will occur to $3 \times 10^{6}$ erg $^{-2}$ and also \cite{thomas2005} + found significant ozone depletion for the case of $10^7$ erg $^{-2}$." + Consequently its possible that a short GRB at a distance of up to 1.5 kpc will have an effect on the biota., Consequently its possible that a short GRB at a distance of up to 1.5 kpc will have an effect on the biota. +" To conclude, for advantageous estimates for the GRB rate in globular clusters it appears possible that the closest such event has left terrestrial signatures in form of an extinction event that is in-printed in the fossil record."," To conclude, for advantageous estimates for the GRB rate in globular clusters it appears possible that the closest such event has left terrestrial signatures in form of an extinction event that is in-printed in the fossil record." +" One example for potentially measurable signatures are radioactive nuclei produced by either the enhanced cosmic ray flux (Daretal,1998) or by high energy gamma-ray photons (Thorsett,1995) connected to the GRB.", One example for potentially measurable signatures are radioactive nuclei produced by either the enhanced cosmic ray flux \citep{dar1998} or by high energy gamma-ray photons \citep{thorsett1995} connected to the GRB. +" Ultra-relativistic shock waves are expected to convert most of their kinetic energy into cosmic rays (Atoyanetal.,2006).", Ultra-relativistic shock waves are expected to convert most of their kinetic energy into cosmic rays \citep{atoyan2006}. +". Following this argument by assuming that the mean kinetic energy estimated for short bursts with Swift--BAT of 2.5x10?? erg (Racusinetal,2011) is converted into cosmic rays and that the cosmic ray jet is still collimated at a distance of 1 kpc this will result in a cosmic ray fluence of 2x10? erg cm? at this distance.", Following this argument by assuming that the mean kinetic energy estimated for short bursts with -BAT of $2.5 \times 10^{52}$ erg \citep{racusin2011} is converted into cosmic rays and that the cosmic ray jet is still collimated at a distance of 1 kpc this will result in a cosmic ray fluence of $2 \times 10^8$ erg $^{-2}$ at this distance. + This corresponds to the integrated energy deposition of galactic cosmic rays for about 100 years., This corresponds to the integrated energy deposition of galactic cosmic rays for about 100 years. + Thus cosmic rays produced by the GRB can in principle create an anomaly of radioactive nuclei., Thus cosmic rays produced by the GRB can in principle create an anomaly of radioactive nuclei. +" However, since terrestrial rocks are typically exposed to cosmic rays much longer than 100 years its quite unlikely that cosmic rays connectedto a GRB will leave measurable traces in form of radioactive isotopes in the geological record."," However, since terrestrial rocks are typically exposed to cosmic rays much longer than 100 years its quite unlikely that cosmic rays connectedto a GRB will leave measurable traces in form of radioactive isotopes in the geological record." +In this paper we add. the effect. of a possible random wimordial magnetic field. as another important. source of ambient pressure.,In this paper we add the effect of a possible random primordial magnetic field as another important source of ambient pressure. + Phe magnetic field contributes to pressure support. which changes the Jeans mass and. consequently. he filtering mass and the quantity of eas that is accreted »w DM halos.," The magnetic field contributes to pressure support, which changes the Jeans mass and, consequently, the filtering mass and the quantity of gas that is accreted by DM halos." + The paper is organized as follows., The paper is organized as follows. + In section 2. we make a short review on the possible origins of primordial magnetic ields. in section ??7 we analvze the effect. of. primordial magnetic fields on the Jeans and filtering masses anc in section ?? we calculate ellects on the barvon mass fraction.," In section \ref{sec:magnetic} we make a short review on the possible origins of primordial magnetic fields, in section \ref{sec:filtering} we analyze the effect of primordial magnetic fields on the Jeans and filtering masses and in section \ref{sec:gas} we calculate effects on the baryon mass fraction." + In section ?? we give our conclusions., In section \ref{sec:conc} we give our conclusions. + The origin of large-scale cosmic magnetic fields in galaxies and. protogalaxies remains a challenging problem in astrophysics (Zweibel&Leiles1997:Ixulsrud.ZweibclWidrow2002:Laganáetal.," The origin of large-scale cosmic magnetic fields in galaxies and protogalaxies remains a challenging problem in astrophysics \citep{Zweibel1997, Kulsrud2008, Souza2008, souza10,Souza2010, Widrow2002,lagana}." + 2010). Understanding the origin of the structures of the present Universe requires a knowledge of the origin of magnetic fields., Understanding the origin of the structures of the present Universe requires a knowledge of the origin of magnetic fields. + The magnetic Giclds fll. interstellar and. intracluster space anc alfect the evolution of galaxies and galaxy clusters., The magnetic fields fill interstellar and intracluster space and affect the evolution of galaxies and galaxy clusters. + There. have been many attempts to explain the origin of cosmic magnetic fields., There have been many attempts to explain the origin of cosmic magnetic fields. + One of the most popular astrophysical theories. for creating seed primordial fields is that they were generated by the Biermann mechanism (Biermann 1950)., One of the most popular astrophysical theories for creating seed primordial fields is that they were generated by the Biermann mechanism \citep{Biermann1950}. +. It has been suggested that this mechanism acts in diverse astrophysical svstems. such as large scale structure formation (Peebles1967:Rees&DIeinhardt19Wasser-man 1978). protogalaxies (Davies& Widrow2000).. cosmological ionizing fronts (Cinedin2000).. star formation and supernova explosions (Llanavamactal.2005:Mi-randaetal. 1998).," It has been suggested that this mechanism acts in diverse astrophysical systems, such as large scale structure formation \citep{Peebles1967, Rees1972, Wasserman1978}, protogalaxies \citep{Davies00}, cosmological ionizing fronts \citep{Gnedin2000a}, star formation and supernova explosions \citep{Hanayama2005, Miranda1998}." +. Another mechanism for creating cosmic/ magnetic fields was suggested by Ichikictal.(2006)., Another mechanism for creating cosmic magnetic fields was suggested by \citet{Ichiki2006}. +. They investigated the seconc-order couplings between photons and electrons. as a possible origin. of magnetic fields. on cosmological scales. before. the epoch of recombination., They investigated the second-order couplings between photons and electrons as a possible origin of magnetic fields on cosmological scales before the epoch of recombination. + Studies of magnetic field ecneration. based on cosmological perturbations. have also been mace (Takahashietal.2005.2006:Clarkeetal.2001:Maecda 2009).," Studies of magnetic field generation, based on cosmological perturbations, have also been made \citep{Takahashi2005, Takahashi2006, Clarke2001, Maeda2009}." +. In our galaxy. the magnetic field is coherent over kpe scales with alternating directions in the arm and inter-arni regions (e.g... Ixronberg1994:Han 2008)).," In our galaxy, the magnetic field is coherent over kpc scales with alternating directions in the arm and inter-arm regions (e.g., \citealt{Kronberg1994, han08}) )." + Such alternations are expected for magnetic fields of primordial origin (Cirasso&Rubinstein 2001)., Such alternations are expected for magnetic fields of primordial origin \citep{Grasso2001}. +. Various observations put upper limits on the intensity of a homogeneous primordial magnetic field., Various observations put upper limits on the intensity of a homogeneous primordial magnetic field. + Observations of the small-seale cosmic microwave background. (CMD) anisotropy. vield an upper comoving limit of 2.98nG. for a homogeneous primordial field (Yamazakietal.2010)., Observations of the small-scale cosmic microwave background (CMB) anisotropy yield an upper comoving limit of $2.98\nG$ for a homogeneous primordial field \citep{Yamazaki2010}. +. Reionization of the Universe puts upper limits of ~0.73nG for a homogeneous primordial field. depending on the assumptions of the stellar population that is responsible for reionizing the Universe (Schleicheretal.2008).," Reionization of the Universe puts upper limits of $\sim 0.7-3 \nG$ for a homogeneous primordial field, depending on the assumptions of the stellar population that is responsible for reionizing the Universe \citep{Schleicher2008}." +. deSouza&Όρμος(2008):Opher(2010h) suggested. that the fluctuations of the plasma. predicted by the Fluctuation Dissipation Theorem. after the quark-hadron transition (QUT). is à natural source for a present primordial magnetic field.," \citet{Souza2008,Souza2010} suggested that the fluctuations of the plasma predicted by the Fluctuation Dissipation Theorem, after the quark-hadron transition (QHT), is a natural source for a present primordial magnetic field." + Phe evolved. the fluctuations after the QUT to the present craancl prediet a present cosmic web of random primorcial magnetic fields., They evolved the fluctuations after the QHT to the present eraand predict a present cosmic web of random primordial magnetic fields. +" “Phe average magnetic field. predicted by them over a region of size Lis D—9pG(0.1pezLy?7,", The average magnetic field predicted by them over a region of size $L$ is $B = 9 \muG ~(0.1 \text{ pc}/L)^{3/2}$. + An average magnetic eld 0.003nG over a 2 kpe region at 210 is. thus. predicted.," An average magnetic field $0.003\nG$ over a $2$ kpc region at $\emph{z} \sim 10$ is, thus, predicted." + Following the procedure of a previous work (Itodriguesotal.2OLO).. which studied the ellects of a homogeneous primordial magnetic field. we study here the influcnce of random inhomogeneous primordial magnetic fields (IPME) on the filtering mass My.," Following the procedure of a previous work \citep{Rodrigues2010}, which studied the effects of a homogeneous primordial magnetic field, we study here the influence of random inhomogeneous primordial magnetic fields (RPMF) on the filtering mass $M_F$." + This quantity describes the highest DAL mass scale for which the baryon accretion is suppressed significantly. as we will cliscuss below.," This quantity describes the highest DM mass scale for which the baryon accretion is suppressed significantly, as we will discuss below." +" First. we celine the filtering scale (ποσα&Hui1998) as the characteristic length scale over which the baryonic perturbations are smoothed out as compared to the dark matter ones as where o, is the density contrast of barvonic matter and or. the total density contrast."," First, we define the filtering scale \citep{Gnedin1997} as the characteristic length scale over which the baryonic perturbations are smoothed out as compared to the dark matter ones as where $\delta_b$ is the density contrast of baryonic matter and $\delta_{tot}$, the total density contrast." +" For & comparable to Ay. the density contrast à, is severely depressed."," For $k$ comparable to $k_F$, the density contrast $\delta_b$ is severely depressed." + As was shown by Cinedin.(2000)... we can relate the comoving wavenumber associated with this length scale with the Jeans wavenumber by the equation where a [lat matter dominated universe is assumed.," As was shown by \citet{Gnedin2000a}, we can relate the comoving wavenumber associated with this length scale with the Jeans wavenumber by the equation where a flat matter dominated universe is assumed." + One finds that the overall suppression of the growth of baryonic density perturbations depends on a time-average of the Jeans scale., One finds that the overall suppression of the growth of baryonic density perturbations depends on a time-average of the Jeans scale. + By translating the length scales into mass scales. we can then define the Jeans mass and filtering mass. From equations (3)) and (2)). we can write. where p is the mean matter density.," By translating the length scales into mass scales, we can then define the Jeans mass and filtering mass, From equations \ref{eq:MJMF}) ) and \ref{eq:kj}) ), we can write, where $\bar \rho$ is the mean matter density." + The commonly used. Jeans mass. with negligible magnetic fields. is the mass when the gravitational pressure at the surface of a sphere of radius A; balances the thermal oessure.," The commonly used Jeans mass, with negligible magnetic fields, is the mass when the gravitational pressure at the surface of a sphere of radius $R_J$ balances the thermal pressure." + An adiabatic compression. of the sphere by a change in radius 94? increases the thermal pressure above he gravitational pressure. causing the sphere to increase its radius and oscillate about the equilibrium value 77?;.," An adiabatic compression of the sphere by a change in radius $\delta R$ increases the thermal pressure above the gravitational pressure, causing the sphere to increase its radius and oscillate about the equilibrium value $R_J$ ." + When the thermal pressure is negligible anc we only ve random magnetic fields in the sphere. the definition of the Jeans mass is similar.," When the thermal pressure is negligible and we only have random magnetic fields in the sphere, the definition of the Jeans mass is similar." + Lt is the mass when the magnetic pressure at the surface balances the gravitational oessure., It is the mass when the magnetic pressure at the surface balances the gravitational pressure. + An adiabatic compression of the sphere of radius, An adiabatic compression of the sphere of radius + mass. t," \citep[e.g.,][]{strateva2001,baldry2004}. \citep[e.g.,][and several others]{bell2004b,faber2007,brown2007}. \citep[e.g.,][]{maller2009}." +herefore results iu a selection of both quiesceut ealaxies reddened SECs.," mass, therefore results in a selection of both quiescent galaxies reddened SFGs." + This preseuts a predicament for studies that use such a selection in order to quantity the evolution in the uunuber of passive svstenis., This presents a predicament for studies that use such a selection in order to quantify the evolution in the number of passive systems. +" Tn this Letter. we lighheht the utility of a color-color diaeram. specifically rest-frame CV vs, WF (hereafter referred to as the CV. diagrain). iu distiuguishiug quiescent galaxies from SEC. iuchudiug those SEC that are heavily reddened."," In this Letter, we highlight the utility of a color-color diagram, specifically rest-frame $U-V$ vs. $V-J$ (hereafter referred to as the $UVJ$ diagram), in distinguishing quiescent galaxies from SFGs, including those SFGs that are heavily reddened." + The CV. diagram is σαιο Increasing visibility in studies of galaxy evolution (6.8... 2011)..," The $UVJ$ diagram is gaining increasing visibility in studies of galaxy evolution \citep[e.g.,][]{labbe2005,wuyts2007,williams2009,brammer2009,williams2010,whitaker2010,patel2011,quadri2011,brammer2011}." + In Pateletal.(2011) we hiuted at the possibility of the (WT selection of quiescent aud SFCs being used to also distinguish morphologically carly aud late-type systems., In \citet{patel2011} we hinted at the possibility of the $UVJ$ selection of quiescent and SFGs being used to also distinguish morphologically early and late-type systems. + Hore we iutroduce for the first time iu analysis based onLST ACS imagine aud examine the structural properties of galaxics m CV color space in order to address the prospects of using two rest-frame colors iu classifving both the recent SFUs and morphologies of ealaxies., Here we introduce for the first time an analysis based on ACS imaging and examine the structural properties of galaxies in $UVJ$ color space in order to address the prospects of using two rest-frame colors in classifying both the recent SFHs and morphologies of galaxies. + We use a stellar miass-linited sample of galaxies at tto carry out our analvsis., We use a stellar mass-limited sample of galaxies at to carry out our analysis. + As is well known. many galaxy properties correlate with stellar mass aud it is therefore crucial that one control for stellar mass in interpreting results.," As is well known, many galaxy properties correlate with stellar mass and it is therefore crucial that one control for stellar mass in interpreting results." + The redshift range examined here provides a suitable case study for a saauple of ealaxies in the distant universe., The redshift range examined here provides a suitable case study for a sample of galaxies in the distant universe. + The rest-frame J-band magnitudes at these redshifts represent observed A. which is typically the reddest bandpass accessible frou the erouud for deep wide-field galaxy surveys.," The rest-frame $J$ -band magnitudes at these redshifts represent observed $K_s$, which is typically the reddest bandpass accessible from the ground for deep wide-field galaxy surveys." + We asstume a cosnoloev with ZZ=rüns," We assume a cosmology with $H_0=70$ ," +probability cüstribution.,probability distribution. + The number of steps required. for the chain convergence scales linearly with the number of dimensions of the parameter space: typically 107 steps are required for reliable convergence., The number of steps required for the chain convergence scales linearly with the number of dimensions of the parameter space; typically $\times 10^4$ steps are required for reliable convergence. + In this paper we use the Metropolis. (?) algorithm for generating the chain. which can be used with an arbitrary distribution. the proposal distribution. for generating new locations of the chain.," In this paper we use the Metropolis \citep{Newman} algorithm for generating the chain, which can be used with an arbitrary distribution, the proposal distribution, for generating new locations of the chain." + We use a Gaussian. proposal distribution. centred at the current. location in the parameter space.," We use a Gaussian proposal distribution, centred at the current location in the parameter space." + During an initial period. the burn-in period. the width of the proposal distribution in all dimensional directions is set to vield the asvimptoticallv optimal acceptance rate of 23.4% for the Metropolis algorithm (?)..," During an initial period, the burn-in period, the width of the proposal distribution in all dimensional directions is set to yield the asymptotically optimal acceptance rate of $23.4\%$ for the Metropolis algorithm \citep{Roberts}." + At the end of the AMICAIC simulation we check the convergence of the chain using the bootstrap method. (2).., At the end of the MCMC simulation we check the convergence of the chain using the bootstrap method \citep{Efron}. + We also calculate. the global maximum likelihood value for all parameters. using a conjugate directions search (?).., We also calculate the global maximum likelihood value for all parameters using a conjugate directions search \citep{Brent}. + The greatest. computational challenge in constructing the chain is the [fast evaluation of the matrix 6) in Eqs. (18))& ((19))., The greatest computational challenge in constructing the chain is the fast evaluation of the matrix $C^{-1}$ in Eqs. \ref{premoved}) \ref{C'}) ). + Lf 250 timing-residuals are measured. for each of the pulsars (50 weeks lor 5 wears). the sizeof he matrix €' becomes (5000 5000).," If $250$ timing-residuals are measured for each of the pulsars (50 weeks for 5 years), the sizeof the matrix $C$ becomes $(5000\times 5000)$ ." + We find. it takes about 20 seconds to invert €' and thus about 1.5 times as much to arrive to the next point in the chain., We find it takes about $20$ seconds to invert $C$ and thus about $1.5$ times as much to arrive to the next point in the chain. + TPherefore. or the required 10 chain »oints to get the convergent distribution. we need of order l month of the single-processor computational time.," Therefore, for the required $~10^5$ chain points to get the convergent distribution, we need of order $~1$ month of the single-processor computational time." + On a cluster this can be done in a couple of days., On a cluster this can be done in a couple of days. + We emphasize that this is an order n°? oocess., We emphasize that this is an order $n^3$ process. + For matrices of (20002000) the calculation can ο done overnight on a single modern workstation. but. for (107107) the caleulation is already a serious challenge.," For matrices of $(2000\times 2000)$ the calculation can be done overnight on a single modern workstation, but for $(10^4\times 10^4)$ the calculation is already a serious challenge." + For the currently projected size of the datasets (2). the amount of timine-resicuals will most likely not exceed. the 250 (Llobbs. private communications).," For the currently projected size of the datasets \citep{Manchester}, the amount of timing-residuals will most likely not exceed the $250$ (Hobbs, private communications)." + Thus. the brute-force method presented here is not computationally expensive for the projected data volume over the next 5 vears.," Thus, the brute-force method presented here is not computationally expensive for the projected data volume over the next 5 years." + For some mocdels (e.g. the power law spectal density or pulsar timing nolse) the likelihood function proves o be not normalisable., For some models (e.g. the power law spectal density for pulsar timing noise) the likelihood function proves to be not normalisable. + This would. pose a serious woblem in combination with uniform priors as the nuisance parameters then cannot be marginalised and he posterior cannot represent a probability distribution., This would pose a serious problem in combination with uniform priors as the nuisance parameters then cannot be marginalised and the posterior cannot represent a probability distribution. + Although this is à sign that our model is incorrect (infinite Bavesian Evidence/normalisation). this can be easily solved with a cdillerent. parameterisation.," Although this is a sign that our model is incorrect (infinite Bayesian Evidence/normalisation), this can be easily solved with a different parameterisation." + We can always change coordinates in parameter space to a set for which all xuwameters have a finite domain. which guarantees. that our likelihood function is normalisable.," We can always change coordinates in parameter space to a set for which all parameters have a finite domain, which guarantees that our likelihood function is normalisable." + This procedure. is equivalent to choosing a dilferent. prior (the Jacobian in the case of à coordinate transformation) for the original set., This procedure is equivalent to choosing a different prior (the Jacobian in the case of a coordinate transformation) for the original set. + We therefore argue that we need to choose an appropriate prior for the non-normalisable parameters., We therefore argue that we need to choose an appropriate prior for the non-normalisable parameters. + We propose to use a Lorentzian shaped profile: where 5; is the parameter for which we are construction a prior. and AA; is some typical width/value for this τω.," We propose to use a Lorentzian shaped profile: where $\gamma_i$ is the parameter for which we are construction a prior, and $\Delta_i$ is some typical width/value for this parameter." + As an example we show the likelihood function andthe xior for the pulsar timing noise spectral index parameter of Eq. (13)), As an example we show the likelihood function andthe prior for the pulsar timing noise spectral index parameter of Eq. \ref{eq:CPN-power}) ) + in Fig. 1.., in Fig. \ref{fig:likelihood-prior}. + The likelihood function seems to drop o zero for high ο. but it actually has a non-negligible value or all 5; greater than the maximum likelihood value.," The likelihood function seems to drop to zero for high $\gamma_i$, but it actually has a non-negligible value for all $\gamma_i$ greater than the maximum likelihood value." + The oadness of the prior is chosen such that it does not change he representation of the significant. part of the likelihood in he posterior. but it does make sure that the posterior. is normalisable.," The broadness of the prior is chosen such that it does not change the representation of the significant part of the likelihood in the posterior, but it does make sure that the posterior is normalisable." + In order to generate mock data. we produce a realization of the multi dimensional Gaussian process of Ίσα. (5)).," In order to generate mock data, we produce a realization of the multi dimensional Gaussian process of Eq. \ref{eq:gaussian}) )," + as follows., as follows. + We rewrite Eq. (5)), We rewrite Eq. \ref{eq:gaussian}) ) + is a basis inwhich €' is diagonal: where. Llere A; are the eigenvalues of C. and whereZ is. the transformation matrix which diagonalizes C* Thus we follow the following (1) Diagonalize matrix C'. fined 1 and A;. (2) Choose gy; from random gaussian distributions of widths VA. ," is a basis inwhich $C$ is diagonal: where, Here $\lambda_i$ are the eigenvalues of $C$ , and where$T$ is the transformation matrix which diagonalizes $C$ : Thus we follow the following (1) Diagonalize matrix $C$ , find $T$ and $\lambda_i$ (2) Choose $y_i$ from random gaussian distributions of widths $\sqrt{\lambda_i}$ " +65 degrees of Ereedom (ο).,65 degrees of freedom (dof). + Phe most significant deviation rom the constant model is clearly the 11A1549 resonance emission line doublet., The most significant deviation from the constant model is clearly the $\lambda 1549$ resonance emission line doublet. + Modeling this with a Gaussian profile cads to a highly significant improvements in the goodness of it GNA?=35 for 3 additional dof)., Modeling this with a Gaussian profile leads to a highly significant improvements in the goodness of fit $\Delta\chi^2=35$ for 3 additional dof). + The inferred. properties of this line are reported in Table. 1., The inferred properties of this line are reported in Table 1. +" The CivA1549 line appears to be significantly broader than the Ho line. and ras à E'WILM comparable with the ""verv-broad component of the Lhe tine."," The $\lambda 1549$ line appears to be significantly broader than the $\alpha$ line, and has a FWHM comparable with the `very-broad' component of the $\beta$ line." + The line is also. blueshiftec by ~3000kas with respect to the broad. Balmer lines., The line is also blueshifted by $\sim 3000\kmps$ with respect to the broad Balmer lines. + This appears to be a generic feature of high-ionization lines from AGN (e.g. see Espey et al., This appears to be a generic feature of high-ionization lines from AGN (e.g. see Espey et al. + 1989)., 1989). + This has been interpreted by some authors as evidence for a two-component BLIt (e.g. Collin-SoulIrin et al., This has been interpreted by some authors as evidence for a two-component BLR (e.g. Collin-Souffrin et al. + LOSS)., 1988). + There may also be an absorption trough to the blueside of the 1A1549 lines., There may also be an absorption trough to the blueside of the $\lambda 1549$ lines. +" Modeling this with a Gaussian profile leads to a further improvement in the goodness of fit bv AND=12 for 3 additional dol,", Modeling this with a Gaussian profile leads to a further improvement in the goodness of fit by $\Delta\chi^2=12$ for 3 additional dof. + According to the F-test. this is not a significant improvement at the 90 per cent level.," According to the F-test, this is not a significant improvement at the 90 per cent level." + Thus. we cannot conclusively determine the reality of this feature and shall not discuss it further.," Thus, we cannot conclusively determine the reality of this feature and shall not discuss it further." + Formally. the best fit continuum level is £wp=(lt10oreenτς5τα1 .," Formally, the best fit continuum level is $F_{\rm SWP}=(1.1\pm 0.2)\times +10^{-15}\ergpcmsqps\AA^{-1}$ ." + dt ds possible that much of this UV. continuum could. be stellar in origin., It is possible that much of this UV continuum could be stellar in origin. + Thus. this value should be considered only as an upper limit to the UV continuum [lux from the AGN.," Thus, this value should be considered only as an upper limit to the UV continuum flux from the AGN." + LHigh-resolution. UV. imaging with UST will allow the stellar UV. flux to be almost completely separated from the ACGN UV Iux. thereby allowing these two components to be separated.," High-resolution UV imaging with HST will allow the stellar UV flux to be almost completely separated from the AGN UV flux, thereby allowing these two components to be separated." + At the time of writing. such UY imaging has vet to be performed.," At the time of writing, such UV imaging has yet to be performed." + ‘To make this study genuinely multi-waveband in nature. we have supplemented the above new spectra will previously published data.," To make this study genuinely multi-waveband in nature, we have supplemented the above new spectra will previously published data." + Phe remainder of this section will introduce these data., The remainder of this section will introduce these data. + Alid/far infrared (AILRPIR) data were obtained from the (RAS) Faint Source Catalogue (version 2.0) at four wavelengths (12jim. 25 jim. GOjm and LOO yim.)," Mid/far infrared (MIR/FIR) data were obtained from the (IRAS) Faint Source Catalogue (version 2.0) at four wavelengths $12\,\mu{\rm m}$, $25\,\mu{\rm m}$ , $60\,\mu{\rm m}$ and $100\,\mu{\rm m}$ .)" + Cüuricin. Alarcelirossian Mezzetti. (1995). [ind good agreementbetween the LRAS12μαι flux. and the," Giuricin, Marddirossian Mezzetti (1995) find good agreementbetween the IRAS$12\,\mu{\rm m}$ flux and the" +ol the bulge implies a higher effective value of AY/AZ due to two clistinet cases.,of the bulge implies a higher effective value of ${\Delta}Y/{\Delta}Z$ due to two distinct causes. + As the duration of star formation increases. lower-mass AGB ejecta. which are less Ie-enriched. will contribute relatively more to the chemical evolution budget than those of higher mass AGB+WERAIS ejecta.," As the duration of star formation increases, lower-mass AGB ejecta, which are less He-enriched, will contribute relatively more to the chemical evolution budget than those of higher mass AGB+WFRMS ejecta." + Second. late-time Type la SNe. explosions that contribute a lot of metals but no helium. will begin to eo off.," Second, late-time Type Ia SNe, explosions that contribute a lot of metals but no helium, will begin to go off." + Figure 1 of Catelan(2007) implies ¥Y0.31 αἱ Fe/I]=0 for a population with an a-enhancement similar to the bulge., Figure 1 of \citet{2007arXiv0708.2445C} implies $\approx$ 0.31 at $=$ 0 for a population with an $\alpha$ -enhancement similar to the bulge. + This is midway between standard isochrones values and the estimate of Nataletal.(2011d).., This is midway between standard isochrones values and the estimate of \citet{2011arXiv1109.2118N}. + We note that there has been some skepticism regarding WERAIS as (he source of GC helium because {μον enrich metals as well as helium. aud because GCs have a weak gravitational potential well that may not hold on to these ejecta.," We note that there has been some skepticism regarding WFRMS as the source of GC helium because they enrich metals as well as helium, and because GCs have a weak gravitational potential well that may not hold on to these ejecta." + Neither of those concerns apply to the bulge., Neither of those concerns apply to the bulge. + The abundances from Bensbyοἱal.(2011) suggest that the sodium-oxvgen anti-correlation seen in GCs and thought to trace high-mass AGB and/or WERMS ejecta. is present in metal-rich bulge stars and trends [Fe/1l].," The abundances from \citet{2011A&A...533A.134B} suggest that the sodium-oxygen anti-correlation seen in GCs and thought to trace high-mass AGB and/or WFRMS ejecta, is present in metal-rich bulge stars and trends [Fe/H]." + We reler to a new class of models (Chungetal.2011:Bekki2012). motivated by the need (o explain the UV-upturn of old bulges and ellipticals. which are best explained by the presence of blue horizontal branch stars.," We refer to a new class of models \citep{2011ApJ...740L..45C,2012ApJ...747...78B} motivated by the need to explain the UV-upturn of old bulges and ellipticals, which are best explained by the presence of blue horizontal branch stars." + Chungetal.(2011) and Bekki(2012) both posit imperfect mixing between AGB and SNe ejecta. thereby having stars form directly from the eas of helium-rieh. AGB ejecta without dilution from SNe ejecta.," \citet{2011ApJ...740L..45C} and \citet{2012ApJ...747...78B} both posit imperfect mixing between AGB and SNe ejecta, thereby having stars form directly from the gas of helium-rich AGB ejecta without dilution from SNe ejecta." + If this process occured in other spheroids. it likely also occured in (he bulge. aud vice versa.," If this process occured in other spheroids, it likely also occured in the bulge, and vice versa." + These models also make the testable prediction that there shoulel be a large helium spread at fixed metallicity., These models also make the testable prediction that there should be a large helium spread at fixed metallicity. + There is another effect that may be al play: helium sedimentation., There is another effect that may be at play: helium sedimentation. + Simulations of hot eas in galaxy clusters by Chuzhov&Loeb(2004) predict that helium prelerentially accretes onto cluster cores. as: They argue that values of AYzz0.12 can be reached by cD galaxies. which could explain the UV upturn of these galaxies by creating more extreme blue IB stars.," Simulations of hot gas in galaxy clusters by \citet{2004MNRAS.349L..13C} predict that helium preferentially accretes onto cluster cores, as: They argue that values of ${\Delta}Y\approx0.12$ can be reached by cD galaxies, which could explain the UV upturn of these galaxies by creating more extreme blue HB stars." + While the effect in the bulge should be much smaller. it still may contribute to helium enhancement.," While the effect in the bulge should be much smaller, it still may contribute to helium enhancement." +Our IDL code implementing this procedure is availableonline!!.,Our IDL code implementing this procedure is available. +. It requires the aat midexposure and target coordinates (0. 0) in 12000 as inputs.," It requires the at midexposure and target coordinates $\alpha$ , $\delta$ ) in J2000 as inputs." + We outline its procedure here., We outline its procedure here. + More explicit details. as well as the calling procedure and dependencies. are commented inside the code.," More explicit details, as well as the calling procedure and dependencies, are commented inside the code." + We compute Ac using Craig Markwardts to read the leap second table. and his program to compute the TT-TDB correction. which uses a 79]-term Fairhead and Bretagnon analytical approximation to the full numerical integration. with an error of 23 ns (Fairhead&Bretagnon 1990).," We compute $\Delta_{C}$ using Craig Markwardt's to read the leap second table, and his program to compute the TT-TDB correction, which uses a 791-term Fairhead and Bretagnon analytical approximation to the full numerical integration, with an error of 23 ns \citep{fairhead90}." +. Our code will automatically update its leap second table the first time it runs after every January 1 or July 1. but this requires a periodic Internet connection and the use of the program.," Our code will automatically update its leap second table the first time it runs after every January 1 or July 1, but this requires a periodic Internet connection and the use of the program." + [t will terminate on failure to update. but this protection can be bypassed for those that elect to (or have to) update their table by hand.," It will terminate on failure to update, but this protection can be bypassed for those that elect to (or have to) update their table by hand." + By default. we ignore the ~ 30j/s TT(BIPM) - TTCTAD correction. which would require a constant. Internet connection. would not apply to data acquired 1n the previous month. and is likely negligible for most applications.," By default, we ignore the $\sim30 \mu$ s TT(BIPM) - TT(TAI) correction, which would require a constant Internet connection, would not apply to data acquired in the previous month, and is likely negligible for most applications." + However. our code can optionally correct. for it rf an up-to-date file is supplied.," However, our code can optionally correct for it if an up-to-date file is supplied." + To read and interpolate the ephemeris from JPL. we use Craig Markwardt’s routines and for the Earth. Sun. and other planets.," To read and interpolate the ephemeris from JPL, we use Craig Markwardt's routines and for the Earth, Sun, and other planets." + If the observing station is space-borne. the smaller ephemeris used with those programs does not include satellites. so we use an Expect script to automate a telnet session to the HORIZONS system and automatically retrieve the ephemeris. which we quadratically interpolate to the desired times using IDEsINTERPOL.," If the observing station is space-borne, the smaller ephemeris used with those programs does not include satellites, so we use an Expect script to automate a telnet session to the HORIZONS system and automatically retrieve the ephemeris, which we quadratically interpolate to the desired times using IDL's." + The accuracy of this interpolation depends on how quickly the object’s position is changing and the step size of the ephemeris., The accuracy of this interpolation depends on how quickly the object's position is changing and the step size of the ephemeris. + HORIZONS can only return ~90.000 data points per query. so the smallest step size (1 minute) limits the calculation to a range of 60 days.," HORIZONS can only return $\sim90,000$ data points per query, so the smallest step size (1 minute) limits the calculation to a range of 60 days." + For the geocenter. a 100 minute step size is sufficient for 60 ns accuracy. but. for example. a 2 minute step size is required for I ας accuracy for theEST (though it is still limited by its clock accuracy).," For the geocenter, a 100 minute step size is sufficient for 60 ns accuracy, but, for example, a 2 minute step size is required for 1 $\mu$ s accuracy for the (though it is still limited by its clock accuracy)." + We have found that a 10 minute step size is adequate for 1 ms timing for most objects and allows a range of nearly 2 vr., We have found that a 10 minute step size is adequate for 1 ms timing for most objects and allows a range of nearly 2 yr. + If the observer is on the Earth. and the coordinates (latitude. longitude. and elevation) are given. we correct for the additional delay.," If the observer is on the Earth, and the coordinates (latitude, longitude, and elevation) are given, we correct for the additional delay." + If no observer-specific information is given. we assume the observer is at the geocenter. and the result will be biased by ~10 ms (Fig. 5)).," If no observer-specific information is given, we assume the observer is at the geocenter, and the result will be biased by $\sim10$ ms (Fig. \ref{fig:geocenter}) )." +" If the target’s ephemeris can be returned by HORIZONS and its unique name is given. we use our Expect script to generate its ephemeris too. and calculate the exact A,.. (eq. [7]])."," If the target's ephemeris can be returned by HORIZONS and its unique name is given, we use our Expect script to generate its ephemeris too, and calculate the exact $\Delta_{R\odot}$ (eq. \ref{eq:exactroemer}] ])." + If not. and instead the distance Is given. we use the two- approximation to the spherical wave solution (eq. [8]]).," If not, and instead the distance is given, we use the two-term approximation to the spherical wave solution (eq. \ref{eq:roemercorr}] ])." + Otherwise. we use the plane wave approximation (eq. [2]]).," Otherwise, we use the plane wave approximation (eq. \ref{eq:roemer}] ])." + Lastly. we include the Shapiro correction and the additional Einstein correction due to the position of the observer with respect to the geocenter. either from the surface of the Earth (if given the coordinates). or the spacecraft.," Lastly, we include the Shapiro correction and the additional Einstein correction due to the position of the observer with respect to the geocenter, either from the surface of the Earth (if given the coordinates), or the spacecraft." + In the geocentric case. our code agrees with to 200 ns (peak to peak) and the authors of BARYCEN report that their code agrees with to | js. The ephemeris we generate for a location on the surface of the Earth agrees with HORIZONS to 20 nano-It-s. and the geocentric BJDs we calculate from HORIZONS ephemeris agree with the BJDs we calculate using Craig Markwardt's routines within 10 ns.," In the geocentric case, our code agrees with to 200 ns (peak to peak) and the authors of BARYCEN report that their code agrees with to 1 $\mu$ s. The ephemeris we generate for a location on the surface of the Earth agrees with HORIZONS to 20 nano-lt-s, and the geocentric BJDs we calculate from HORIZONS ephemeris agree with the BJDs we calculate using Craig Markwardt's routines within 10 ns." + The near-exact agreements between these methods is not surprising. and do not necessarily indicate that they are accurate to better than | js. Our code was inspired byEARYCEN and both rely on Craig Markwardt’s routines (the difference comes from the fact that we index the JPL ephemeris with instead of JD44). and all methods use JPL’s DE405 ephemerts.," The near-exact agreements between these methods is not surprising, and do not necessarily indicate that they are accurate to better than 1 $\mu$ s. Our code was inspired by and both rely on Craig Markwardt's routines (the difference comes from the fact that we index the JPL ephemeris with instead of ), and all methods use JPL's DE405 ephemeris." + The primary advantage of our code is that it includes the tto ecorrection (but can optionally ignore it)., The primary advantage of our code is that it includes the to correction (but can optionally ignore it). + The choice of starting with is a departure from what is typically done with such time stamp calculators. but we feel this is a far more robust starting point.," The choice of starting with is a departure from what is typically done with such time stamp calculators, but we feel this is a far more robust starting point." + The current confusion has shown that many assume aas the starting point. which ts likely due to a lack of explicitness in the programs and/or unfamiliarity with various time standards.," The current confusion has shown that many assume as the starting point, which is likely due to a lack of explicitness in the programs and/or unfamiliarity with various time standards." + Our hope is that people are unlikely to make the opposite mistake (assume the input should be instead of JDuyc)) since our code is very explicit and calculating the ts almost always a trivialcalculation from the DATE-OBS FITS header keyword., Our hope is that people are unlikely to make the opposite mistake (assume the input should be instead of ) since our code is very explicit and calculating the is almost always a trivialcalculation from the DATE-OBS FITS header keyword. + Additionally. our code can easily correct for the observer's," Additionally, our code can easily correct for the observer's" +that a delay has indeed been observed in some other cases 22).,that a delay has indeed been observed in some other cases . + At 21:22:40.86 UT on 24 October 2008. the Fermi Gamma-ray Burst Monitor (GBM) triggered on081024B.," At 21:22:40.86 UT on 24 October 2008, the Fermi Gamma-ray Burst Monitor (GBM) triggered on." +. The light curve of the burst was characterized by à narrow spike of about 0.1 s (hereafter interval a). followed by a longer pulse. of about 0.7 s (hereafter interval b: Abdo et al.," The light curve of the burst was characterized by a narrow spike of about 0.1 s (hereafter interval a), followed by a longer pulse, of about 0.7 s (hereafter interval b; Abdo et al." + 2010)., 2010). + There is no evidence of emission after 0.8 s in GBM detectors covering the 8 keV - 5 MeV energy range (?)., There is no evidence of emission after 0.8 s in GBM detectors covering the 8 keV - 5 MeV energy range . +. An event with energy 3.1+0.2 GeV was detected after 0.55 s. while a second event of 1.7x0.1 GeV was detected after 2.18 5(2).. A time-resolved spectral analysis was performed in intervals a. b. and one third interval (hereafter interval ο) in-between 0.8 s and 2.9 s after the trigger.," An event with energy $3.1\pm0.2$ GeV was detected after 0.55 s, while a second event of $1.7\pm0.1$ GeV was detected after 2.18 s. A time-resolved spectral analysis was performed in intervals a, b, and one third interval (hereafter interval c) in-between 0.8 s and 2.9 s after the trigger." + The best-fit spectra were obtained by simultaneously fitting the signal from the GBM detectors in the energy range 8 keV - 36 MeV. and the LAT detectors (selecting transient events above 100 MeV; Abdo et a1.2010).," The best-fit spectra were obtained by simultaneously fitting the signal from the GBM detectors in the energy range 8 keV - 36 MeV, and the LAT detectors (selecting transient events above 100 MeV; Abdo et al.2010)." + In interval a. the best fit to the GBM data is obtained using a power law with a low energy spectral index ofc=-ἰ0378 and exponential cutoff around Έρως~2.7 MeV1).. though its value is only marginally constrained.," In interval a, the best fit to the GBM data is obtained using a power law with a low energy spectral index of $\alpha=-1.03^{+0.23}_{-0.19}$ and exponential cutoff around $E_{peak}\sim 2.7$ MeV, though its value is only marginally constrained." + The fluence in the 100 MeV - 10 GeV energy range was estimated to be <4x107? erg/em-. while the fluence measured in the 20 keV - 2 MeV range was (1.7+0.3)x1077 erg/emr. The emission during interval b was fit with a Band plus a power-law model. or an exponential cut-off power-law plus a power-law model.," The fluence in the 100 MeV - 10 GeV energy range was estimated to be $<4\times10^{-10}$ $^{2}$, while the fluence measured in the 20 keV - 2 MeV range was $(1.7\pm0.3)\times10^{-7}$ $^{2}$ The emission during interval b was fit with a Band plus a power-law model, or an exponential cut-off power-law plus a power-law model." +" The firstyielded best-fit parameter values of JNa2-1033-01?511. go.ΡΞΓΣ.2]-091H η.and. Ενωο=2-02),ΩΙ MeVWw1).. The second yielded best-fit values ofa=-0.714 and E,=κ. MeV for the cutoff power-law component: andB=—1.687507 for the power-law component Finally. during interval c. the emission is more accurately represented by a simple power-law. with a best-fit photon index ofp=1.6751).."," The firstyielded best-fit parameter values of $\alpha= -1.03^{+0.17}_{-0.14}$, $\beta= -2.1^{+0.11}_{-0.14}$ ,and $E_{peak}=2.0^{+1.9}_{-1.0}$ MeV. The second yielded best-fit values of $\alpha=-0.7^{+0.4}_{-0.3}$ and $E_{peak}=1.6^{+1.5}_{-0.6}$ MeV for the cutoff power-law component; and $\beta=-1.68^{+0.10}_{-0.06}$ for the power-law component Finally, during interval c, the emission is more accurately represented by a simple power-law, with a best-fit photon index of $\beta=-1.6^{+0.4}_{-0.1}$." + Thefluence measured in the 20 keV to 2 MeV energy range during this interval was (1.343.2)x107? erg/em-. with most of the energy being emitted in the 100 MeV - 10 GeV range. for a measured fluence of (4.0+2.4)x1077 erg/eme(?).," Thefluence measured in the 20 keV to 2 MeV energy range during this interval was $(4.3\pm3.2)\times10^{-8}$ $^{2}$, with most of the energy being emitted in the 100 MeV - 10 GeV range, for a measured fluence of $(4.0\pm2.4)\times10^{-7}$ $^{2}$." +. also triggered the Suzaku Wide-band All- Monitor (WAM. 50 keV - 5 MeV) at Ty=21:2240.526 UT (?).," also triggered the Suzaku Wide-band All-sky Monitor (WAM, 50 keV - 5 MeV) at $T_0=21:22:40.526$ UT ." +. The light curve showed a double-peaked structure with à Too duration of ~0.4 s. The fluence in 100 - 1000 keV range was Q7x1077 erg em., The light curve showed a double-peaked structure with a $T_{90}$ duration of $\sim 0.4$ s. The fluence in 100 - 1000 keV range was $(2.7^{+0.7}_{-1.0})\times10^{-7}$ erg $^{-2}$. + The peak flux within 0.5 s was nie photons em7 s! in the same energy range., The peak flux within $0.5$ s was $1.1^{+0.3}_{-0.5}$ photons $^{-2}$ $^{-1}$ in the same energy range. + Preliminary results showed that at least 2 MeV photons were detected. andthe time-averaged spectrum from Το to Ty+0.5 s was well fitted by a single power law. with a photon index of —12470(?)..," Preliminary results showed that at least 2 MeV photons were detected, andthe time-averaged spectrum from $T_0$ to $T_0+0.5$ s was well fitted by a single power law, with a photon index of $-1.24^{+0.25}_{-0.19}$." + Swift XRT began observing the field of the Fermi-LAT around 70.3 ks after the trigger(2)., Swift XRT began observing the field of the Fermi-LAT around $70.3$ ks after the trigger. +. Thanks to a series of follow-up observations(??).. if was possible to establish that none of the three sources could be the GRB X-ray counterpart because they were not fading.," Thanks to a series of follow-up observations, it was possible to establish that none of the three sources could be the GRB X-ray counterpart because they were not fading." + The observed dichotomy in the spectral behavior of during the first 3 s of emission. suggests that the properties of the central engine are evolving between interval à and c. During interval c. the observation of ~2 GeV photons implies an optically thin source in the GeV range. while during interval a the absence of emission above ~10 MeV and the unusually steep high energy photon index. suggest that the source is optically thick to pair production.," The observed dichotomy in the spectral behavior of during the first 3 s of emission, suggests that the properties of the central engine are evolving between interval a and c. During interval c, the observation of $\sim 2$ GeV photons implies an optically thin source in the GeV range, while during interval a the absence of emission above $\sim 10$ MeV and the unusually steep high energy photon index, suggest that the source is optically thick to pair production." + Hereafter. we analyze in more detail this scenario. noting however that other explanations may also be invoked.," Hereafter, we analyze in more detail this scenario, noting however that other explanations may also be invoked." + For instance. an alternative possibility is that there is no emission at all in the GeV range: this would be the case if interval a is dominated by emissiot from a photosphere. rather than from an absorbed synchrotror spectrum.," For instance, an alternative possibility is that there is no emission at all in the GeV range: this would be the case if interval a is dominated by emission from a photosphere, rather than from an absorbed synchrotron spectrum." + We refer the reader interested in this alternative explanation to papers such as e.g. loka (2010). Mizuta et al. (," We refer the reader interested in this alternative explanation to papers such as e.g. Ioka (2010), Mizuta et al. (" +2010). Pe'er Ryde (2010). Toma et al. (,"2010), Pe'er Ryde (2010), Toma et al. (" +2010). anc references therein.,"2010), and references therein." +" In the IS model?).. the central engine is supposec to emit a flow with Lorentz factor Γ. which 1s assumed to vary on a typical timescale f, (corresponding to an observed temporal variability of δρ=(1+ 24). with an amplitude of~F."," In the IS model, the central engine is supposed to emit a flow with Lorentz factor $\Gamma$, which is assumed to vary on a typical timescale $t_v$ (corresponding to an observed temporal variability of $\delta t_{obs}=(1+z)t_{v}$ ), with an amplitude $\delta \Gamma \sim \Gamma$." +" The shells collide at a radius R=20-cr,6xLO!PS7.2 em. where [5=0/1079 and (5=44/007s)."," The shells collide at a radius $R \approx +2\Gamma^2ct_v=6 \times 10^{13} \Gamma^2_{2.5}t_{v,-2}$ cm, where $\Gamma_{2.5}=\Gamma/10^{2.5}$ and $t_{v,-2}=t_v/(10^{-2}\rm~s)$." +" The internal energy released in each collision is distributed among electrons. magnetic field. and protons with fractions e. εν. and (1—€,). respectively."," The internal energy released in each collision is distributed among electrons, magnetic field, and protons with fractions $\epsilon_e$ , $\epsilon_B$ and $(1-\epsilon_e)$ , respectively." +" The electrons are accelerated in theshocks to a power-law distribution of energy N(y)«y "". and radiatively cool by the combination of synchrotron and SSC processes. the timescales of which are f,Giin,cloyBoy "," The electrons are accelerated in theshocks to a power-law distribution of energy $N(\gamma) +\propto \gamma^{-p}$ , and radiatively cool by the combination of synchrotron and SSC processes, the timescales of which are $t_{syn} \sim 6 \pi m_ec/\sigma_T B^{2}\gamma$ " +time. and an additional factor of —LO can be obtained if one assumes ionizing emissivity. ¢~. expected of Population III stars (2)..,"time, and an additional factor of $\sim10$ can be obtained if one assumes ionizing emissivity, $\epsilon_\gamma$, expected of Population III stars \citep{Schaerer03}." + This seems unlikely. although such a strong redshift evolution in ionizing efficiency is implied if the ?. lensed sample of +~9 LAEs is genuine (??)..," This seems unlikely, although such a strong redshift evolution in ionizing efficiency is implied if the \citet{Stark07} lensed sample of $z\sim9$ LAEs is genuine \citep{SLE07, MF08LAE}." + Furthermore. ci. depends linearly on fice. which we assumed to be f...=0.02 (see 2.2.19).," Furthermore, $\epsilon_{\rm fid}$ depends linearly on $f_{\rm esc}$, which we assumed to be $f_{\rm esc}=0.02$ (see \ref{sec:flux}) )." + To our knowledge. no observations exist that hint at significantly larger average values of fi... (e.g.2??)..," To our knowledge, no observations exist that hint at significantly larger average values of $f_{\rm esc}$ \citep[e.g.][]{Inoue06,Shapley06,Siana07}." + Theoretically. escape fractions of order unity €f...~ 1) only appear associated with minihalos that contain a single massive star (2).," Theoretically, escape fractions of order unity $f_{\rm esc}\sim 1$ ) only appear associated with minihalos that contain a single massive star \citep{Whalen04}." + Aguin. we point out that we do not model reionization and feedback. self-consistentlv.," Again, we point out that we do not model reionization and feedback self-consistently." +" Our conclusions on the strength of feedback effects are thus conservative. in that results fromWAZAP suggest most halos would have been exposed to a UVB for shorter periods of time than our choice of 2,=14 implies (see discussion in 2.13."," Our conclusions on the strength of feedback effects are thus conservative, in that results from suggest most halos would have been exposed to a UVB for shorter periods of time than our choice of $\zon=14$ implies (see discussion in \ref{sec:mark_sims}) )." +" We are also conservative in neglecting the build-up of the UVB from z,,=14. assuming a constant distribution calculated at 2 throughout the entire interval Z42."," We are also conservative in neglecting the build-up of the UVB from $\zon=14$, assuming a constant distribution calculated at $z$ throughout the entire interval $\zon \rightarrow z$." +" On the other hand. as we point out above. we assume a minimum mass of Mai,c1.7>.LOCAL. when generating ionization and flux fields. roughly corresponding to Ziq,=LO’ K at >=7."," On the other hand, as we point out above, we assume a minimum mass of $\Mmin\ge1.7 \times 10^8 \Msun$ when generating ionization and flux fields, roughly corresponding to $\Tvir=10^4$ K at $z=7$." + But the same virial temperature corresponds to a somewhat lower Mi at higher redshifts., But the same virial temperature corresponds to a somewhat lower $\Mmin$ at higher redshifts. + If star formation is indeed allowed down to exactly Zip=104 K. the contribution of neglected halos with Al«LT10M. can be approximated with a 40% increase in the effective efficiency cj; at 2=LO (assuming the ionizing photon contribution traces the collapsed fraction. as was done in this work).," If star formation is indeed allowed down to exactly $\Tvir=10^4$ K, the contribution of neglected halos with $M<1.7\times10^8\Msun$ can be approximated with a $\sim40\%$ increase in the effective efficiency $\toteff$ at $z=10$ (assuming the ionizing photon contribution traces the collapsed fraction, as was done in this work)." + This uncertainty is smaller the other uncertainties in Click:, This uncertainty is smaller the other uncertainties in $\toteff$. +" Even assuming our source ionizing luminosity prescriptions are realistic. we do not expect to accurately model the tails of the UVB distributions. due to the following effects: Nevertheless. the tails of the UVB «distribution are not important in answering the pertinent question. of ""does UV radiative feedback significantly affect the progress of the bulk of reionization""."," Even assuming our source ionizing luminosity prescriptions are realistic, we do not expect to accurately model the tails of the UVB distributions, due to the following effects: Nevertheless, the tails of the UVB distribution are not important in answering the pertinent question of “does UV radiative feedback significantly affect the progress of the bulk of reionization”." + Tonizing fluxes close to the means of the UVB distributions are more relevant in answering this question., Ionizing fluxes close to the means of the UVB distributions are more relevant in answering this question. + Given our generalized parametrizations. we are confident our models are sufficiently accurate for these purposes.," Given our generalized parametrizations, we are confident our models are sufficiently accurate for these purposes." + Thus we do not expect to loose sleep worrving about the effects mentioned in the previous paragraph., Thus we do not expect to loose sleep worrying about the effects mentioned in the previous paragraph. + In this paper. we quantify the importance of UV radiative feedback during the middle and late stages of reionization.," In this paper, we quantify the importance of UV radiative feedback during the middle and late stages of reionization." + Specitically. we concern ourselves with halos capable of atomic cooling. duum141 K. We first run suites of spherically-symmetric halo collapse simulations using various values of z. A. and οι.," Specifically, we concern ourselves with halos capable of atomic cooling, $\Tvir\gsim10^4$ K. We first run suites of spherically-symmetric halo collapse simulations using various values of $z$, $M$, and $J_{21}$." + We then generate parametrized UV flux distributions at >= 7. 10. and 13. using semi-numerical. large-scale simulations of halo and ionization fields.," We then generate parametrized UV flux distributions at $z=$ 7, 10, and 13, using semi-numerical, large-scale simulations of halo and ionization fields." + Combining these two results. we estimate how efficient is radiative feedback at hindering the progress of reionization. during its advanced stages (when ων<?. and zp ts the fraction of the post-shock thermal energy in magnetic field (see Panaitescu Kumar 20014 for details)."," Here, $E$ is the isotropic equivalent kinetic energy of the outflow, $\epsel$ is the fractional energy in electrons, $p$ is the index of the power-law distribution of the electron Lorentz factor $N(\gamma) \propto \gamma^{-p}$, and $\epsmag$ is the fraction of the post-shock thermal energy in magnetic field (see Panaitescu Kumar 2001a for details)." +" The break frequencies. satisfyM i,xEu>1/2 Boe XEU?p⋅ ⊽⇝⊐↴πο synchrotron-dominated. electron cooling.. and p.x[E65252770LP) when inverse Compton losses exceed synchrotron Mecooling."," The break frequencies satisfy $\nu_p \propto +E^{1/2} \epsel^2 \epsmag^{1/2}$ , $\nu_c \propto E^{-1/2} n^{-1} +\epsmag^{-3/2}$ for synchrotron-dominated electron cooling, and $\nu_c +\propto [E^{-p/2} n^{-2} \epsel^{-2(p-1)} \epsmag^{-p/2}]^{1/(4-p)}$ when inverse Compton losses exceed synchrotron cooling." + The above equations show that for p.~2. which is the average value for this parameter determined by Panaitescu Kumar (2001b) from numerical modeling of eight GRB afterglows. the afterglow flux is roughly proportional to the kinetic energy E.," The above equations show that for $p \sim 2$, which is the average value for this parameter determined by Panaitescu Kumar (2001b) from numerical modeling of eight GRB afterglows, the afterglow flux is roughly proportional to the kinetic energy $E$." + Since short GRBs have a fluence on average ~20 times smaller than that of long GRBs. other parameters being equal. we expect the afterglows of short GRBs to be ~20 times dimmer than the afterglows of long GRBs.," Since short GRBs have a fluence on average $\sim 20$ times smaller than that of long GRBs, other parameters being equal, we expect the afterglows of short GRBs to be $\sim 20$ times dimmer than the afterglows of long GRBs." + The equations show that the afterglow flux in short bursts would be further suppressed if these bursts occur in a lower density medium compared to long bursts., The equations show that the afterglow flux in short bursts would be further suppressed if these bursts occur in a lower density medium compared to long bursts. + The expressions for the radio and optical flux have an explicit dependence on 1., The expressions for the radio and optical flux have an explicit dependence on $n$. + Even though the formula for the X-ray flux does not have an explicit dependence. this flux is also suppressed since. for low n. the cooling frequency i». moves above the X-ray band and so the X-ray afterglow light-curve is described by equation (3)) rather than equation (3)).," Even though the formula for the X-ray flux does not have an explicit dependence, this flux is also suppressed since, for low $n$, the cooling frequency $\nu_c$ moves above the X-ray band and so the X-ray afterglow light-curve is described by equation \ref{optic}) ) rather than equation \ref{xray}) )." + Finally. 1f the breaks observed at one to a few days in the optical emission of several GRB afterglows are due to collimation of the outflow (Rhoads 1999; Sari et al.," Finally, if the breaks observed at one to a few days in the optical emission of several GRB afterglows are due to collimation of the outflow (Rhoads 1999; Sari et al." + 1999; Kumar Panaitescu 2000). then the ~20 times smaller kinetic energy of the jets in short GRBs will cause the jet break time t;xEU? to occur ~3 times earlier in these bursts compared to long GRBs.," 1999; Kumar Panaitescu 2000), then the $\sim 20$ times smaller kinetic energy of the jets in short GRBs will cause the jet break time $t_j \propto E^{1/3}$ to occur $\sim 3$ times earlier in these bursts compared to long GRBs." + This will further diminish. the brightness of short-GRB afterglows (at a fixed observing time) by a factor ofabout23., This will further diminish the brightness of short-GRB afterglows (at a fixed observing time) by a factor of about $2-3$. + These conclusions are illustrated in Figure 2. which compares the radio. optical. and X-ray emission of a typical long-GRB afterglow with that. predicted. for short-GRB afterglows with lower values of FE and ».," These conclusions are illustrated in Figure 2, which compares the radio, optical, and X-ray emission of a typical long-GRB afterglow with that predicted for short-GRB afterglows with lower values of $E$ and $n$." + The numerical calculations of the afterglow dynamics and emission. of radiation were done by the methods described in Panaitescu Kumar (2000)., The numerical calculations of the afterglow dynamics and emission of radiation were done by the methods described in Panaitescu Kumar (2000). + The parameters for the long-GRB afterglow were chosen such that at one day after the burst the model yields a radio flux of ~0.5 mJy. an optical brightness of R~20 and a 2-10 keV X-ray flux of ~10.Moreau7s1 in rough agreement with observations.," The parameters for the long-GRB afterglow were chosen such that at one day after the burst the model yields a radio flux of $\sim 0.5$ mJy, an optical brightness of $R \sim 20$ and a 2–10 keV X-ray flux of $\sim 10^{-11} \cgs$, in rough agreement with observations." + We see from Fig., We see from Fig. + 2 that the radio emission from a typical short-GRB afterglow will most likely be very difficult to detect., 2 that the radio emission from a typical short-GRB afterglow will most likely be very difficult to detect. + The same is true also for the optical emission. where only early (51/2 day) observations as deep as the measurements made by Groot (1998) for GRB 970828 and by Fynbo (2001) for GRB 000630 are likely to be successful.," The same is true also for the optical emission, where only early $\siml 1/2$ day) observations as deep as the measurements made by Groot (1998) for GRB 970828 and by Fynbo (2001) for GRB 000630 are likely to be successful." + The best chance for detecting the afterglow of a short GRB ts with X-ray observations., The best chance for detecting the afterglow of a short GRB is with X-ray observations. + BeppoSax will need to observe earlier than ~1/2 day. and CXO. HETE II and Swift earlier than ~2 days.," BeppoSax will need to observe earlier than $\sim 1/2$ day, and CXO, HETE II and Swift earlier than $\sim 2$ days." + Such observations are quite feasible., Such observations are quite feasible. + Because of the roughly linear dependence of the afterglow brightness on the kinetic energy FE. any difference in the average redshifts of short and long GRBs will not alter the above conclusions.," Because of the roughly linear dependence of the afterglow brightness on the kinetic energy $E$, any difference in the average redshifts of short and long GRBs will not alter the above conclusions." + The redshift enters into the estimate of £. and through it in the estimate of the afterglow luminosity. but it factors out when the luminosity is converted to the observed flux.," The redshift enters into the estimate of $E$, and through it in the estimate of the afterglow luminosity, but it factors out when the luminosity is converted to the observed flux." + The fluences above 25 keV of GRBs detected by BATSE are positively. correlated. with the durations of these bursts; long bursts (durations longer than a few seconds) are on average 20 times more energetic than short bursts., The fluences above 25 keV of GRBs detected by BATSE are positively correlated with the durations of these bursts; long bursts (durations longer than a few seconds) are on average 20 times more energetic than short bursts. + Moreover. the ~ three dozen long GRBs for which afterglows have been detected so far (following their accurate localization by BeppoSAX and the Interplanetary Network) are on average 40 times brighter (in fluence) than typical short GRBs.," Moreover, the $\sim$ three dozen long GRBs for which afterglows have been detected so far (following their accurate localization by BeppoSAX and the Interplanetary Network) are on average 40 times brighter (in fluence) than typical short GRBs." + Thus we expect the relativistic outflow of a long GRB to have about 20 times the kinetic energy of the outflow from a short GRB., Thus we expect the relativistic outflow of a long GRB to have about 20 times the kinetic energy of the outflow from a short GRB. + If the other parameters that influence the dynamics of the GRB remnant and the emission of radiation are roughly the same. we predict that the afterglows of short GRBs should be a factor of 10 or more dimmer than the afterglows of long GRBs.," If the other parameters that influence the dynamics of the GRB remnant and the emission of radiation are roughly the same, we predict that the afterglows of short GRBs should be a factor of 10 or more dimmer than the afterglows of long GRBs." + If short GRBs arise from merging NS-NS or NS-BH binaries which may have traveled upto or beyond the very tenuous outskirts of their host galaxies. and if long GRBs are due to the core collapse of massive stars which die in the dense molecular clouds where they were formed. then the densities #7 of the media surrounding these two types of GRBs may differ by a few orders of magnitude.," If short GRBs arise from merging NS–NS or NS–BH binaries which may have traveled upto or beyond the very tenuous outskirts of their host galaxies, and if long GRBs are due to the core collapse of massive stars which die in the dense molecular clouds where they were formed, then the densities $n$ of the media surrounding these two types of GRBs may differ by a few orders of magnitude." + This could further seriously diminish the prospects of detecting radio and optical afterglows of short GRBs since the afterglow brightness in these bands is proportional to 71/2, This could further seriously diminish the prospects of detecting radio and optical afterglows of short GRBs since the afterglow brightness in these bands is proportional to $n^{1/2}$. + We conclude that the best chance of detecting afterglows of short GRBs is with early X-ray observations within | day after the GRB., We conclude that the best chance of detecting afterglows of short GRBs is with early X-ray observations within 1 day after the GRB. + Rapid and deep optical follow-up within a few hours after the mam event may also lead to a detection., Rapid and deep optical follow-up within a few hours after the main event may also lead to a detection. + Radio observations appear the least promising (Fig., Radio observations appear the least promising (Fig. + 2)., 2). + Of course. short GRBs significantly brighter than average could be as energetic as some of the long GRBs for which afterglows have been seen (Fig.," Of course, short GRBs significantly brighter than average could be as energetic as some of the long GRBs for which afterglows have been seen (Fig." + 1)., 1). + The afterglows of such unusually bright short GRBs could be detected even beyond a day. particularly if the magnetic field strength is close to equipartition (25.» 1)," The afterglows of such unusually bright short GRBs could be detected even beyond a day, particularly if the magnetic field strength is close to equipartition $\epsmag\to1$ )." + But such bursts should be in the minority., But such bursts should be in the minority. + On the other hand. if future observations indicate that the afterglows of most short GRBs are as bright as those of long GRBs. it would imply that one or more of the assumptions we have made in our analysis is invalid.," On the other hand, if future observations indicate that the afterglows of most short GRBs are as bright as those of long GRBs, it would imply that one or more of the assumptions we have made in our analysis is invalid." + One possibility is that the ~-efficiency is significantly lower in short bursts than inlong bursts. as disussed in Kumar (1999). and another is that the efficiency spans a wide range in both types of bursts. indicating a highly inhomogeneous outflow (Kumar Piran 2000).," One possibility is that the $\gamma$ -efficiency is significantly lower in short bursts than inlong bursts, as disussed in Kumar (1999), and another is that the efficiency spans a wide range in both types of bursts, indicating a highly inhomogeneous outflow (Kumar Piran 2000)." +(feet= 2) with of cloud-Iree regions.,$f_{\rm sed}=2$ ) with of cloud-free regions. + We have found that this is generally the case: a partly cloudy model presents a similar thermal profile to a model with a thinner cloud. a point we return to in $44.," We have found that this is generally the case: a partly cloudy model presents a similar thermal profile to a model with a thinner cloud, a point we return to in 4." + The synthetic spectrum for a converged LU?) atmospheric. profile is obtained. [rom Equation (1)., The synthetic spectrum for a converged $T(P)$ atmospheric profile is obtained from Equation (1). + We compute absolute magnitudes aud colors with the ullracool dwarf evolution models of Sammon&Miley(2008)., We compute absolute magnitudes and colors with the ultracool dwarf evolution models of \citet{Sau08}. +. Figure 2 shows synthetic near-intrarecl photometry from the partly clouclly models., Figure 2 shows synthetic near-infrared photometry from the partly cloudly models. + For a fired Tag. as h is increased (he model colors briskly move lo the blue in J—A and J—H.," For a $\teff$, as $h$ is increased the model colors briskly move to the blue in $J-K$ and $J-H$." + The J band flix increases as / increases [rom 0 to 0.75. but then cdims slightly for cloud Iree models (/=1).," The $J$ band flux increases as $h$ increases from 0 to 0.75, but then dims slightly for cloud free models $h=1$ )." + This is because atimospheres with even a small cloud cover are warmer in the atmospheric region from which the J band flux emerges., This is because atmospheres with even a small cloud cover are warmer in the atmospheric region from which the $J$ band flux emerges. + On the other hand. Mj; is relatively constant across the transition [rom =0 to h— 1a constant Tog but shows a similar dimming as /—1.," On the other hand, $M_H$ is relatively constant across the transition from $h=0$ to $h=1$ at constant $\teff$ but shows a similar dimming as $h \rightarrow 1$." + The evolution of model dwarls with fixed fica produces trajectories that do not exhibit a rapid L to T transition as a global homogenous cloud sinks (oo gradually. below the photosphere (Burrows οἱ al., The evolution of model dwarfs with fixed $f_{\rm sed}$ produces trajectories that do not exhibit a rapid L to T transition as a global homogenous cloud sinks too gradually below the photosphere (Burrows et al. + 2006: Sammon Marley. 2008. Fig.," 2006; Saumon Marley 2008, Fig." + 4)., 4). + With the cloud model. the L to T dwarf transition can only be modeled with an increase of (he cloud sedimentation parameter /44.Figure 2 demonstrates (hat the transition ean also be described as a progressive increase in cloud-I[ree areas al a fixed. fig and Teg~1200Ix.," With the \citet{Ack01} cloud model, the L to T dwarf transition can only be modeled with an increase of the cloud sedimentation parameter $f_{\rm sed}$.Figure 2 demonstrates that the transition can also be described as a progressive increase in cloud-free areas at a fixed $f_{\rm sed}$ and $\teff \sim 1200\,\rm K$." + The L/T transition dwarf colors and the J band brightening are well fit by this approach., The L/T transition dwarf colors and the J band brightening are well fit by this approach. + llowever. 1200IX is slightlv cooler than the observed Zar temperature of the transition of ~1300Ix (Golimowski et al.," However, $\,$ K is slightly cooler than the observed $\teff$ temperature of the transition of $\sim 1300\,\rm K$ (Golimowski et al." + 2004: Stephens οἱ al., 2004; Stephens et al. + 2009) and if Zig [alls appreciably across the transition the J band bump would be weakened (Fig., 2009) and if $\teff$ falls appreciably across the transition the J band bump would be weakened (Fig. + 2)., 2). + For a different choice of fa and model gravity. a different transition Zar would be expected., For a different choice of $f_{\rm sed}$ and model gravity a different transition $T_{\rm eff}$ would be expected. + As noted in Saumon Marley. there is an offset of ~0.3 to the blue in the J—A color of models [rom (he bulk of L and T dwarf photometry.," As noted in Saumon Marley, there is an offset of $\sim 0.3$ to the blue in the $J-K$ color of models from the bulk of L and T dwarf photometry." + This may. arise from shortcomings in (he A band pressure-induced. opacitv of molecular hydrogen., This may arise from shortcomings in the $K$ band pressure-induced opacity of molecular hydrogen. + Nonetheless. the trend of the late T cdwarl J—A color can be better reproduced with models with ~0.5—0.75.," Nonetheless, the trend of the late T dwarf $J-K$ color can be better reproduced with models with $h \sim 0.5-0.75$." + In the Mj vs. J—FH diagram. the behavior of field L dwarls and late T dwarls are better reproduced by the cloudy freq=2 ancl the cloudless sequences. respectively allhoughthe latter would also be better matched with partly cloudy models with ~0.5— 0.75. This suggests (he spectra of late T. dwarls could be influenced by clouds. contrary to the usual assumption (Durgasseretal. 2010)..," In the $M_H$ vs. $J-H$ diagram, the behavior of field L dwarfs and late T dwarfs are better reproduced by the cloudy $f_{\rm sed}=2$ and the cloudless sequences, respectively althoughthe latter would also be better matched with partly cloudy models with $h \sim 0.5 - 0.75$ This suggests the spectra of late T dwarfs could be influenced by clouds, contrary to the usual assumption \citep{Bur10}. ." +thermally unstable.,thermally unstable. + Figure., Figure. + 3 shows the distribution of mass in the p—n phase space at two different times., \ref{fig:pe_phase} shows the distribution of mass in the $p-n$ phase space at two different times. + The compression by a weak perpendicular shock is somewhat smaller than that by a parallel shock., The compression by a weak perpendicular shock is somewhat smaller than that by a parallel shock. + The compression ratio changes from 2.70 for a parallel shock to 1.87 for a perpendicular shock., The compression ratio changes from 2.70 for a parallel shock to 1.87 for a perpendicular shock. + The gas behind the transmitted shock is therefore only marginally cooler and less dense., The gas behind the transmitted shock is therefore only marginally cooler and less dense. +" However, contrary to what occurs in the parallel case, a slow-mode shock does not arise in the upstream parts of the cloud."," However, contrary to what occurs in the parallel case, a slow-mode shock does not arise in the upstream parts of the cloud." + This can be easily seen in Figs., This can be easily seen in Figs. + 4 and 5 which show the logarithm of the density for the perpendicular case as a function of position for different slices and different times., \ref{fig:peboundary} and \ref{fig:peboundary_x} which show the logarithm of the density for the perpendicular case as a function of position for different slices and different times. +" Slow-mode waves, and therefore slow-mode shocks, do not propagate perpendicular to the magnetic field."," Slow-mode waves, and therefore slow-mode shocks, do not propagate perpendicular to the magnetic field." +" However, as the intercloud shock sweeps across the cloud, a slow-mode shock does arise at the sides of the cloud."," However, as the intercloud shock sweeps across the cloud, a slow-mode shock does arise at the sides of the cloud." + This slow-mode shock is not as strong as in the parallel case., This slow-mode shock is not as strong as in the parallel case. +" Thus, it does not trigger a condensation near the boundary."," Thus, it does not trigger a condensation near the boundary." + Figure 3 ," Figure \ref{fig:pe_phase} + " +allowed range of II to values of i<—1. we find a lower bound on II as a function of ie shown by the thick solid line in this figure.,"allowed range of H to values of $w < -1$, we find a lower bound on H as a function of $w$ shown by the thick solid line in this figure." + Η we use this lower bound on II. aud compare the predicted age as a [unetion of ic with the WMADP upper limit. we derive a bound woo—]1.22.," If we use this lower bound on H, and compare the predicted age as a function of $w$ with the WMAP upper limit, we derive a bound $w>-1.22$." + If. we were instead to allow the full HIST range for HE in deriving this limit. the lower bound would decrease slightly to w2—1.27.," If we were instead to allow the full HST range for H in deriving this limit, the lower bound would decrease slightly to $w>-1.27$." + We emphasize that the bound we have derived here is conservative., We emphasize that the bound we have derived here is conservative. + À tighter bound would no doubt be possible if à trulv. global analvsis of all the WALAP data were carried out. allowing we<—1. including possible correlations between (he inferred WAIAP age and other cosmic parameters.," A tighter bound would no doubt be possible if a truly global analysis of all the WMAP data were carried out allowing $w <-1$, including possible correlations between the inferred WMAP age and other cosmic parameters." + We hope the WMAP team will perform such an analysis., We hope the WMAP team will perform such an analysis. + For the moment. however. if one combines the result here with the WALAP-derivecl upper bound on iw. one thus finds an allowed region —1.22«ie<—.78.," For the moment, however, if one combines the result here with the WMAP-derived upper bound on $w$ , one thus finds an allowed region $-1.22 o obtain the disc-averaged flux from Earth at the top of the liatmosphere.1 where Ay. is Earth's‘ radiusli οaud + is he spacecraft range."," 2) We divide the flux observed from the spacecraft by $(R_{\oplus}/r)^{2}$ to obtain the disc-averaged flux from Earth at the top of the atmosphere, where $R_{\oplus}$ is Earth's radius and $r$ is the spacecraft range." +" 3) We use a I&urucz for the solar specific flux at 1 AU. axd convert it to fhx iu cach of he TRI wavebauds using the 0.1 pau top-hat xdidpasses,"," 3) We use a Kurucz for the solar specific flux at 1 AU, and convert it to flux in each of the HRI wavebands using the 0.1 $\mu$ m top-hat bandpasses." + 1) Dividing the result of steps 2) aud 3) bx cach other. we obtain the top-ofthe-ai1iosphiere reflectance of the wet at the observed pje.," 4) Dividing the result of steps 2) and 3) by each other, we obtain the top-of-the-atmosphere reflectance of the planet at the observed phase." + 5j We further divide he reflectance bv the scaed. Lambert plase function (fla)=(Giualpha|(xaj)cosalpharight)): 1916). thus obtaining the plauct’s appareut albedo. AY.," 5) We further divide the reflectance by the scaled Lambert phase function \citep[$f(\alpha)=\frac{2}{ +, thus obtaining the planet's apparent albedo, $A^{*}$." + The precise definition of AY is given iu Equation 5: for now it is sufficient to think of it as the average albedo of the planet. weighted bv the ilhuuinatioun and visibility of various regions at that uonent in time.," The precise definition of $A^{*}$ is given in Equation 5; for now it is sufficient to think of it as the average albedo of the planet, weighted by the illumination and visibility of various regions at that moment in time." + Unlike the observatious presented 1ji Cowanetal. (2009).. the viewing ecomery is sufficletly cüffereut for he two polar observations tha we treat them separately.," Unlike the observations presented in \cite{Cowan_2009}, the viewing geometry is sufficiently different for the two polar observations that we treat them separately." + Iu articular. a sinele exoλαο could be observed by he sale stationary observer with the two viewing econetries of Cowanctal.(2009) since the sil-observer atitude was essentially eqiwtorial at both epochs (see Table 1).," In particular, a single exoplanet could be observed by the same stationary observer with the two viewing geometries of \cite{Cowan_2009} since the sub-observer latitude was essentially equatorial at both epochs (see Table 1)." +" Although the si)-5ellar latitude varies with xiase for non-zero obliquitiOs, the zub-observer latitude is constant. provided that one can neglect precession (for nore details on viewing geonetry. see 1))."," Although the sub-stellar latitude varies with phase for non-zero obliquities, the sub-observer latitude is constant, provided that one can neglect precession (for more details on viewing geometry, see \ref{viewing_geometry}) )." + By contrast. he two time series prescutcxd in the current paper have sub-observer latitudes of 627 N aud 717 S. respectively.," By contrast, the two time series presented in the current paper have sub-observer latitudes of $^{\circ}$ N and $^{\circ}$ S, respectively." + The time-averaged spectra for he EPOXI polar iux equatorial observations are shown in Figure DMi au the apparent albedo values are listed in Table DMi," The time-averaged spectra for the EPOXI polar and equatorial observations are shown in Figure \ref{average_albedo_spectrum}, and the apparent albedo values are listed in Table \ref{apparent_albedos}." + The literature abounds with vaguely-defiued “reflectance” lucasurements: as a result of differing definitions of reflectance used bv differeut EPOXI ean members. the albedos reported iu Cowanetal.(2009) were about 2/3} of the correct value. (," The literature abounds with vaguely-defined “reflectance” measurements: as a result of differing definitions of reflectance used by different EPOXI team members, the albedos reported in \cite{Cowan_2009} were about $2/3$ of the correct value. (" +Note that this παοτι offset lac uo iurpact on the color variations auc analvsis presenutec in that paper.),Note that this uniform offset had no impact on the color variations and analysis presented in that paper.) + We preseut the corrected values « »pareut albedo in Table 3 aud Figure 3., We present the corrected values of apparent albedo in Table 3 and Figure 3. + The major eatures of the time-averaged broadband albedo specrui of Earth are: 1) a blue rap shortward of 550 um due to Raleigh scattering. 2) a slight rise im albedo owiucds longer wavelengths due to continents. and 3)j a steep dip in albedo at 950 nii due to water vapor absorption.," The major features of the time-averaged broadband albedo spectrum of Earth are: 1) a blue ramp shortward of 550 nm due to Rayleigh scattering, 2) a slight rise in albedo towards longer wavelengths due to continents, and 3) a steep dip in albedo at 950 nm due to water vapor absorption." + Sienificautlv. apart from a 1niforiu offset. the polar aud equatorial observations have mdistinguishable albedo spectra.," Significantly, apart from a uniform offset, the polar and equatorial observations have indistinguishable albedo spectra." + As in Cowanetal.(2009) WO οπλο Lo prior, As in \cite{Cowan_2009} we assume no prior +dispersion of 2.5 kui/s. FromEq. (3)),dispersion of $2.5$ km/s. FromEq. \ref{eq:heating}) ) +" with g=3 we then obtain: Since many of the recent dynamical models suggest mean dark matter densities within the stellar core radius of UM Z0.1 M. 7. corresponding to a central light ratio of z15 M. Τεν, (Lake1990:Pryor&IKonueudysonetal. 2006). pay,=0.1 AL. P? will be accepted as a conservative reference value."," with $g=3$ we then obtain: Since many of the recent dynamical models suggest mean dark matter densities within the stellar core radius of UMi $\gtrsim 0.1$ $_{\odot}$ $^{-3}$, corresponding to a central mass-to-light ratio of $\gtrsim 15$ $_{\odot}/$ $_{\odot}$ \citep{lak90,pry90, +irw95,mat98,wil06}, $\rho_{\rm dm}=0.1$ $_{\odot}$ $^{-3}$ will be accepted as a conservative reference value." + The mean-square radius of the subpopulation increases in time with σε. according to the relation r?~az(Q2. where 9 is the orbital frequency in the coustaut-density core.," The mean-square radius of the subpopulation increases in time with $\sigma_{s}$, according to the relation $\bar{r^{2}}\simeq +\sigma_{s}^{2}/\Omega^{2}$, where $\Omega$ is the orbital frequency in the constant-density core." +" If the core is dominated by the dark matter compoucut pay/O?=(IxG/3)1. then If o,=2.5 laus. the mean radius Vr?2σιοτε60 pe."," If the core is dominated by the dark matter component $\rho_{\rm dm}/\Omega^{2}=(4\pi G/3)^{-1}$, then If $\sigma_{s}=2.5$ km/s, the mean radius $\sqrt{\bar{r^{2}}}\simeq \sigma_{s}/\Omega\approx 60$ pc." + This correspouds to à la radius of 25.5 pe for a Gaussian deusity profile. implying an anenlar size of almost 2’ at the distance of UAG (~66 kpc).," This corresponds to a $1\,\sigma$ radius of $25.5$ pc for a Gaussian density profile, implying an angular size of almost $2'$ at the distance of UMi $\sim 66$ kpc)." + This value is comparable to but slightly larger than the observed 16 radius of the secondary peak ~1.65.," This value is comparable to but slightly larger than the observed $1\,\sigma$ radius of the secondary peak $\simeq 1.6'$." +" As a cousequeuce 9,=2.5 uns otherwise. the stellar subpopulation would appear more extended and diffuse than it is observed."," As a consequence $\sigma_{s}\lesssim 2.5$ km/s; otherwise, the stellar subpopulation would appear more extended and diffuse than it is observed." + This upper value is in agreement with the observations of 100., This upper value is in agreement with the observations of K03. +" Qur estimates for the size and velocity dispersion of the subpopulation are independent of the eccentricity of the orbit because there is little variation of the macroscopic xoperties of the halo. py. a, or O. within the core where the chunp is orbiting."," Our estimates for the size and velocity dispersion of the subpopulation are independent of the eccentricity of the orbit because there is little variation of the macroscopic properties of the halo, $\rho_{h}$, $\sigma_{h}$ or $\Omega$, within the core where the clump is orbiting." + Nevertheless. the dark halo could have suffered significant evolution due to two-body processes and. tidal stirring.," Nevertheless, the dark halo could have suffered significant evolution due to two-body processes and tidal stirring." +" For Mj,X10° AL. relaxation Xocesses Induce an insieuificaut change iu the iuternal xoperties of the halo (c.e.. Jinetal. 2005))."," For $M_{h}\lesssim 10^{5}$ $_{\odot}$ relaxation processes induce an insignificant change in the internal properties of the halo (e.g., \citealt{jin05}) )." +" Tidal heating can lead to a reduction of both the deusitv of dark matter xwticles aud its velocity dispersion (οσοι, Maveretal.2001:Readctal. 20063)."," Tidal heating can lead to a reduction of both the density of dark matter particles and its velocity dispersion (e.g., \citealt{may01, rea06}) )." +" Since the phase-space density. py,0j. or collisionless svstenis is nearlv coustant or decreases with tine. the rate of energw gained bv the clump due o encounters with VMOs should have been more intense in the past."," Since the phase-space density, $\rho_{h}/\sigma_{h}^{3}$, for collisionless systems is nearly constant or decreases with time, the rate of energy gained by the clump due to encounters with VMOs should have been more intense in the past." + The inclusion of evolution of halo propertics w tidal effects would lead to a stringent upper mass Init., The inclusion of evolution of halo properties by tidal effects would lead to a stringent upper mass limit. +" If the stellar progenitor cluster became uubouud Inunediately after formation when supernovae expel the eas content (Goodwin1997: IK03). ος should be greater than the age of the cluster ty,~10 Cir."," If the stellar progenitor cluster became unbound immediately after formation when supernovae expel the gas content \citealt{goo97}; K03), $t_{2.5}$ should be greater than the age of the cluster $t_{H}\sim 10$ Gyr." + This requirement combined with Eq. (1)), This requirement combined with Eq. \ref{eq:t25}) ) + implies: If initially the stellar cluster is eravitationally bound. the increase in the internal cncrev gained by eucouuters with VMOs will eventually exceed its binding euerev after a time fy.," implies: If initially the stellar cluster is gravitationally bound, the increase in the internal energy gained by encounters with VMOs will eventually exceed its binding energy after a time $t_{be}$." + Let us estimate fj. the time at which the cluster becomes uubound.," Let us estimate $t_{be}$ , the time at which the cluster becomes unbound." + R03 iter a total mass of the cluster. AL). of 3&LO! ALL.," K03 infer a total mass of the cluster, $M_{cl}$, of $3\times 10^{4}$ $_{\odot}$." + Tf this cluster followed the recently observed relation between radius aud iass of Larsen(2001)... rp2E pc.," If this cluster followed the recently observed relation between radius and mass of \citet{lar04}, $r_{1/2}\approx 4$ pc." +" Adopting the refercuce values of the dark matter halo (pay,=0.1 M. aud σι=20 sun/s) aud rescaling the survival diagram of EKlessen&Durkert(1996) (their figure 11) for the parameters of UM. we infer that more than 95% of the clusters with nass 3s104 AL. will become unbound after fj;23 Cyr if Af,3510fPALL."," Adopting the reference values of the dark matter halo $\rho_{\rm dm}=0.1$ $_{\odot}$ $^{-3}$ and $\sigma_{h}=20$ km/s) and rescaling the survival diagram of \citet{kle96} (their figure 11) for the parameters of UMi, we infer that more than $95\%$ of the clusters with mass $3\times 10^{4}$ $_{\odot}$ will become unbound after $t_{be}\approx 3$ Gyr if $M_{h}\geq 3.5\times 10^{3} f^{-1}$ $_{\odot}$." +" Therefore. in order to have a dynamically cold subpopulation with σι«2.5 kmi/s. as hat observed in UAG at the present time typ~10 Civ. we need fo.52tytre. Which implies the following uppernuit for Mj, Other corrosive effects such as mass loss bv stellar evolution or tidal heating may also accelerate the dissolution of the cluster."," Therefore, in order to have a dynamically cold subpopulation with $\sigma_{s}<2.5$ km/s, as that observed in UMi at the present time $t_{H}\sim 10$ Gyr, we need $t_{2.5}\geq t_{H}-t_{be}$, which implies the following upperlimit for $M_{h}$ Other corrosive effects such as mass loss by stellar evolution or tidal heating may also accelerate the dissolution of the cluster." +" Therefore. our estimates for tp, and. hence. for Mj. are upper Huits."," Therefore, our estimates for $t_{be}$ and, hence, for $M_{h}$, are upper limits." + The survival probability after collisions with VAIOsIncreases for progenitors that are more compact., The survival probability after collisions with VMOsincreases for progenitors that are more compact. + For instance. if the progenitor were a supercluster with a core radius r.z0.5 pe aud central density ~3«Lot M. 7. the probability of its remaining eravitationally bound after 6 Cyr is ~25%.for My=6.5<10011 AL...," For instance, if the progenitor were a supercluster with a core radius $r_{c}\approx 0.5$ pc and central density $\sim 3\times 10^{4}$ $_{\odot}$ $^{-3}$, the probability of its remaining gravitationally bound after $6$ Gyr is $\sim 25\%$,for $M_{h}=6.5\times 10^{3} f^{-1}$ $_{\odot}$." +" Hence. there may be a nou-neglieible probability that such a supercluster has survived bound for 6 Gyr aud that during the subsequent 4 Cyr it is dynamically heated by 6.5«lof1 NL, VMOS to reach a,=2.5 lau/s at the xeseut time."," Hence, there may be a non-negligible probability that such a supercluster has survived bound for $6$ Gyr and that during the subsequent $4$ Gyr it is dynamically heated by $6.5\times 10^{3} f^{-1}$ $_{\odot}$ VMOs to reach $\sigma_{s}=2.5$ km/s at the present time." + Unfortunately. the evaporation time for this supercluster. setting the scale for dynamical dissolution * iuternal processes. is verv short.," Unfortunately, the evaporation time for this supercluster, setting the scale for dynamical dissolution by internal processes, is very short." +" Tn fact. for such a stellar cluster. the evaporation time is ~20f,4,. with fj, he halfinass relaxation time (Cuedin&Ostriker1997)."," In fact, for such a stellar cluster, the evaporation time is $\sim 20 t_{rh}$, with $t_{rh}$ the half-mass relaxation time \citep{gne97}." +. The resulting evaporation time is =1 Car for au average stellar mass zd ALD. aud. hence. internal processes would rave produced a fast desiutegration of such a cluster.," The resulting evaporation time is $\lesssim 1$ Gyr for an average stellar mass $\geq 1$ $_{\odot}$ and, hence, internal processes would have produced a fast desintegration of such a cluster." + We conclude that the upper lait eiveu iu Eq. (7)), We conclude that the upper limit given in Eq. \ref{eq:mh}) ) + is realistic and robust., is realistic and robust. +" Our approximations break down when the halo oulv contains a few VALOs: at least 5 objects within a radius of GOO pe are required. inplviug that our analysis is restricted tomasses Af,<2<10*£ AL..."," Our approximations break down when the halo only contains a few VMOs; at least $5$ objects within a radius of $600$ pc are required, implying that our analysis is restricted to masses $M_{h}<2\times 10^{7}f$ $_{\odot}$." + In Fig. 2..," In Fig. \ref{fig:massfraction}," + the observational limits on VMOs over a wide range of masses anc dark matter fractions are shown., the observational limits on VMOs over a wide range of masses and dark matter fractions are shown. + The analvsis of the survival of Foruax's CC's rules out the mass range that would be interesting for explaining the origin of dark matter cores in dwarf galaxies (I&02: Coerdtetal.2006:Sáuchez-Saleedo 20063). because the relaxation timescale for VALOs of mass x:5<104 M. exceeds the Uhibble tine.," The analysis of the survival of Fornax's GCs rules out the mass range that would be interesting for explaining the origin of dark matter cores in dwarf galaxies (K03; \citealt{goe06, san06}) ), because the relaxation timescale for VMOs of mass $\leq 5\times 10^{4}$ $_{\odot}$ exceeds the Hubble time." + Moreover. it was found that the inteerity of cold small-scale clusteriue seen in some dSpls inrposes iiore stringent constraints ou the mass of VAIOs.," Moreover, it was found that the integrity of cold small-scale clustering seen in some dSphs imposes more stringent constraints on the mass of VMOs." + A source of mucertaiuty is the mean deusitv ofdark matter within the core of dSphs., A source of uncertainty is the mean density of dark matter within the core of dSphs. + In theparticulary case of UAG aud according to the scaling relations compiled im Roniueudv 1).. the corresponding central dark matter deusity is 0.35 M... 7.," In theparticular case of UMi and according to the scaling relations compiled in \citet{kor04}, , the corresponding central dark matter density is $0.35$ $_{\odot}$ $^{-3}$ ." + A slightly larger value Las been derived from its luternal dvnauiucs (Willsimsonetal.2006)., A slightly larger value has been derived from its internal dynamics \citep{wil06}. +. At a density pay=0.35 M. 72 Eq. (7))," At a density $\rho_{\rm dm}=0.35$ $_{\odot}$ $^{-3}$ , Eq. \ref{eq:mh}) )" +" naplies that AL,20000 AU. e.g. ?2?7..," The Galactic potential exerts a force on Oort cloud comets, and is important for the steady state flux of comets with $a > 20000$ AU, e.g. \cite{Byl1983,Heisler86,Matese89}." + Phe Galactic tidal force has a dominant component that is perpendicular to the Galactic plane: the radial component is 10 times weaker than the perpendicular component 2.., The Galactic tidal force has a dominant component that is perpendicular to the Galactic plane; the radial component is 10 times weaker than the perpendicular component \cite{Heisler86}. + For this reason. many studies (c.g. 77)) have assumed that the radial Galactic tidal field component is negligible.," For this reason, many studies (e.g. \citealt{Matese1995,Wick2008}) ) have assumed that the radial Galactic tidal field component is negligible." + Other studies have included: the radial component. for more accurate moclelling of cometary motion. such as in ??..," Other studies have included the radial component, for more accurate modelling of cometary motion, such as in \cite{Matese96,Brasser01}." + Phe radial component of the tide has 2001 found to have an clleet on the long-term evolution of he comets’ perihelia. on the distribution of the longitudes of he perihelion (?).. and the origin of chaos in the cometary motion (7)..," The radial component of the tide has been found to have an effect on the long-term evolution of the comets' perihelia, on the distribution of the longitudes of the perihelion \citep{Matese96}, and the origin of chaos in the cometary motion \citep{Breiter2008}." + In recent large scale. simulations. ?.— found hat a fundamental role is plavecl by perturbations due ο passing stars on comets. contrary to the investigations during the previous two decades. starting with ?..," In recent large scale simulations, \cite{Rickman08} found that a fundamental role is played by perturbations due to passing stars on comets, contrary to the investigations during the previous two decades, starting with \cite{Heisler86}." + Phe stellar »erturbations. do of course act together with the Galactic ido.," The stellar perturbations, do of course act together with the Galactic tide." + The topic of this paper is the ellect on comets due to he Galactic tide alone., The topic of this paper is the effect on comets due to the Galactic tide alone. + We use a realistic model of the local Galaxy. which is well constrained. by observations. which contains a disc. bulge and halo.," We use a realistic model of the local Galaxy, which is well constrained by observations, which contains a disc, bulge and halo." + We follow the orbit of the Sun in this model using recent constraints on the Solar motion., We follow the orbit of the Sun in this model using recent constraints on the Solar motion. + This motion allows us to compute the change in the vertical and radial components of the Galactic tide with time. and the change in the tidal force due to the radial motion of the Sun is fully accounted for.," This motion allows us to compute the change in the vertical and radial components of the Galactic tide with time, and the change in the tidal force due to the radial motion of the Sun is fully accounted for." + Qualitatively. the tidal effect on the cometary orbits can be evaluated by studying the change in angular momentunir averaged over one orbit.," Qualitatively, the tidal effect on the cometary orbits can be evaluated by studying the change in angular momentum averaged over one orbit." + Phe Galactic tidal force periodically, The Galactic tidal force periodically +"fine-structure constant work significantly; velocity shifts which vary with wavelength — i.e., effects which would shift one absorption feature with respect to another at a different wavelength — are most important (e.g., Webb et al.","fine-structure constant work significantly; velocity shifts which vary with wavelength – i.e., effects which would shift one absorption feature with respect to another at a different wavelength – are most important (e.g., Webb et al." + 1999; Murphy et al., 1999; Murphy et al. + 2009)., 2009). +" Thus, we are most interested in the relative intra-order shifts within each exposure of typically 100 ms~! and occasionally as high as 500 ms-!."," Thus, we are most interested in the relative intra-order shifts within each exposure of typically 100 $\ms$ and occasionally as high as 500 $\ms$." +" The cause of these intra-order shifts is not completely understood, but some possibilities will be discussed below."," The cause of these intra-order shifts is not completely understood, but some possibilities will be discussed below." + Another way of visualizing the velocity shifts in Figures 1 and 2 is to plot the shift distributions., Another way of visualizing the velocity shifts in Figures \ref{fig:vshiftallu} and \ref{fig:vshiftalll} is to plot the shift distributions. + These are shown in Figure 3 which are just histograms of the shifts for each of the exposures., These are shown in Figure \ref{fig:shifthisto} which are just histograms of the shifts for each of the exposures. +" The shift from each fine wavelength bin is given equal weight in the figure, which, if normalized, can therefore be interpreted as a sort of probability of finding a shift of that value."," The shift from each fine wavelength bin is given equal weight in the figure, which, if normalized, can therefore be interpreted as a sort of probability of finding a shift of that value." +" We use this histogram in this way below when we investigate the effect these shifts might have on measurements of Ac,", We use this histogram in this way below when we investigate the effect these shifts might have on measurements of $\delalpha$. +" Of course, the shift values for nearby pixels are strongly correlated due to our smoothing, but this is not important for how we use these distributions below."," Of course, the shift values for nearby pixels are strongly correlated due to our smoothing, but this is not important for how we use these distributions below." + We give the values of the means and standard deviations for these histograms in Table 2.., We give the values of the means and standard deviations for these histograms in Table \ref{tab:means}. +" Again, it is only the width (sigma) of each histogram that is relevant for fine-structure constant work, and not the overall average shift which is the histogram mean."," Again, it is only the width (sigma) of each histogram that is relevant for fine-structure constant work, and not the overall average shift which is the histogram mean." +" As discussed above, the exposure-dependent, overall average velocity shifts are of the magnitude one may expect from errors in the position of the QSO in the spectrograph slit."," As discussed above, the exposure-dependent, overall average velocity shifts are of the magnitude one may expect from errors in the position of the QSO in the spectrograph slit." +" These types of shifts could also be caused by grating shifts, temperature/pressure drifts, etc."," These types of shifts could also be caused by grating shifts, temperature/pressure drifts, etc." +" In preliminary work using the UVES iodine cell on exposures toward bright stars, we do find that varying the position of the star within the slit can give shifts between Th/Ar and iodine calibrations of around 1500 ms-!, making this a likely contributor."," In preliminary work using the UVES iodine cell on exposures toward bright stars, we do find that varying the position of the star within the slit can give shifts between Th/Ar and iodine calibrations of around 1500 $\ms$, making this a likely contributor." +" Next, we would like to explore the possibility that there is a relatively constant intra-order distortion that repeats for each order and is constant between exposures."," Next, we would like to explore the possibility that there is a relatively constant intra-order distortion that repeats for each order and is constant between exposures." +" If the intra-order distortion pattern for a given object exposure can be well approximated from a subsequent Io exposure, either of the QSO or of a nearby bright star, then one can correct the Th/Ar wavelength scale of the former, i.e., a sort of calibration transfer function can be established and applied."," If the intra-order distortion pattern for a given object exposure can be well approximated from a subsequent $_2$ exposure, either of the QSO or of a nearby bright star, then one can correct the Th/Ar wavelength scale of the former, i.e., a sort of calibration transfer function can be established and applied." +" We are interested in the effect of wavelength calibration on Aa; where Avj; is the velocity differencebetween two lines, i and j within the one spectrum."," We are interested in the effect of wavelength calibration on $\delalpha$, where $\Delta v_{ij}$ is the velocity difference two lines, $i$ and $j$ within the one spectrum." + Examination of Figures 1 and 2 might give one the impression that there is a pattern of intra-order velocity offsets that repeats in each echelle order., Examination of Figures \ref{fig:vshiftallu} and \ref{fig:vshiftalll} might give one the impression that there is a pattern of intra-order velocity offsets that repeats in each echelle order. +" To test this hypothesis, we overlaid all the echelle orders of each exposure on their common CCD pixel scale and then"," To test this hypothesis, we overlaid all the echelle orders of each exposure on their common CCD pixel scale and then" +we choose N=LL sapling frequencies i; equallv spaced. in οσαΕμάς scale.from 1017 to 1.5ς1075 IIz.,"we choose $N=41$ sampling frequencies $\nu_i$ equally spaced, in logarithmic scale,from $10^{15}$ to $1.5\times10^{18}$ Hz." + Also. to calculate EMS and EN we assmme qa=LOPAL. which allows us to significantly reduce the computational time needed to produce the spectra with respect to a larger outer radius.," Also, to calculate $L^{\rm MN}$ and $L^{\rm Kerr}$ we assume $r_{\rm out}=10^3 M$, which allows us to significantly reduce the computational time needed to produce the spectra with respect to a larger outer radius." + The regions of parameter space which are viable οσον) 2-0.↴∖↽∖⋡∖ , The regions of parameter space which are viable present $\log_{10}(\chi_{\rm red}^2)<0$ . +"As expected.2 44, presentspresent a πα ήaround «* =O8Ll. 4=0 (due to Eq. (22)."," As expected, $\chi_{\rm red}^2$ presents a minimum around $a^\star=0.84$, $q=0$ (due to Eq. \ref{chi2}) )," + - is exactly <0 there). but also the surroundiug e is in agreenient with the data (see the right panel of Fig. 8)).," $\chi_{\rm red}^2$ is exactly $0$ there), but also the surrounding “valley” is in agreement with the data (see the right panel of Fig. \ref{whole}) )." +" Moreover. a larger “valley” (featuring a central ""basin) with xz,xl exists ο ας0:3 and α20.5. separated from the first one by a saddle."," Moreover, a larger “valley” (featuring a central “basin”) with $\chi_{\rm red}^2<1$ exists for $q\lesssim-0.3$ and $a\gtrsim-0.5$, separated from the first one by a saddle." +" The physical interpretation of these two allowed ""vallevs is quite straightforward.", The physical interpretation of these two allowed “valleys” is quite straightforward. +" They stretch across the red line in Fig. δι,"," They stretch across the red line in Fig. \ref{whole}," + which corresponds the (a.4) for which (o.q)=g(ea5.q0). where ατανα=0) is the efficiency of the err model that we use to minick the data for 1133 This fact is easy to uuderstaud.," which corresponds the $(a,q)$ for which $\eta(a,q)=\eta(a=a^\star,q=0)$, where $\eta(a=a^\star,q=0)$ is the efficiency of the Kerr model that we use to mimick the data for M33 This fact is easy to understand." +" In our analyds ο πας that the bolometric Iuninositv. Lj,=te.qiue is fixed and given by (Logg=g(ea*.q0)AF, where Af denotes the accretion rate of NE. N-T."," In our analysis we assume that the bolometric luminosity, $L_{\rm bol}=\eta(a,q) \dot{M} c^2$ is fixed and given by $\ell^\star L_{\rm edd}=\eta(a=a^\star,q=0) \dot{M}^\star c^2$, where $\dot{M}^\star$ denotes the accretion rate of M33 X-7." + The accretion rate AL is coustrained to be close to AT* in order for the spectrum to reproduce that of N33 N-77 at low frequencies., The accretion rate $\dot{M}$ is constrained to be close to $\dot{M}^\star$ in order for the Manko-Novikov spectrum to reproduce that of M33 X-7 at low frequencies. + This is because AL basically regulates the slope of the spectrum at low frequeucies: from Eq. (?2)), This is because $\dot{M}$ basically regulates the slope of the spectrum at low frequencies: from Eq. \ref{eq-lum}) ) + one gets Liv)~T at small frequencies. but TxM! because of Eq. (??))," one gets $L(\nu)\sim T$ at small frequencies, but $T\propto \dot{M}^{1/4}$ because of Eq. \ref{fluxeq}) )" + and the blackbody assiuption., and the blackbody assumption. + Therefore. if ALOM one obtains that it must he καν)~μα=aq0).," Therefore, if $\dot{M}\sim\dot{M}^\star$ one obtains that it must be $\eta(a,q)\sim\eta(a=a^\star,q=0)$." + We stress that we have determined. these two allowed regions uuder the conservative assumption (15)) for the error σ., We stress that we have determined these two allowed regions under the conservative assumption \ref{err}) ) for the error $\sigma$. + Iu Eq. (15)), In Eq. \ref{err}) ) + we basically asstuned that the errors determined by Liuetal.(2008.2010) for (6 and e were uncorrelated. which could result iu an estinate slightly larger than the real observational errors.," we basically assumed that the errors determined by \citet{m33x7,m33x7e} for $\ell$ and $a$ were uncorrelated, which could result in an estimate slightly larger than the real observational errors." + This is hiuted at also by Fig. &.., This is hinted at also by Fig. \ref{whole}. + Tf one assumes q=0 if one adopts the I&c-DIT hypothesis) Fig., If one assumes $q=0$ if one adopts the Kerr-BH hypothesis) Fig. + 5 shows that the allowed spins would be 0.65πα©0.95. whereas Linctal.(2008. fud 4*=O1c0.05.," \ref{whole} shows that the allowed spins would be $0.65\lesssim a\lesssim0.95$, whereas \citet{m33x7,m33x7e} find $a^\star=0.84\pm0.05$." +" If our naive assunption overstiiated the real observational errors bv a factor V/10nas=23.16.a x5, would decrease by a factor 10. effectively restricting the allowed (e.g) to the 1 regionsotfof Fig."," If our naive assumption overstimated the real observational errors by a factor $\sqrt{10}\approx3.16$, $\chi_{\rm red}^2$ would decrease by a factor 10, effectively restricting the allowed $(a,q)$ to the regions of Fig." +"Fie 8. where log,ide-11.", \ref{whole} where $\log_{10}(\chi_{\rm red}^2)<-1$. +" OneOno canc seefoo that forfov o9¢—=0. logy:gig)21 would be ruled out."," For example, if the errors were $\sqrt{10}\approx3.16$ larger than our assumption, only the region with $\log_{10}(\chi_{\rm red}^2)>1$ would be ruled out." + We discuss possibο sources of svstematic error in the next section., We discuss possible sources of systematic error in the next section. + We stress. lowe that the presence of significant svstenmiaties wolld not oulv jeopardize our test of the theorem. but would represent a very serious problem also for the spin ueasureimieuts with the coutimmun fitting technique. even if the Ieu-DBII hypothesis is adopted. (," We stress, however, that the presence of significant systematics would not only jeopardize our test of the no-hair theorem, but would represent a very serious problem also for the spin measurements with the continuum fitting technique, even if the Kerr-BH hypothesis is adopted. (" +This can be uuderstος by looking at Fig.,This can be understood by looking at Fig. + 8. for g=0: as can be seen. the allowed interval for ο erows rapidly if the eror increases.}," \ref{whole} for $q=0$: as can be seen, the allowed interval for $a$ grows rapidly if the error increases.)" + The coutiuuuan fitting method is a very promusing technique for probing the space-time of stellar-anass DIT cauclicates., The continuum fitting method is a very promising technique for probing the space-time of stellar-mass BH candidates. + Nevertheless. it is Huportaut to keep iu müud that there are sources of of systematic errors that still need to be understood iu order to obtain robust estimates of the spin parameter (f one assunes the Ίνα hvpothesis) or constraints on the anomalous quadrupole moment with this iiethod.," Nevertheless, it is important to keep in mind that there are sources of of systematic errors that still need to be understood in order to obtain robust estimates of the spin parameter (if one assumes the Kerr-BH hypothesis) or constraints on the anomalous quadrupole moment with this method." + The main source of uucertaiuty is the estimate of the hardening factor. sometimes called color factor. ρω.," The main source of uncertainty is the estimate of the hardening factor, sometimes called color factor, $f_{col}$." + Because in he inner part of the disk the teixperatire exceeds 10° Is. nou-thermal processes are non-neeheible aud the spectrum observed by a distant observer is not the blackhbody-like spectrmm coniputec| from the disks effective temperature T.," Because in the inner part of the disk the temperature exceeds $10^6$ K, non-thermal processes are non-negligible and the spectrum observed by a distant observer is not the blackbody-like spectrum computed from the disk's effective temperature $T$." + The hardening factor takes this effect iuto account. bv replacing Z7 with the color temperature Ti=£41. aud its vpical values are in the range f;=1.5—2.0.," The hardening factor takes this effect into account, by replacing $T$ with the color temperature $T_{col} = f_{col} T$, and its typical values are in the range $f_{col}= 1.5 - 2.0$." + The computation of the hardening factor requires a reliable model of he disk atinosphere aud its iuportauce has been already stressed in Lietal.(2005)., The computation of the hardening factor requires a reliable model of the disk atmosphere and its importance has been already stressed in \citet{li05}. +. Significant progresses to address his issue have been done in Davisetal.(2005). aud in Davis&IIubeux(οί06).., Significant progresses to address this issue have been done in \citet{davis} and in \citet{davis2}. + The continuum fitting technique also assiunes that the spin of the compact object is perpendicular to the iuner part ofthe accretion disk to within a few degrees., The continuum fitting technique also assumes that the spin of the compact object is perpendicular to the inner part of the accretion disk to within a few degrees. + For stelar-anass DIT caudidates in Nav binary systeiis. we expect this to )o truc. on the basis of binary population svuthesis (Fragosetal.2010).," For stellar-mass BH candidates in X-ray binary systems, we expect this to be true, on the basis of binary population synthesis \citep{bps}." +. While the Bardecu-Petterson effect may also be respousible for this effect. for voung objects the timescale necessary to align the ceutral wart of the disk turus out to be too loug.," While the Bardeen-Petterson effect \citep{b-p} may also be responsible for this effect, for young objects the timescale necessary to align the central part of the disk turns out to be too long." + However. there are also observational data (Maccarone2002) aud theoretical arguments (Fragileetal.2001) sugeestine that tilted disks may be possilde.," However, there are also observational data \citep{tilt1} and theoretical arguments \citep{tilt2} suggesting that tilted disks may be possible." + This assumption will be checked. by uture A-ray polaruuctry observations (Lietal.2009:Schuittiman&IE&rolik2009. 2010).. such as the GEMS mission scheduled for2011.," This assumption will be checked by future X-ray polarimetry observations \citep{li09,schnittman09,schnittman10}, such as the GEMS mission scheduled for2014." + Iu our curent analysis. we have also neelected the effect of light bending. because this is just a preliminary study o determine whether the coutiuuuu fitting method can conceivably be used to coustrain deviations from the kerr uetric.," In our current analysis, we have also neglected the effect of light bending, because this is just a preliminary study to determine whether the continuum fitting method can conceivably be used to constrain deviations from the Kerr metric." + While the effect of light bending must be taken iuto account in a complete analysis of the observational data. it hasbeen quite commonly neglected in simular preliminary studies appeared in the literature 2010)..," While the effect of light bending must be taken into account in a complete analysis of the observational data, it has been quite commonly neglected in similar preliminary studies appeared in the literature \citep{harko_gs,harko_ws,harko_hl,harko_cs,harko_ns}. ." +Gillietal.(2006). studied stars with planets. so their stars are all metal-rich.,"\cite{Gilli06} studied stars with planets, so their stars are all metal-rich." + The top anc centre panels of show the distributions of rotation velocity (top) and age (centre) within the thin disc (green). the thick cise (red)) and he intermediate population (blue) when the local stellar »opulation is divided in this wav.," The top and centre panels of show the distributions of rotation velocity (top) and age (centre) within the thin disc (green), the thick disc (red) and the intermediate population (blue) when the local stellar population is divided in this way." + In the top panel the thick disc stands out for the extent to which its V -distribution extends to low V., In the top panel the thick disc stands out for the extent to which its $V$ -distribution extends to low $V$. + However. its peak laes circular rotation wonky ~l0kms.+ because it has a significant extension to V0.," However, its peak lags circular rotation by only $\sim 10\kms$ because it has a significant extension to $V>0$." + On account of its long tail. the average asvmametric drift of the thick disc is ~22.5kms.7. which is slower than hat of the thin disc by ~ISkms," On account of its long tail, the average asymmetric drift of the thick disc is $\sim 22.5\kms$, which is slower than that of the thin disc by $\sim 18 \kms$." + The intermediate population is much more svnimetrically distributed in V and. like the V-distribution of the thin disc. peaks near V—0 with an average drift of ~LOkms+.," The intermediate population is much more symmetrically distributed in $V$ and, like the $V$ -distribution of the thin disc, peaks near $V=0$ with an average drift of $\sim 10\kms$." + Note that these velocities are relative to the local standard: of. rest (LS). rather than the Sun. which is rotating faster than the LSR by ον5kms+ (ef.Dehnen&Binney 1998).," Note that these velocities are relative to the local standard of rest (LSR), rather than the Sun, which is rotating faster than the LSR by $\sim5\kms$ \citep[cf.][]{DehnenB}. ." + Hence, Hence +ratio to decrease with metallicity.,ratio to decrease with metallicity. + Lo agreement. with the results of Eldridee&Vink(2006) we find that the single-star models that scale the mass-loss rate of WR stars with initial metallicity agree with the observed. trend., In agreement with the results of \citet{evink} we find that the single-star models that scale the mass-loss rate of WR stars with initial metallicity agree with the observed trend. + The binary moclels in this case give a lower WCOC/WN ratio than the single star models., The binary models in this case give a lower WC/WN ratio than the single star models. + This is because. as can be seen in Figures 2. and 3.. the lifetimes of WIN stars increase by a greater [actor than the lifetimes of WC stars in binaries.," This is because, as can be seen in Figures \ref{RSGS} and \ref{WNLS}, the lifetimes of WN stars increase by a greater factor than the lifetimes of WC stars in binaries." + If we combine a population of single and. binary stars the resulting ratio is too low and requires an increase in the WC population relative to the WN population to regain an improved agreement., If we combine a population of single and binary stars the resulting ratio is too low and requires an increase in the WC population relative to the WN population to regain an improved agreement. + The result is similar to that found by Vanbeveren.VanDever&Belkus(2007)., The result is similar to that found by \citet{vanbevwr}. +. There are many studies which investigate the connection between SNe anc massive stars., There are many studies which investigate the connection between SNe and massive stars. + Some studies: consider single-star evolution and predict the initial parameter space and the relative rate of dillerent SN tvpes (Ilegeret.al.μιWA). while other studies are concerned with the evolution of binary-stars (Pocdsiadlowski.Joss&Hsu1992:deDonder&Vanbeveren2003:Izzard.Ramirez-RuizTout.," Some studies consider single-star evolution and predict the initial parameter space and the relative rate of different SN types \citep{H03,ETsne,hmm2004}, while other studies are concerned with the evolution of binary-stars \citep{podsibin1,vanb03,izzysne}." + 2004).. In this section we use our single- and binarv-star models to predict the relative SN rates and determine how they vary with metallicity., In this section we use our single- and binary-star models to predict the relative SN rates and determine how they vary with metallicity. + Firstly. we link our models to cach SN type then. secondly. we predict how the relative SN rates vary with metallicity.," Firstly, we link our models to each SN type then, secondly, we predict how the relative SN rates vary with metallicity." + Core-collapse SNe are. classified according to their lighteurve shapes and spectra., Core-collapse SNe are classified according to their lightcurve shapes and spectra. + Matching stellar models to observed SNe is dificult and example schemes can be found in Legeretal.(2003) and Eldridge&Tout(2004b)., Matching stellar models to observed SNe is difficult and example schemes can be found in \citet{H03} and \citet{ETsne}. +. Here we check the amount of hydrogen in the progenitor model: if there is more than O.OOLAL. of hydrogen left in the stellar envelope the SN is of type LL. otherwise type Ib/c. There are many subtypes. of SNe.," Here we check the amount of hydrogen in the progenitor model: if there is more than $_{\odot}$ of hydrogen left in the stellar envelope the SN is of type II, otherwise type Ib/c. There are many subtypes of SNe." + Phe main distinguishing criterion is the mass of the hydrogen or helium envelope at the time of explosion but sometimes the cireumstellar environment. must also be considered. (Llegeretal.2003:Eldridge&Tout 2004b).," The main distinguishing criterion is the mass of the hydrogen or helium envelope at the time of explosion but sometimes the circumstellar environment must also be considered \citep{H03,ETsne}." +. In this paper we group SN LL sub-twpes (c.g. P. L) together as type HE and SN Ib and le together as tvpe Ib/c. In our single-star models the initial mass range of Ib/c progenitors is restricted. to the most massive stars (Eldridge&Tout2004b).," In this paper we group SN II sub-types (e.g. P, L) together as type II and SN Ib and Ic together as type Ib/c. In our single-star models the initial mass range of Ib/c progenitors is restricted to the most massive stars \citep{ETsne}." +. In our binary-star models the full range of masses can lead to tvpe Ib/c SNe., In our binary-star models the full range of masses can lead to type Ib/c SNe. + SN rates in dillerent galaxy types have been measured for some time (Cappellaroetal.1997:Cappellaro.Evans&‘Turatto1999). and. more recently. SNe observations have been used to determine how the relative rate of tvpe Ib/c to type IE SNe varies with metallicity (Prantzos&Boissicr 2003).," SN rates in different galaxy types have been measured for some time \citep{capp,capp2} and, more recently, SNe observations have been used to determine how the relative rate of type Ib/c to type II SNe varies with metallicity \citep{snevsZ}." +. The errors especially in the absolute rates of the searches are considerable owing to the small sanmiple size and the uncertainties in the completeness., The errors especially in the absolute rates of the searches are considerable owing to the small sample size and the uncertainties in the completeness. + The relative rates are less uncertain as the selection cllects are of similar magnitude and cancel., The relative rates are less uncertain as the selection effects are of similar magnitude and cancel. + We plot our predicted. SN rate. ratios against the observed. ratios in. Fig. δι, We plot our predicted SN rate ratios against the observed ratios in Fig. \ref{typeIbc2II}. + The observations indicate a general trend of a decreasing rate of type Ib/e SNe relative to type HE as metallicity decreases., The observations indicate a general trend of a decreasing rate of type Ib/c SNe relative to type II as metallicity decreases. + This is as expected owing to the decreasing strength of stellar wines with reduced metallicity meaning that fewer stars lose all the hydrogen before core-collapse., This is as expected owing to the decreasing strength of stellar winds with reduced metallicity meaning that fewer stars lose all the hydrogen before core-collapse. + We find that our theoretical predictions agree with the trend. indicated. by the observations., We find that our theoretical predictions agree with the trend indicated by the observations. + However the single, However the single +photometry aud spectroscopy. and couclue that rings with siguilicautly great. inclination can be detected by today racial velocity precision of 1 m/s. Schlichting&Chane(2011) study the nature ol vines that can exist arouud exoplanets. axl conclude that ‘tues arouud close-in planets cau slow uou-trivial Laplacian plaues.,"photometry and spectroscopy, and conclude that rings with significantly great inclination can be detected by today radial velocity precision of 1 m/s. \cite{Schlichting2011} study the nature of rings that can exist around exoplanets, and conclude that rings around close-in planets can show non-trivial Laplacian planes." + This is caused by the increased effects of the planet's quadrupole moment., This is caused by the increased effects of the planet's quadrupole moment. + These so called warped rilgs€» furiish importaut cues about the planet interior aud spin period., These so called warped rings furnish important clues about the planet interior and spin period. + Despite all these proposed methods. LO e@NO-lWOOH OF dlanetary riugs have been observed so far.," Despite all these proposed methods, no exo-moon or planetary rings have been observed so far." + Here. we propose a 1yodel of panetary transit simulatjon that may be used in the search lor exo-moons tlough their signature iu the ight curve of their host plajets.," Here, we propose a model of planetary transit simulation that may be used in the search for exo-moons through their signature in the light curve of their host planets." + Beside the toons. the moclel nay also simulate the t‘ausit ola panet with a ring arouud it.," Beside the moons, the model may also simulate the transit of a planet with a ring around it." + The model we propose here is capable of geuerating transE. light curves nunmericalls. uulike Ixippiο(2011).," The model we propose here is capable of generating transit light curves numerically, unlike \cite{Kipping2011}." +. Albeit the larger processing: time needed to fi ight curves ine this methocl. it has te actvallage of being easily adaptable to iucude new ealures. as additjonal moous. changes iui lie riug plaie Or stals»ots.," Albeit the larger processing time needed to fit light curves using this method, it has the advantage of being easily adaptable to include new features, as additional moons, changes in the ring plane or starspots." + ΤΙe goa is to apply his model to he observatious of the CoRoT aud Ixepey space telescopes. lookitjs) for the photomeric signas that may iudice:ile the presence of mootnO “Vines a‘ouud exoplanets.," The goal is to apply this model to the observations of the CoRoT and Kepler space telescopes, looking for the photometric signals that may indicate the presence of moons or rings around exoplanets." + Our model does not consider the detection o ‘the warped rings slWILL w 11.., Our model does not consider the detection of the warped rings shown by \cite{Schlichting2011}. +. Sue1 ugs are predicted arouil close-i1 exoplanets. witl orbita pe‘iod of a ew days.," Such rings are predicted around close-in exoplanets, with orbital period of a few days." + ThiS. our model is limited to the detectiou of riigs located in the planet's equatorial plane. with larger semijajor axis.," Thus, our model is limited to the detection of rings located in the planet's equatorial plane, with larger semi-major axis." + As the occturatce of such warped riugs depeids on the quacdrupole moment Jo and on tle density of the planet. i is clillicul to stablish a general criterion to the validity of our 1uodel.," As the occurance of such warped rings depends on the quadrupole moment $_{2}$ and on the density of the planet, it is difficult to stablish a general criterion to the validity of our model." +" For example. [or the case o “all exoplajet. with density 3 ο em ""and Jo = 7. warpe rugs occur Or seiui-major axis below 0.05 AU (see Figure 6 ou Schlichting&Chane (2011)))."," For example, for the case of an exoplanet with density 3 g $^{-3}$ and $_{2}$ = $^{-2}$, warped rings occur for semi-major axis below 0.05 AU (see Figure 6 on \cite{Schlichting2011}) )." + Planets with largere semi-niajor axis wi| have rings located iu the planet equatorial plane aud couk be detected yy our umoclel., Planets with larger semi-major axis will have rings located in the planet equatorial plane and could be detected by our model. + The uext section describes the uodel used iu this work. whereas Section 3 presents the application «X this model to a few sπάν cases.," The next section describes the model used in this work, whereas Section 3 presents the application of this model to a few study cases." + Section [ discusses the detectability threshold oL moon aud ring systems., Section 4 discusses the detectability threshold of moon and ring systems. + Finally. tle last section lists our main conclusions.," Finally, the last section lists our main conclusions." + The model used here is based on that of Silva(2003). where the star is considered a disc with limb darkening aud the planet a completely dark disc.," The model used here is based on that of \citet{Silva2003}, where the star is considered a disc with limb darkening and the planet a completely dark disc." + Both stellar aud. planetary parameters cau be fit by the model., Both stellar and planetary parameters can be fit by the model. + To miuimize the number of free parameters. we consider a simple model where the imoon's orbit is coplanar with the planetary oue. aid is also cireular.," To minimize the number of free parameters, we consider a simple model where the moon's orbit is coplanar with the planetary one, and is also circular." + Looking at the Solar Systems moos. we see that these assuimptious are a little limiting.," Looking at the Solar System's moons, we see that these assumptions are a little limiting." + However. as this is our first," However, as this is our first" +are correct. and the error bars are not underestimated. the results for all of these planets imply that dramatic revisions to models of these atmospheres are needed.,"are correct, and the error bars are not underestimated, the results for all of these planets imply that dramatic revisions to models of these atmospheres are needed." + Given the uncertainties in the reduction of IRAC transit data. it may be up to to confirm speculations about the molecules present at the terminator of436b.," Given the uncertainties in the reduction of IRAC transit data, it may be up to to confirm speculations about the molecules present at the terminator of." +. We now evaluate the observability of the differences in the models by comparing them through the eyes ofJ/WST., We now evaluate the observability of the differences in the models by comparing them through the eyes of. +. We have developed a code that simulates spectra by computing the number of photons detected using a model of the host star. a transmission model of the planet. and estimates of the total efficiency (detected electrons per incident photon) at each wavelength for the various dispersive spectroscopic modes.," We have developed a code that simulates spectra by computing the number of photons detected using a model of the host star, a transmission model of the planet, and estimates of the total efficiency (detected electrons per incident photon) at each wavelength for the various dispersive spectroscopic modes." + Noise is also modeled and added to the simulated spectra., Noise is also modeled and added to the simulated spectra. + The star GJ 436 ts relatively bright over the 0.7—5 jim spectral region. and the transmission models predict that wwill have absorption features from many species over this wavelength range.," The star GJ 436 is relatively bright over the $0.7 - 5$ $\mu$ m spectral region, and the transmission models predict that will have absorption features from many species over this wavelength range." + Therefore we illustrate the model similarities and differences with simulations of observations using the NIRSpee R=A/àAÀ—100 spectroscopie mode over this spectralrange., Therefore we illustrate the model similarities and differences with simulations of observations using the NIRSpec $R \equiv \lambda / \delta \lambda \sim 100$ spectroscopic mode over this spectralrange. + The double-pass CaF> prism used in this mode provides spectroscopic resolution varying from R~30 at 1.2 jim to R>200 at A4.3 jim. We approximate this with à fourth order polynomial fit over the 0.7—5 jim range. and we assume that the prism has total transmission efficiency of 0.8] after two passes.," The double-pass $_{2}$ prism used in this mode provides spectroscopic resolution varying from $R \simeq 30$ at $\lambda \sim 1.2$ $\mu$ m to $R > 200$ at $\lambda > 4.3$ $\mu$ m. We approximate this with a fourth order polynomial fit over the $0.7 - 5$ $\mu$ m range, and we assume that the prism has total transmission efficiency of 0.81 after two passes." + We estimate that the optical efficiency of NIRSpec's 14 reflective surfaces (tePlateetal.2005). is approximately 0.58 over A=1—5 ym. consistent with the values calculated by the NIRSPee team (P. Jakobsen. private communication 2003) and assumed by Demingetal.(2009) after removing the grating blaze function.," We estimate that the optical efficiency of NIRSpec's 14 reflective surfaces \citep{tePlate05} is approximately 0.58 over $\lambda = +1 - 5$ $\mu$ m, consistent with the values calculated by the NIRSPec team (P. Jakobsen, private communication 2003) and assumed by \citet{Deming09} + after removing the grating blaze function." + We adopt a quantum efficiency of 0.75 across the entire A=1—5 jm spectral range. consistent with the NIRSpec detector requirements (Rauscheretal. 2007).," We adopt a quantum efficiency of 0.75 across the entire $\lambda = 1 - 5$ $\mu$ m spectral range, consistent with the NIRSpec detector requirements \citep{BRauscher07}." +. The telescope is estimated to have total reflectivity of 0.9 across this wavelength range., The telescope is estimated to have total reflectivity of 0.9 across this wavelength range. + Total efficiency was modeled to decrease linearly by a factor of 2.0 as wavelength decreases from 1.0 to 0.7 jam. driven mostly by reduction in reflectivity in the 14 reflective NIRSpec surfaces.," Total efficiency was modeled to decrease linearly by a factor of 2.0 as wavelength decreases from 1.0 to 0.7 $\mu$ m, driven mostly by reduction in reflectivity in the 14 reflective NIRSpec surfaces." + Like Demingetal.(2009).. we assume there will be no losses from the 166 wide entrance slit and that the only significant noise sources are photon noise and systematic noise due to small guiding errors during exposures.," Like \citet{Deming09}, we assume there will be no losses from the 6 wide entrance slit and that the only significant noise sources are photon noise and systematic noise due to small guiding errors during exposures." + Photon noise is simulated by adding Poisson noise appropriate for the number of detected photo-electrons in each resolution bin., Photon noise is simulated by adding Poisson noise appropriate for the number of detected photo-electrons in each resolution bin. + We adopt the systematic noise value of 5«10? estimated by Demingetal. (2009)., We adopt the systematic noise value of $5 \times 10^{-5}$ estimated by \citet{Deming09}. +. We do assume that this noise is Gaussian in its distribution although Demingetal.(2009) found that it was somewhat non-Gaussian., We do assume that this noise is Gaussian in its distribution although \citet{Deming09} found that it was somewhat non-Gaussian. + Even with high precision JWST instruments. we will suffer systematic noise at these modest but significant levels.," Even with high precision JWST instruments, we will suffer systematic noise at these modest but significant levels." +" In the ""J-(in-transit/star)” computation. any additional natural or instrumental noise occurmnng at frequencies greater than the inverse of the transit observation period will impact the extracted spectrum."," In the ""1-(in-transit/star)"" computation, any additional natural or instrumental noise occurring at frequencies greater than the inverse of the transit observation period will impact the extracted spectrum." + This simulation program was coded in C. and it uses the public domain RANLIB package for simulating photon noise and Gaussian systematic noise.," This simulation program was coded in C, and it uses the public domain RANLIB package for simulating photon noise and Gaussian systematic noise." + A high fidelity stellar model of the GJ 436 host star was not readily available. so we used a model of GJ 411 which has M2 V spectral type. similar to the M2.5 V type of GJ 436.," A high fidelity stellar model of the GJ 436 host star was not readily available, so we used a model of GJ 411 which has M2 V spectral type, similar to the M2.5 V type of GJ 436." +" Using our simulation code. we re-binned the Kuruez(2009) R=1000 model of GJ 411 to the instrumental resolution of the NIRSpec prism at each wavelength interval over À20.7—5 jim. Next. our code computed the number of stellar photons from this binned flux. reducing it by the ratio of the squared model planet radius divided by the squared stellar radius (assumed to be 3.2«10"" em) at each wavelength."," Using our simulation code, we re-binned the \citet{Kurucz09} $R = 1000$ model of GJ 411 to the instrumental resolution of the NIRSpec prism at each wavelength interval over $\lambda = 0.7 - 5$ $\mu$ m. Next, our code computed the number of stellar photons from this binned flux, reducing it by the ratio of the squared model planet radius divided by the squared stellar radius (assumed to be $3.2 \times 10^{10}$ cm) at each wavelength." + We used a distance of 10.2 pe to GJ 436 and an integration time of 1800 s for these calculations., We used a distance of 10.2 pc to GJ 436 and an integration time of 1800 s for these calculations. + This integration time is ~33% shorter than the 2740 s duration of the transit (Pontetal.2009)., This integration time is $\sim 33\%$ shorter than the 2740 s duration of the transit \citep{Pont09}. +.. We used the resultant simulated in-transit spectrum and the simulated stellar spectrum of equal integration time to compute the absorption depth at each wavelength. | - (in-transit / star).," We used the resultant simulated in-transit spectrum and the simulated stellar spectrum of equal integration time to compute the absorption depth at each wavelength, 1 - (in-transit / star)." + This is plotted for mmodels in Figure 11.., This is plotted for models in Figure \ref{jwst}. +" Models a. ο, and ""e (shown in black. blue. and red respectively) are plotted in the top panel of Figure 11.."," Models `a', `c', and `e' (shown in black, blue, and red respectively) are plotted in the top panel of Figure \ref{jwst}." + These are simulations of the models in the top panel of Figure 6.., These are simulations of the models in the top panel of Figure \ref{double}. +" Models ο”. g. ""h'. and ""i' are plotted in the bottom panel in red. purple. cyan and green respectively. and are simulations of the models in Figure 9.."," Models `e', `g', `h', and `i' are plotted in the bottom panel in red, purple, cyan and green respectively, and are simulations of the models in Figure \ref{photo}." + The absorption features are labeled here for clarity., The absorption features are labeled here for clarity. +" In particular. in the top panel the differences between the water rich model (black) and water poor models (red and blue) are readily apparent. as is the strong CO» feature at 4.3 j/m and CO feature at 4.5 jim. In the bottom panel. the absorption features due to nonequilibrium HCN and C3H» are clearly apparent. as is CH, absorption from 3-4 j/m. The prospects for detailed characterization of this planet. and others with/WST.. is good."," In particular, in the top panel the differences between the water rich model (black) and water poor models (red and blue) are readily apparent, as is the strong $_2$ feature at 4.3 $\mu$ m and CO feature at 4.5 $\mu$ m. In the bottom panel, the absorption features due to nonequilibrium HCN and $_2$ $_2$ are clearly apparent, as is $_4$ absorption from 3-4 $\mu$ m. The prospects for detailed characterization of this planet, and others with, is good." + Given the high brightness of ((K26.1] or Kag=7.9 mag). it is likely that its observation will require use of a detector subarray that is smaller in the dispersion direction than the ~350 pixel length of the complete 0.6—5 um R~100 spectrum (Tumlinson2008).," Given the high brightness of $K = 6.1$ or $K_{\rm AB} = 7.9$ mag), it is likely that its observation will require use of a detector subarray that is smaller in the dispersion direction than the $\sim 350$ pixel length of the complete $0.6 - +5$ $\mu$ m $R \sim 100$ spectrum \citep{Tum08}." +. Therefore. we find that acquiring the entire spectrum shown at the signal-to-noise in Figure 11. may require 2 or 3 transits.," Therefore, we find that acquiring the entire spectrum shown at the signal-to-noise in Figure \ref{jwst} may require 2 or 3 transits." + These observations may be best acquired in the higher resolution R=1000 mode for stars as bright as GJ 436., These observations may be best acquired in the higher resolution $R = 1000$ mode for stars as bright as GJ 436. + At A25—10 jim MIRI low resolution spectrograph (LRS: R ~ 100) observations were also simulated for these models in a similar fashion using details of LRS models and actual measured performance., At $\lambda = 5 - 10$ $\mu$ m MIRI low resolution spectrograph (LRS; R $\sim$ 100) observations were also simulated for these models in a similar fashion using details of LRS models and actual measured performance. + These simulations are shown in Figure 12. and are another independent way of looking at the effects of nonequilibrium chemistry in the atmosphere of436b., These simulations are shown in Figure \ref{ir} and are another independent way of looking at the effects of nonequilibrium chemistry in the atmosphere of. +". In the top panel (models ""à. ο and e? are shown as black. blue. and red respectively). water is the main opacity source in this wavelength range."," In the top panel (models `a', `c' and `e' are shown as black, blue, and red respectively), water is the main opacity source in this wavelength range." +" The bottom panel (showing models ""e. g. ""hb. and v as red. purple. cyan. and green respectively) shows the clear distinction of HCN and C5H» between the different models shown at 7 gm. Absorption from CH, is shown at 9.5 im as well."," The bottom panel (showing models `e', `g', `h', and `i' as red, purple, cyan, and green respectively) shows the clear distinction of HCN and $_2$ $_2$ between the different models shown at 7 $\mu$ m. Absorption from $_2$ $_4$ is shown at 9.5 $\mu$ m as well." +" Observations using MIRI will be the only way to probe the 9.5 ;/m feature created by the presence of C,H4.", Observations using MIRI will be the only way to probe the 9.5 $\mu$ m feature created by the presence of $_2$ $_4$ . + The simulations were also made for a total integration time of 30 m in transit and 30 m on the star., The simulations were also made for a total integration time of 30 m in transit and 30 m on the star. + The flux of GJ 436 is less than | Jy over this wavelength range. faint enough for its entire ΑΞ5--10 jim spectrum to be acquired simultaneously. which is an advantage MIRI will have over NIRSpec observations that require multiple transits to obtain the full spectrum.," The flux of GJ 436 is less than 1 Jy over this wavelength range, faint enough for its entire $\lambda = 5 - 10$ $\mu$ m spectrum to be acquired simultaneously, which is an advantage MIRI will have over NIRSpec observations that require multiple transits to obtain the full spectrum." +detected at the expected position of the T-type brown dwarf binary (see Tab.,detected at the expected position of the T-type brown dwarf binary (see Tab. + 2. and Fig. 3))., \ref{tab:log} and Fig. \ref{fig:atcamaps}) ). + Since short duration flares could be missed in the 2-day images. we have generated maps down to I-hour duration but still detected no source (typical rms notse levels of 120 and 155 at 4.8 and 8.64 GHz. respectively).," Since short duration flares could be missed in the 2-day images, we have generated maps down to 1-hour duration but still detected no source (typical rms noise levels of $120$ and $155$ at 4.8 and 8.64 GHz, respectively)." + Our non-detection limits areconsistent. with those of Blank(2005) but we went deeper since we observed e Ind Bab about twice as long., Our non-detection limits areconsistent with those of \citet{blank05} but we went deeper since we observed $\epsilon$ Ind Bab about twice as long. + At the distance of the binary (3.626 pc). the 3o upper limits correspond to radio luminosities. Lg. of 1.23«1015 and 1.74«10% at 4.8 and 8.64 GHz. respectively.," At the distance of the binary $3.626$ pc), the $3\sigma$ upper limits correspond to radio luminosities, $L_\mathrm{R}$, of $1.23 \times 10^{12}$ and $1.74 \times 10^{12}$ at 4.8 and 8.64 GHz, respectively." + observed e Ind Bab at two different times., observed $\epsilon$ Ind Bab at two different times. + We reduced both data sets with the CIAO 3.1 software in combination with CALDB 2.29., We reduced both data sets with the CIAO 3.1 software in combination with CALDB 2.29. + The data were taken in VERY FAINT mode which allowed us to further reduce the background level., The data were taken in VERY FAINT mode which allowed us to further reduce the background level. + We later merged both event files into one single event file (total exposure of 62.5 ksec)., We later merged both event files into one single event file (total exposure of $62.5$ ksec). + No signal was detected at the expected position of e Ind Bab (Tab. 2)):, No signal was detected at the expected position of $\epsilon$ Ind Bab (Tab. \ref{tab:log}) ); + this was confirmed with several source detection algorithms., this was confirmed with several source detection algorithms. + Figure 4. shows an extract of the ACIS-S image (0.2—8 keV)., Figure \ref{fig:chandraim} shows an extract of the ACIS-S image $0.2-8$ keV). + Blank(2005) tentatively associated the source IWGA J220-5647 with ε Ind Bab., \citet{blank05} tentatively associated the source 1WGA J220-5647 with $\epsilon$ Ind Bab. + However. thanks the high spatial resolution ofChandra. we assign the source to a nearby bright X-ray source instead (see Fig. 4)).," However, thanks the high spatial resolution of, we assign the source to a nearby bright X-ray source instead (see Fig. \ref{fig:chandraim}) )." + No optical or near-infrared counterpart to this source could be found in Digitized Sky Survey and Two Micron All Sky Survey images., No optical or near-infrared counterpart to this source could be found in Digitized Sky Survey and Two Micron All Sky Survey images. + No events were detected within 174 of the encircled energy at 0.3 keV) of the expected position of e Ind Bab in the 0.2—8 keV range., No events were detected within $1\farcs 4$ of the encircled energy at 0.3 keV) of the expected position of $\epsilon$ Ind Bab in the $0.2-8$ keV range. + Note that. without the energy filtering. 4 events were detected but all had energies above 10 keV casting severe doubt that they were due to the source rather than the background.," Note that, without the energy filtering, 4 events were detected but all had energies above 10 keV casting severe doubt that they were due to the source rather than the background." + Furthermore. increasing the extraction radius to only allows the detection of a single event.," Furthermore, increasing the extraction radius to only allows the detection of a single event." + To estimate the background contribution. we used a concentric annulus with an inner radius of 3” and an outer radius caleulated such that the annulus’ area was 100 times larger than the area of the circle around the binary (i.e. r4= 14/73).," To estimate the background contribution, we used a concentric annulus with an inner radius of $3$ and an outer radius calculated such that the annulus' area was 100 times larger than the area of the circle around the binary (i.e, $r_\mathrm{out} = 14\farcs 3$ )." + A total of 77 events were detected: consequently. the scaled estimated background contribution is 0.77 events. i.e. à mean background rate of 0.012..," A total of 77 events were detected; consequently, the scaled estimated background contribution is $0.77$ events, i.e., a mean background rate of $0.012$." + We then followed the approach of Kraftetal.(1991) to determine the upper confidence limit using a Bayesian confidence level of which corresponded to 2.99 counts., We then followed the approach of \citet{kraft91} to determine the upper confidence limit using a Bayesian confidence level of which corresponded to $2.99$ counts. + To convert this count rate of 0.048 into an X-ray luminosity. we used one plasma component with solar photospheric abundances (Grevesse&Sauval1998) using the APEC 1.3.1 code (Smithetal.2001) in the XSPEC software (Arnaud.1996).," To convert this count rate of $0.048$ into an X-ray luminosity, we used one plasma component with solar photospheric abundances \citep{grevesse98} using the APEC 1.3.1 code \citep{smith01} in the XSPEC software \citep{arnaud96}." +. We obtained count rates in. the 0.2—8 keV band and X-ray fluxes in the 0.1—10 keV band., We obtained count rates in the $0.2-8$ keV band and X-ray fluxes in the $0.1-10$ keV band. + The latter fluxes were converted into X-ray luminosities. Lx. using the distance of e Ind Bab.," The latter fluxes were converted into X-ray luminosities, $L_\mathrm{X}$, using the distance of $\epsilon$ Ind Bab." + For plasma temperatures of 0.4 to 1.0 keV. the conversion factor is constant. 1.8. 6.5«107 perks!..," For plasma temperatures of $0.4$ to $1.0$ keV, the conversion factor is constant, i.e., $6.5 \times 10^{24}$ per." + For cooler plasma temperatures. the conversion factor increases by factors of 1.16.1.46.1.74. and 3.25 for KT=0.3.0.2.0.15. and 0.1 keV. respectively.," For cooler plasma temperatures, the conversion factor increases by factors of $1.16, 1.46, 1.74$, and $3.25$ for $kT = 0.3, 0.2, 0.15$, and $0.1$ keV, respectively." + Similarly. the factor increases by 1.20.1.33.1.53. and 1.82 for ΚΤΞ1.5.2.3. and 5 keV. respectively.," Similarly, the factor increases by $1.20, 1.33, 1.53$, and $1.82$ for $kT = 1.5, 2, 3$, and $5$ keV, respectively." + Therefore. assuming KT.=0.4—1.0 keV. we obtain Lx<3.16«107..," Therefore, assuming $kT=0.4-1.0$ keV, we obtain $L_\mathrm{X} \la 3.16 \times 10^{23}$." + In the worst case (kT20.1 keV). our upper limit increases to 1.0«1074..," In the worst case $kT=0.1$ keV), our upper limit increases to $1.0 \times 10^{24}$." + Since the ATCA could not separate the binary and would have barely done so. our upper limits (Lj and Lx) can either be attributed to one binary component or the other.," Since the ATCA could not separate the binary and would have barely done so, our upper limits $L_\mathrm{R}$ and $L_\mathrm{X}$ ) can either be attributed to one binary component or the other." + Table 3 gives the upper limits of the luminosity ratios to the bolometric luminosity for each component., Table \ref{tab:lum} gives the upper limits of the luminosity ratios to the bolometric luminosity for each component. +" Our radio upper limits. Ly/Lpep107765—10779 Hz"", do not go as deep as for dMe stars. which are typically detected with ratios of the order of 1075 Hz7!."," Our radio upper limits, $L_\mathrm{R}/L_\mathrm{bol}<10^{-16.8}-10^{-16.0}$ $^{-1}$, do not go as deep as for dMe stars, which are typically detected with ratios of the order of $10^{-18}$ $^{-1}$." + However. the limit at 8.68 GHz is deeper for e Ind Ba than the upper limit obtained at 5.46 GHz with the VLA by Berger(2002) fora TG brown dwarf (our limit at 8.64 GHz for ε Ind Bb is. however. equivalent).," However, the limit at 8.64 GHz is deeper for $\epsilon$ Ind Ba than the upper limit obtained at 8.46 GHz with the VLA by \citet{berger02} for a T6 brown dwarf (our limit at 8.64 GHz for $\epsilon$ Ind Bb is, however, equivalent)." + Berger hypothesized that the radio luminosity relative to the bolometric luminosity would increase with later spectral type. and their strong detection of an L dwarf in radio appears to support this (Bergeretal.2005).," Berger hypothesized that the radio luminosity relative to the bolometric luminosity would increase with later spectral type, and their strong detection of an L dwarf in radio appears to support this \citep{berger05}." +. Similarly. despite the lack of sensitivity of current radio instruments. such a trend is also suggested in a small survey of southern late-M and L dwarfs (Burgasser&Putnam2005).," Similarly, despite the lack of sensitivity of current radio instruments, such a trend is also suggested in a small survey of southern late-M and L dwarfs \citep{burgasser05}." +. On the other hand. our upper limits for T dwarfs do not indicate that this trend continues into the T dwarf domain.," On the other hand, our upper limits for T dwarfs do not indicate that this trend continues into the T dwarf domain." + Deep observations of T dwarfs can. in principle. be very useful since they provide data points at low Tuy: however. the exposure required to achieve the necessary sensitivity for comparison with dMe dwarfs (Le.. Le/Lpo<10775—107? Hz! ) must await the advent of the next generation of radio telescopes.," Deep observations of T dwarfs can, in principle, be very useful since they provide data points at low $T_\mathrm{eff}$; however, the exposure required to achieve the necessary sensitivity for comparison with dMe dwarfs (i.e., $L_\mathrm{R}/L_\mathrm{bol}<10^{-18}-10^{-19}$ $^{-1}$ ) must await the advent of the next generation of radio telescopes." +" In contrast. the sensitivity of allows us to obtain a low Ly/Lpo, ratio."," In contrast, the sensitivity of allows us to obtain a low $L_\mathrm{X}/L_\mathrm{bol}$ ratio." + We reach an upper limit about 10—100 times lower than the Ly/Zgj4 ratios observed in active dMe stars (e.g..Flemingetal.1995.2003).," We reach an upper limit about $10-100$ times lower than the $L_\mathrm{X}/L_\mathrm{bol}$ ratios observed in active dMe stars \citep[e.g.,][]{fleming95,fleming03}." + In fact. our limit is close to the ratio observed in the Sun (as a star) at its activity maximum and to the ratio observed in early-dM stars that do not show Ho in emission (Flemingetal. 1995).," In fact, our limit is close to the ratio observed in the Sun (as a star) at its activity maximum and to the ratio observed in early-dM stars that do not show $\alpha$ in emission \citep{fleming95}." +. Although X-ray observations of ultracool dwarfs are rare (e.g..Rutledgeetal.2000:Schmitt&Liefke2002:2004:StelzerBergeral. 2005).. the X-ray emission in such dwarfs appears to declineet like the Ha emission.," Although X-ray observations of ultracool dwarfs are rare \citep[e.g.,][]{rutledge00,schmitt02,martin02,fleming03,briggs04,stelzer04,berger05}, the X-ray emission in such dwarfs appears to decline like the $\alpha$ emission." + Most X-ray detections were actually obtained during flares. with only afew objects detected in quiescence.," Most X-ray detections were actually obtained during flares, with only a few objects detected in quiescence." + Our non-detection of the T-type e Ind Bab with reinforces the view that the X-ray emission in ultracool dwarfs declines significantly with later spectral type., Our non-detection of the T-type $\epsilon$ Ind Bab with reinforces the view that the X-ray emission in ultracool dwarfs declines significantly with later spectral type. + Bergeretal.(2005) suggested that magnetic activity 15 strong in. ultracool dwarfs. in fact much stronger than in dMe stars. but that it manifests itself mostly 1n the radio. as atmospheric conditions in such dwarfs become unfavorable for Ha and X-ray emission due to the decoupling of the magnetic field from the neutral photospheric gas (Meyer&Meyer-Hofmeister1999:Mohantyetal. 2002).," \citet{berger05} suggested that magnetic activity is strong in ultracool dwarfs, in fact much stronger than in dMe stars, but that it manifests itself mostly in the radio, as atmospheric conditions in such dwarfs become unfavorable for $\alpha$ and X-ray emission due to the decoupling of the magnetic field from the neutral photospheric gas \citep{meyer99,mohanty02}. ." +. Taken alone. the lack of X-rays from e Ind Bab could. in principle. support this view.," Taken alone, the lack of X-rays from $\epsilon$ Ind Bab could, in principle, support this view." + However. Berger(2002) noted that fast rotators C»10 s!) have high Ly/Lo4 ratios.," However, \citet{berger02} noted that fast rotators $>10$ ) have high $L_\mathrm{R}/L_\mathrm{bol}$ ratios." + But e Ind Bab does not follow this trend: Smithetal.(2003) found that the TI component is a fast rotator (vsini=28 ))., But $\epsilon$ Ind Bab does not follow this trend: \citet{smith03} found that the T1 component is a fast rotator $v \sin i = 28$ ). + Note that the stellar radius and period are similar to those of the L3.5 dwarf detected in radio (but not in X-raysor Ha) by Berger (2005).., Note that the stellar radius and period are similar to those of the L3.5 dwarf detected in radio (but not in X-raysor $\alpha$ ) by \citet{berger05}. . + Possibly. the suggested trend observed in late- dwarfs does not hold in the old. cool T dwarfs (Tory=800—1300 K).," Possibly, the suggested trend observed in late-M/early-L dwarfs does not hold in the old, cool T dwarfs $T_\mathrm{eff} = +800-1300$ K)." + Our observation thus suggests a physical, Our observation thus suggests a physical +case at the center of M31 (?)..,case at the center of M31 \citep{lauer93}. + There are also many candidate nuclear disks observed in othersystems (????????2).. ," There are also many candidate nuclear disks observed in othersystems \citep{lauer:ngc4486b, + lauer:centers, + houghton:ngc1399.nuclear.disk, + thatte:m83.double.nucleus,debattista:vcc128.binary.nucleus, + afanasiev:2002.ngc5055.nuclear.disk, + seth:ngc404.nuclear.disk,ledo:2010.nuclear.disk.compilation}. ." +"Figure 1 (top panel) shows the stellar surface density profiles at the end of the ""nuclear-scale"" and “ultra-high” resolution simulations of ?,, which extend inwards from =10— 100pc with ~ O.1pc resolution; we show results in the quasi steady state phase of all simulations with significant inflows, >0.3M5yr into «1 pc, sustained for >10° yr."," Figure \ref{fig:cusp.examples} (top panel) shows the stellar surface density profiles at the end of the ""nuclear-scale"" and “ultra-high” resolution simulations of \citet{hopkins:zoom.sims}, which extend inwards from $\gtrsim10-100\,$ pc with $\sim0.1\,$ pc resolution; we show results in the quasi steady state phase of all simulations with significant inflows, $\ge 0.3\,\msun\,{\rm yr^{-1}}$ into $<1\,$ pc, sustained for $>10^{5}\,$ yr." +" These SPH simulations include gas, stars, star formation, and a black hole as an additional collisionless particle; the simulations are idealized problems focused on studying the nonlinear evolution of gravitationally unstable systems in the potential of a massive black hole."," These SPH simulations include gas, stars, star formation, and a black hole as an additional collisionless particle; the simulations are idealized problems focused on studying the nonlinear evolution of gravitationally unstable systems in the potential of a massive black hole." + ? show that the central dynamicsand inflows are dominated by the nuclear m=1 modes., \citet{hopkins:inflow.analytics} show that the central dynamicsand inflows are dominated by the nuclear $m=1$ modes. +" In Figure 1 the absolute stellar mass densities depend on the initial conditions (e.g., total gas mass), but the slopes are more robust; the simulations shown span a wide range in initial gas fractions, prescriptions for star formation and gas physics, initial stellar and gas mass profiles, and bulge-to-disk ratios (see Tables 1-3 in ?)), but converge to similar slopes."," In Figure \ref{fig:cusp.examples} the absolute stellar mass densities depend on the initial conditions (e.g., total gas mass), but the slopes are more robust; the simulations shown span a wide range in initial gas fractions, prescriptions for star formation and gas physics, initial stellar and gas mass profiles, and bulge-to-disk ratios (see Tables 1-3 in \citealt{hopkins:zoom.sims}) ), but converge to similar slopes." +" Comparing with the observed power law slopes of ellipticals (bottom panel), the agreement is reasonable."," Comparing with the observed power law slopes of ellipticals (bottom panel), the agreement is reasonable." +" In thisLetter, we provide a physical explanation for these results."," In this, we provide a physical explanation for these results." +" Physically, the lopsided or eccentric disk mode (azimuthal wavenumber m=1 or amplitude οςcos$) is unique in any nearly Keplerian potential (?).."," Physically, the lopsided or eccentric disk mode (azimuthal wavenumber $m=1$ or amplitude $\propto \cos{\phi}$ ) is unique in any nearly Keplerian potential \citep{tremaine:slow.keplerian.modes}." + Gravitational torques from other modes are suppressed by the gravity of the BH., Gravitational torques from other modes are suppressed by the gravity of the BH. +" However, the resonant response between the epicyclic and orbital frequencies allows for global, low frequency m=1 modes that can exert strong torques on the gas by inducing orbit crossing and shocks (e.g., ??))."," However, the resonant response between the epicyclic and orbital frequencies allows for global, low frequency $m=1$ modes that can exert strong torques on the gas by inducing orbit crossing and shocks (e.g., \citealt{chang:m31.eccentric.disk.model, hopkins:inflow.analytics}) )." +" Because of the importance of the m=1 modes for redistributing gas inside the potential of the BH, we now focus on the physics of these m=1 modes, in particulartheir propagation to smaller radii."," Because of the importance of the $m = 1$ modes for redistributing gas inside the potential of the BH, we now focus on the physics of these $m = 1$ modes, in particulartheir propagation to smaller radii." +" Consider an initially axisymmetric, thin, planar disk (surface density ©) with a BH of mass Μπη at the coordinate center; we use cylindrical coordinates throughout (R, ¢, z)."," Consider an initially axisymmetric, thin, planar disk (surface density $\Sigma$ ) with a BH of mass $M_{\rm BH}$ at the coordinate center; we use cylindrical coordinates throughout $R$ , $\phi$, $z$ )." +" The initial potential in the disk plane canbe written oΦο(Κ), and other properties are defined in standard terms: where V. is the circular velocity, €) the angular velocity, and & the epicyclic frequency."," The initial potential in the disk plane canbe written $\Phi_{0} = \Phi_{0}(R)$, and other properties are defined in standard terms: where $V_{c}$ is the circular velocity, $\Omega$ the angular velocity, and $\kappa$ the epicyclic frequency." + We use c; to denote the sound speed in a gaseous disk and o; the vertical dispersion in a stellar disk., We use $c_{s}$ to denote the sound speed in a gaseous disk and $\sigma_{z}$ the vertical dispersion in a stellar disk. +" We consider a linear perturbation ©—Xo(R)-Mi(R,Q) (where 2) is the total gas+stellar disk surface density) in a frame rotating with the perturbation pattern speed 2,, and decompose the perturbation into linearly independent modes: where m is the azimuthal wavenumber, |a|=|a(R)| the effective mode amplitude, k the radial wavenumber, and the complex w the mode frequency."," We consider a linear perturbation $\Sigma \rightarrow \Sigma_{0}(R) + \Sigma_{1}(R,\,\phi)$ (where $\Sigma$ is the total gas+stellar disk surface density) in a frame rotating with the perturbation pattern speed $\Omega_{p}$, and decompose the perturbation into linearly independent modes: where $m$ is the azimuthal wavenumber, $|a|=|a(R)|$ the effective mode amplitude, $k$ the radial wavenumber, and the complex $\omega$ the mode frequency." +" With these definitions, the mode pattern speed is 2,= Re(w)/m, and the mode growth rate Im(w)."," With these definitions, the mode pattern speed is $\Omega_{p}\equiv {\rm Re}(\omega)/m$ , and the mode growth rate$\gamma\equiv {\rm Im}(\omega)$ ." +" We adopt a power-law disk as a convenient reference model: =%, It is straightforward to show then that", We adopt a power-law disk as a convenient reference model: = It is straightforward to show then that +the arguments given there must therefore. be taken with caution. until proper calculations will be available).,"the arguments given there must therefore be taken with caution, until proper calculations will be available)." + It should however be noted that. given the proximity to the iron edge. the parameters of the Kes line are necessarily dillicult to estimate. and may suller from a too simple moceling of the edge (Palmeri ct al.," It should however be noted that, given the proximity to the iron edge, the parameters of the $\beta$ line are necessarily difficult to estimate, and may suffer from a too simple modeling of the edge (Palmeri et al." + 2002)., 2002). + The Ni to Fe We line ratio is aboutG4... suggesting a possible Ni overabundance (see again the discussion in Alolendi et al.," The Ni to Fe $\alpha$ line ratio is about, suggesting a possible Ni overabundance (see again the discussion in Molendi et al." + 2003. with the same caution given above).," 2003, with the same caution given above)." + In Table 1.. the EW of the lines with respect to the unabsorbed continuum (to make easier the comparison with the expected value for the iron Ίνα presented. in. Matt 2002). are also given.," In Table \ref{bestfit}, the EW of the lines with respect to the unabsorbed continuum (to make easier the comparison with the expected value for the iron $\alpha$ presented in Matt 2002), are also given." + Ehe value reported in Fig., The value reported in Fig. + 1: of Matt. (2002) are for Alorrison AleCanmon (1983) abundances. and a power aw index of 2.," 1 of Matt (2002) are for Morrison McCammon (1983) abundances, and a power law index of 2." + We therefore caleulated the expected Fe Ίνα »operties using the code described in Matt (2002). adopting he Anders Crevesse abundances and the best fit. value or E. Ng. and js.," We therefore calculated the expected Fe $\alpha$ properties using the code described in Matt (2002), adopting the Anders Grevesse abundances and the best fit value for $\Gamma$, $_{\rm H}$, and $_{\rm Fe}$." + The expected. value of the ratio. f. tween the Compton Shoulder and the line core is 0.44. to »e compared with. a measured value of. 0.1.ΕυULULLης.," The expected value of the ratio, $f$, between the Compton Shoulder and the line core is 0.44, to be compared with a measured value of $0.12 \pm^{0.04}_{0.05}$." + f does no depend much on the geometry. but rather on the column density (Matt. 2002).," $f$ does not depend much on the geometry, but rather on the column density (Matt 2002)." + Phe observed value would corresponc o à column density of a few 07 em or which values around 100 eV. of the EW are expected. (a value of abou 20 eV is instead expected for 1073 em. 7).," The observed value would correspond to a column density of a few $\times10^{23}$ $^{-2}$, for which values around 100 eV of the EW are expected (a value of about 20 eV is instead expected for $\times10^{24}$ $^{-2}$ )." + Phe observer EW is instead. about 13 06V. His then possible that the matter is very inhomogeneous. with a denser blob just on he line of sight (which is what the fit can measure) bu an average optical depth an order of magnitude less. and a covering factor. taking into account the uncertainties on the »ower law. index. of about 0.1.0.2.," The observed EW is instead about 13 eV. It is then possible that the matter is very inhomogeneous, with a denser blob just on the line of sight (which is what the fit can measure) but an average optical depth an order of magnitude less, and a covering factor, taking into account the uncertainties on the power law index, of about 0.1–0.2." + The lower (with respec o the line of sight) average column density. along with the relative small covering factor. would explain the failure of he Matt et al. (," The lower (with respect to the line of sight) average column density, along with the relative small covering factor, would explain the failure of the Matt et al. (" +1999) moclel in fitting the data.,1999) model in fitting the data. + Because there is evidence that the absorbing material has a covering [actor less than 1. part of the Xray illuminated: surface should. be directly visible. producing a Compton reflection component (George Fabian. 1991: Matt. Perola Piro 1991) as commonly observed. in Comptonthick AGN (Matt et al.," Because there is evidence that the absorbing material has a covering factor less than 1, part of the X–ray illuminated surface should be directly visible, producing a Compton reflection component (George Fabian 1991; Matt, Perola Piro 1991) as commonly observed in Compton–thick AGN (Matt et al." + 2000 ancl references therein)., 2000 and references therein). + As discussed. above. the average column censity is possibly as low as a few 101 7: however. below the iron line energy. the rellection component for this column density is very similar to that for Comptonthick matter (Matt ct al.," As discussed above, the average column density is possibly as low as a few $\times10^{23}$ $^{-2}$; however, below the iron line energy the reflection component for this column density is very similar to that for Compton–thick matter (Matt et al." + 2003)., 2003). + This component could therefore account for the excess emission below 5 keV (see Fig. 2..," This component could therefore account for the excess emission below 5 keV (see Fig. \ref{allsp}," + where the whole 0.3-13 keV spectrum is shown. after being fitted with the baseline model). anc down to about 2 keV. (the further excess at lower energies should have a cillerent origin).," where the whole 0.3-13 keV spectrum is shown, after being fitted with the baseline model), and down to about 2 keV (the further excess at lower energies should have a different origin)." + Fitting the 2-13 keV spectrum with the baseline model gives \ =104.968 cd.o.f..," Fitting the 2-13 keV spectrum with the baseline model gives $\chi^2$ =104.9/68 d.o.f.," + and a very Lat (D—0.6) power law., and a very flat $\Gamma$ =0.6) power law. + The acidition of a pure Compton rellection component (with the photon index linked to that of the absorbed power law. and fixed to 1.6) improves the [it significantlv. giving v7—79.9/68 d.o.L. The value of 2. 0.003. implies that the visible part of the illuminated: matter is very small (2? is equal to 1 [or 2- visible solid angle. ie. a covering factor of 0.5).," The addition of a pure Compton reflection component (with the photon index linked to that of the absorbed power law, and fixed to 1.6) improves the fit significantly, giving $\chi^2$ =79.9/68 d.o.f.. The value of $R$, 0.003, implies that the visible part of the illuminated matter is very small $R$ is equal to 1 for $\pi$ visible solid angle, i.e. a covering factor of 0.5)." + As the source lies on the Galactic plane. absorption from interstellar matter is likely to be significant.," As the source lies on the Galactic plane, absorption from interstellar matter is likely to be significant." + We then added an absorption component. but the fit does not significantly iniprove (A-1179 68 d.o.L).," We then added an absorption component, but the fit does not significantly improve $\chi^2$ =77.9/68 d.o.f.)." + The best-fit face value for the column density of this further absorber is about 1077 2. ancl #=0.0045. (," The best-fit face value for the column density of this further absorber is about $\times10^{22}$ $^{-2}$, and $R$ =0.0045. (" +LC this is indeed the column density of the interstellar absorption. the emission below 2 keV is likelv due toanother. nearby. confusing source.),"If this is indeed the column density of the interstellar absorption, the emission below 2 keV is likely due toanother, nearby confusing source.)" + The other parameters are similar to those listed in Table 1.., The other parameters are similar to those listed in Table \ref{bestfit}. + The iron line EW with respect to the reflection component. is very laree. 28 keV. implying that almost all of the line is related to the transmitted component.," The iron line EW with respect to the reflection component is very large, $\sim$ 28 keV, implying that almost all of the line is related to the transmitted component." + Of course. part of the excess emission may be due to photons scattered in. transmission rather than reflection. i.e. escaping from the far side (with respect to the N-rav source) of the obscuring matter.," Of course, part of the excess emission may be due to photons scattered in transmission rather than reflection, i.e. escaping from the far side (with respect to the X-ray source) of the obscuring matter." + The small value of Z2 may. at the first glance. appears rather surprising. given the value of the covering. factor deduced. from the iron line EW and the CS (about 0.1).," The small value of $R$ may, at the first glance, appears rather surprising, given the value of the covering factor deduced from the iron line EW and the CS (about 0.1)." + ]t may be explained if e... the absorber has a Lat configuration (similar to the ‘torus’ envisaged in Unification AMocels for AGN). seen at high inclination.," It may be explained if, e.g., the absorber has a flat configuration (similar to the `torus' envisaged in Unification Models for AGN), seen at high inclination." + LGR. J16318-4848. exhibits a complex variability pattern during the NMM-Newton. observation (sec Fig. 3))., IGR J16318-4848 exhibits a complex variability pattern during the XMM-Newton observation (see Fig. \ref{fig1_mg}) ). + The ph flux varied. by : factor of 2.5 during the first S ks. stabilized at a constant level of 20.155 (O.5-15 keV band) for the next 13 ks and than underwent a sudden burst. brightening by a [actor 2-3 within 2500.1000 s. “Phis behavior is associated with spectral variability.," The pn flux varied by a factor of 2.5 during the first 8 ks, stabilized at a constant level of $\simeq$ $s^{-1}$ (0.5-15 keV band) for the next 13 ks and than underwent a sudden burst, brightening by a factor $\simeq$ 3 within $\simeq$ 500–1000 s. This behavior is associated with spectral variability." + In., In Fig. + big. 4 we show the count. spectra extracted in the 3 consecutive dillerent. time intervals highlighted in Fig. 3: , \ref{fig2_mg} we show the count spectra extracted in the 3 consecutive different time intervals highlighted in Fig. \ref{fig1_mg}: : +0δ ks. S ks. and. 18.525 ks (elapsed time) after the observation," 0–8 ks, 8--18.5 ks, and 18.5–25 ks (elapsed time) after the observation" +dimension as measured ou 2MASS images. and (12) corresponding linear dimecusion.,"dimension as measured on 2MASS images, and (12) corresponding linear dimension." + For the sake of homogeneity we measured the optical imajor angular cdiueusion on first (DSS) aud second eeuecration. (NDSS) digitized sky survey ages using the Canadian Astronomy Data Centre extraction tool fcacdewww., For the sake of homogeneity we measured the optical major angular dimension on first (DSS) and second generation (XDSS) digitized sky survey images using the Canadian Astronomy Data Centre extraction tool ). +dao.urc.cafcadcbin/ectdss}. For larger angular size objects we used film copies of Seluuidt plates from the ESO. red tual) πτ- ⋜⋯≼↧↕↴↕↘↴⋝↕⋯∖⊔↕↑↻∶↖↖⇁↖↖↽↖↖↽∙↥⋅≺⋈∖∙⋜↧↸⊳∙↿∐↘↽↿∐↘↽↴∖↴↑∏↸∖↸∖↴∖↴≼⊳∪↻↸∖⋅≓ htial) «kv survevs., For larger angular size objects we used film copies of Schmidt plates from the ESO red ) and UK blue ) sky surveys. + Pairs. and multiplets. are very colon amoung embedded open clusters., Pairs and multiplets are very common among embedded open clusters. + Distances aud ages . ~= ∣∎⋅⋅ 119 »⋅ in ," Distances and ages are from the WEBDA database (Mermilliod 1996) –, except those indicated in the table notes." +The clusters are indeed voung chough M - a to related to the nebular complexes., The clusters are indeed young enough to be embedded or related to the nebular complexes. + & Cols., Cols. + 10 to will be discussed in Sect., 10 to 12 will be discussed in Sect. + I., 4. + . | | | Siice. embedded: clusters are expected to occur in the area of nebulae. we concentrated search efforts on known optical and radio nebulae. mostv HII regions but also reflection nebulae aud supernova reimuauts.," Since embedded clusters are expected to occur in the area of nebulae, we concentrated search efforts on known optical and radio nebulae, mostly HII regions but also reflection nebulae and supernova remnants." + The search emploved the recently available 2MASS AIL-Sky Release huages provided v ncans of the 2MASS 5iIvey Vistalization huage Server facilitv im the web interface, The search employed the recently available 2MASS All-Sky Release Images provided by means of the 2MASS Survey Visualization Image Server facility in the web interface. +"ipac.caltech.cdiy/. We extracted JITI&, iunages with 5’ <5! centred ou the coordidates: of each nebula.", We extracted $_s$ images with $^{\prime}\times$ $^{\prime}$ centred on the coordinates of each nebula. + For the nebulae wit resizes lareer than 5'« 5 we took additional nuages of V «10 or 15/ «15., For the nebulae with sizes larger than $^{\prime}\times$ $^{\prime}$ we took additional images of $^{\prime}\times$ $^{\prime}$ or $^{\prime}\times$ $^{\prime}$. + The Is. baud nuages allow one to xobe deeper iu more absorbed regious. and the J ane II wand muages were TisCC mostly as control of the presence of brigit stars and as additional check for chster resolvabilitv.," The $_s$ band images allow one to probe deeper in more absorbed regions, and the J and H band images were used mostly as control of the presence of bright stars and as additional check for cluster resolvability." + For he resulting IR star clusters we deermined accurate oositions and dimensions from their nuages in FITS ornat using developed by Doug Mink., For the resulting IR star clusters we determined accurate positions and dimensions from their images in FITS format using developed by Doug Mink. + SAOIIAGE uses information in a 2MASS image 1οcr to transform linear to equatorial coordinates., SAOIMAGE uses information in a 2MASS image header to transform linear to equatorial coordinates. + Centers and angular dimensions are estimated visually on he 2\LASS Dy images., Centers and angular dimensions are estimated visually on the 2MASS $_s$ images. + The optical nebula designations throughout this study are from (ο (Cederblad 1916). Toftleit (Ποπίαί 1953). Camm (Coun 1955). Sh2- (Sharpless 1959). ROW (Rodgers ct al.," The optical nebula designations throughout this study are from Ced (Cederblad 1946), Hoffleit (Hoffleit 1953), Gum (Gum 1955), Sh2- (Sharpless 1959), RCW (Rodgers et al." + 1960). GC (Ceoreclin CGeoreclin 1970a). Cole (Ceorgelin Ceoreclin 197053. vdBII-RN (van den Bereli Παμε 1975). ESO (Lauberts 1982). BFS (Blitz ct al.," 1960), GG (Georgelin Georgelin 1970a), GeGe (Georgelin Georgelin 1970b), vdBH-RN (van den Bergh Herbst 1975), ESO (Lauberts 1982), BFS (Blitz et al." + 1982). Bran (Braud et al.," 1982), Bran (Brand et al." + 1986). BRC (Sugitani Oeura 1991).," 1986), BRC (Sugitani Ogura 1994)." + Some sinall angular size nebulae are from Wray (1966)., Some small angular size nebulae are from Wray (1966). + The radio nebula CG designations are from various studies. namely Wilson et al. (," The radio nebula G designations are from various studies, namely Wilson et al. (" +1970). Caswell (1987) aud I&uchar Clark (1997).,"1970), Caswell (1987) and Kuchar Clark (1997)." + MSIE is from Mills et al. (, MSH is from Mills et al. ( +1961) and refereuces therein. and MIIR youn Alathewsou et al. (,"1961) and references therein, and MHR from Mathewson et al. (" +1962).,1962). + We also inclicate some infrared nebulae related to sources in the AFGL aud IRAS caalogues., We also indicate some infrared nebulae related to sources in the AFGL and IRAS catalogues. + We mereed he differeut catalogues aud lists of nebulae into a radio/iufrared aud an opical nebula fles., We merged the different catalogues and lists of nebulae into a radio/infrared and an optical nebula files. + We cross-ideutified nebulae iu cach file. and then between the," We cross-identified nebulae in each file, and then between the" +the correlalon function of clusters has been stucied mostly up to a scale of ~100Ape. and was characterized by parameers of the power law. the correlation leugth. ry. and the slope of the correlation fiction. 5.,"the correlation function of clusters has been studied mostly up to a scale of $\sim 100$, and was characterized by parameters of the power law, the correlation length, $r_0$, and the slope of the correlation function, $\gamma$." + Values found in the present paper aud eiven in Table 2 are in the rauge found previously (sec. for example. Dalicall West (1992). Croft (1997). Cuzzo (1999). Lee Park (1999). Aloscardiui (2000). Collins (2000)).," Values found in the present paper and given in Table 2 are in the range found previously (see, for example, Bahcall West (1992), Croft (1997), Guzzo (1999), Lee Park (1999), Moscardini (2000), Collins (2000))." + Within the errors the correlation function pariunoeters for Abell clusters coincide with values found iu Paper TT., Within the errors the correlation function parameters for Abell clusters coincide with values found in Paper III. + The shape of the, The shape of the +It thus appears that the metallicity distribution. as derived from high-resolution spectroscopy. on the upper RGB of the II dSph galaxy is dominated by one metallicity with few outliers.,"It thus appears that the metallicity distribution, as derived from high-resolution spectroscopy, on the upper RGB of the I dSph galaxy is dominated by one metallicity with few outliers." + That the outliers are real and not caused by measurement errors is further demonstrated by inspection of the stellar spectra and refsect:obs))., That the outliers are real and not caused by measurement errors is further demonstrated by inspection of the stellar spectra \\ref{fig:spectra} and \\ref{sect:obs}) ). + The stars in our study span about ddex., The stars in our study span about dex. + ? finda total spread of about ddex and ? a spread of ddex., \citet{norris2008} find a total spread of about dex and \citet{martin07} a spread of dex. + Both of these studies include more stars than ours., Both of these studies include more stars than ours. + The position on the sky of our stars do not indicate that. e.g.. the most metal-poor star is at the outskirts of II. In fact. the overall shape and extent of the II dSph are currently poorly constrained.," The position on the sky of our stars do not indicate that, e.g., the most metal-poor star is at the outskirts of I. In fact, the overall shape and extent of the I dSph are currently poorly constrained." + The radial velocity selected stars from ? and ? appear to have complementary sky coverage.," The radial velocity selected stars from \citet{martin07} + and \citet{norris2008} appear to have complementary sky coverage." + All our stars are also studied by ?.. so are radial velocity members (see their 11).," All our stars are also studied by \citet{norris2008}, , so are radial velocity members (see their 1)." + ? have observed stars in the Hercules dSph galaxy and found atypical abundance ratios., \citet{koch2008Her} have observed stars in the Hercules dSph galaxy and found atypical abundance ratios. + The Hercules dSph galaxy is one of the ultra-faint. newly discovered dSph galaxies (??)..," The Hercules dSph galaxy is one of the ultra-faint, newly discovered dSph galaxies \citep[][]{belokurovcats,aden}." + One star in Draco. a classical dSph galaxy. also shows this unusual abundance pattern (Dra-119?)..," One star in Draco, a classical dSph galaxy, also shows this unusual abundance pattern \citep[Dra-119][]{fulbright2004Draco}." + We find one star in the II dSph galaxy that clearly shows the same unusual [Mg/Ca] pattern. Boo-127 refmgca.fig)).," We find one star in the I dSph galaxy that clearly shows the same unusual [Mg/Ca] pattern, Boo-127 \\ref{mgca.fig}) )." + It is also possible that Boo-094 shows similar traits but not as clearly., It is also possible that Boo-094 shows similar traits but not as clearly. + It is clear that Her-2 and Her-3. Dra-119. and Boo-127 all stand out very clearly from the common trend.," It is clear that Her-2 and Her-3, Dra-119, and Boo-127 all stand out very clearly from the common trend." + Even with large errors in the stellar parameters. Boo-127 cannot be made compatible with the general trend found for the other RGB stars in the IL dSph galaxy.," Even with large errors in the stellar parameters, Boo-127 cannot be made compatible with the general trend found for the other RGB stars in the I dSph galaxy." + Note also that we have 3-4 Mg lines 1n our abundance analysis. while ? only used one.," Note also that we have 3-4 Mg lines in our abundance analysis, while \cite{koch2008Her} only used one." + Our four lines show consistent and high Mg abundances (cf., Our four lines show consistent and high Mg abundances (cf. + 11)., 1). + Thus our results confirm and strengthen the results found for the Draco and Hercules dSph galaxies., Thus our results confirm and strengthen the results found for the Draco and Hercules dSph galaxies. + Additionally. ? and? find that Her-2. Her-3. and Dra-119. respectively. have extremely weak or nonexistent lines resulting in upper limits on the [Ba/H] abundances.," Additionally, \citet{koch2008Her} and \citet{fulbright2004Draco} find that Her-2, Her-3, and Dra-119, respectively, have extremely weak or nonexistent lines resulting in upper limits on the [Ba/H] abundances." + For the stars in the II dSph galaxy. this does not appear to be the case (compare reffig:spectra)).," For the stars in the I dSph galaxy, this does not appear to be the case (compare \\ref{fig:spectra}) )." + We have not derived abundances for Boo-094. because on closer inspection. the lines are not free from blemishes. but they are clearly visible in the stellar spectra.," We have not derived abundances for Boo-094, because on closer inspection, the lines are not free from blemishes, but they are clearly visible in the stellar spectra." + However. for metal-poor stars. like Boo-094. the S/N of the spectrum is clearly important for a positive detection of the line at nnm (compare Fig.1)).," However, for metal-poor stars, like Boo-094, the S/N of the spectrum is clearly important for a positive detection of the line at nm (compare \ref{fig:spectra}) )." + A comparison with Fig.22 in ?. shows that it might be possible that the line ts buried in the noise., A comparison with 2 in \citet{koch2008Her} shows that it might be possible that the line is buried in the noise. + Those spectra also have somewhat lower resolution., Those spectra also have somewhat lower resolution. + Koch (2009. priv.com.)," Koch (2009, priv.com.)" + confirms that this might be a possibility. but that it is unlikely that. if the line was present at a standard level. it could be completely veiled by the noise and lower resolution; hence. the Ba abundance would still be low.," confirms that this might be a possibility, but that it is unlikely that, if the line was present at a standard level, it could be completely veiled by the noise and lower resolution; hence, the Ba abundance would still be low." + Higher resolution. higher S/N spectra of the stars in the Hercules dSph are needed to fully settle the issue.," Higher resolution, higher S/N spectra of the stars in the Hercules dSph are needed to fully settle the issue." + In supernova explosions. freshly synthesized elements are ejected into the nearby interstellar medium.," In supernova explosions, freshly synthesized elements are ejected into the nearby interstellar medium." +" The yields of different elements depend on the mass of the star that is the progenitor (e.g.""??).,"," The yields of different elements depend on the mass of the star that is the progenitor \citep[e.g.][]{woosley1995,1999ApJS..125..439I}." + In models of galactic chemical evolution. itis often assumed that the ejecta from the supernova become well-mixed quickly.," In models of galactic chemical evolution, it is often assumed that the ejecta from the supernova become well-mixed quickly." + This ts the instantaneous recycling approximation (e.g.2).., This is the instantaneous recycling approximation \citep[e.g.][]{pagel1997}. + This works well when we explore the later phases of galactic chemical evolution or study galaxies as a whole: however. m situations where only one or few supernova have had the chance to enrich the interstellar medium. the gas will not be well-mixed. and we might therefore see an atypical composition of elemental abundances in a single star (?)..," This works well when we explore the later phases of galactic chemical evolution or study galaxies as a whole; however, in situations where only one or few supernova have had the chance to enrich the interstellar medium, the gas will not be well-mixed, and we might therefore see an atypical composition of elemental abundances in a single star \citep[][]{karlsson2005}." + Few studies have been done of the effect on elemental abundances in low mass systems such as the ultra-faint dSph galaxies., Few studies have been done of the effect on elemental abundances in low mass systems such as the ultra-faint dSph galaxies. + As opposed to the more robust predictions from models of galactic chemical evolution that concerns giant galaxies such as the Milky Way. models for dSph galaxiePA will be highly vulnerable to any uncertainties in the supernova yields used for the modelling.," As opposed to the more robust predictions from models of galactic chemical evolution that concerns giant galaxies such as the Milky Way, models for dSph galaxies will be highly vulnerable to any uncertainties in the supernova yields used for the modelling." + As such yields remain uncertain. we can only at this point speculate on the origin of the atypical abundance ratios observed.," As such yields remain uncertain, we can only at this point speculate on the origin of the atypical abundance ratios observed." + ? speculate that. if the enrichment histories of the ultra-faint dSph galaxies are largely dominated by inhomogeneous evolution. considerable star-to-star scatter should be observed in these systems.," \citet{koch2008Her} speculate that, if the enrichment histories of the ultra-faint dSph galaxies are largely dominated by inhomogeneous evolution, considerable star-to-star scatter should be observed in these systems." + Apart from Boo-127 (and possiblyBoo- the remaining. stars in. II show considerable homogeneity in their derived Mg and Ca abundances refcamgfe.fig)).," Apart from Boo-127 (and possiblyBoo-094), the remaining stars in I show considerable homogeneity in their derived Mg and Ca abundances \\ref{camgfe.fig}) )." + Also for the two faint systems Coma Berenices, Also for the two faint systems Coma Berenices +Protoplanetary nebulae (PPNe) are known to present very fast bipolar outflows. along with slower components. which are probably the remnants of the mass ejection during the previous AGB phase.,"Protoplanetary nebulae (PPNe) are known to present very fast bipolar outflows, along with slower components, which are probably the remnants of the mass ejection during the previous AGB phase." + The bipolar flows typically reach velocities of 100s7!.. and affect a sizable fraction of the nebular mass. ~ 0.1 — 0.3 citepbujetalOl..," The bipolar flows typically reach velocities of 100, and affect a sizable fraction of the nebular mass, $\sim$ 0.1 – 0.3 \\citep{bujetal01}." + These dense flows actually represent intermediate states in the spectacular evolution from. the spherical and slowly expanding circumstellar envelopes around AGB stars to the planetary nebulae. which usually show bipolar or ring-like symmetries.," These dense flows actually represent intermediate states in the spectacular evolution from the spherical and slowly expanding circumstellar envelopes around AGB stars to the planetary nebulae, which usually show bipolar or ring-like symmetries." + Such. remarkable dynamies is probably the result of the interaction between the AGB and post-AGB winds: axial. very fast post-AGB jets colliding with the denser material driven isotropically away from the star during its AGB phase (e.g.Balick&Frank 2002).," Such remarkable dynamics is probably the result of the interaction between the AGB and post-AGB winds: axial, very fast post-AGB jets colliding with the denser material driven isotropically away from the star during its AGB phase \citep[e.g.][]{balickf02}." + The presently observed bipolar outflows would then correspond to a part of the relatively dense shells ejected during the last AGB phase. mostly their polar regions. accelerated by the shocks that propagate during the PPN phase.," The presently observed bipolar outflows would then correspond to a part of the relatively dense shells ejected during the last AGB phase, mostly their polar regions, accelerated by the shocks that propagate during the PPN phase." + The massive bipolar outflows in PPNe. as well as the unaltered remnants of the AGB shells. usually show strong emission in molecular lines (Bujarrabaletal.2001).," The massive bipolar outflows in PPNe, as well as the unaltered remnants of the AGB shells, usually show strong emission in molecular lines \citep{bujetal01}." +. PPNe have been accurately observed in mm-wave lines. particularly by means of interferometric maps with resolutions ~ 1.," PPNe have been accurately observed in mm-wave lines, particularly by means of interferometric maps with resolutions $\sim$ $''$." + Thanks to those observations. the structure. dynamics. and physical conditions in. these nebulae are often quite well known.," Thanks to those observations, the structure, dynamics, and physical conditions in these nebulae are often quite well known." + However. observations of the low-/ transitions are not very useful for studying the warm gas components.," However, observations of the $J$ transitions are not very useful for studying the warm gas components." +" The studied aand ttransitions of oonly require temperatures of T, ~ 15 K to be excited.", The well-studied and transitions of only require temperatures of $T_{\rm k}$ $\sim$ 15 K to be excited. + Indeed their maximum emissivity occurs for excitation temperatures of 10 — 20 K. and the line intensities and line intensity ratios only slightly depend on the excitation state in relatively warm gas.," Indeed their maximum emissivity occurs for excitation temperatures of 10 – 20 K, and the line intensities and line intensity ratios only slightly depend on the excitation state in relatively warm gas." +" Needless to say. observations in the visible or near infrared ranges tend to select hot regions. with typical temperatures over 1000 K. The proper study of warm regions. 100 K T, 11000 K. therefore requires observations at. intermediate wavelengths. in the far infrared (FIR) and sub-mm ranges."," Needless to say, observations in the visible or near infrared ranges tend to select hot regions, with typical temperatures over 1000 K. The proper study of warm regions, 100 K $T_{\rm k}$ 1000 K, therefore requires observations at intermediate wavelengths, in the far infrared (FIR) and sub-mm ranges." + Because of the role of shocks in PPN evolution. these warm regions are particularly important. for understanding nebular structure and evolution.," Because of the role of shocks in PPN evolution, these warm regions are particularly important for understanding nebular structure and evolution." + In some well-studied cases. 11-92 and 22-56 (Alcoleaetal.2007.Bujarrabal1998.Castro-Carrizoetal. 2002).. the high-velocity. massive outflows are found to be very cold. with temperatures 220 K. which implies very fast cooling in. the shock-accelerated gas.," In some well-studied cases, 1–92 and 2–56 \citep{alcolea07,bujetal98,ccarrizo02}, the high-velocity, massive outflows are found to be very cold, with temperatures 20 K, which implies very fast cooling in the shock-accelerated gas." + No warm component representing the gas recently accelerated by the shock front has been identified in these sources., No warm component representing the gas recently accelerated by the shock front has been identified in these sources. + In other cases such as 6618. interferometric imaging of the lline shows that dense gas in axial structures presents higher temperatures (SánchezContrerasetal.2004.hereafter.SCO4).," In other cases such as 618, interferometric imaging of the line shows that dense gas in axial structures presents higher temperatures \citep[][hereafter, +SC04]{sanchezc04}." +. But. precisely because of their relatively high excitation. the temperature estimate in these components from CO lis very uncertain.," But, precisely because of their relatively high excitation, the temperature estimate in these components from CO is very uncertain." + Indeed. even the presence of such high excitation in the dense bipolar outflows in 6618 remained to be demonstrated.," Indeed, even the presence of such high excitation in the dense bipolar outflows in 618 remained to be demonstrated." + Other attempts to study the warm gas in 6618 were carried out by () Justtanontetal.(2000). from ISO data with low spectral resolution: (7) Pardoetal.(2004).. who focused on the chemistry of the different components: and (4/7) etal. (2007).. who also obtained maps of the ttransition in 6618. but with less detail than in SCOA.," Other attempts to study the warm gas in 618 were carried out by ) \cite{justtanont00} from ISO data with low spectral resolution; ) \cite{pardo04}, who focused on the chemistry of the different components; and ) \cite{naka07}, who also obtained maps of the transition in 618, but with less detail than in SC04." + The Herschel Space Telescope is well-suited to studying warm gas around evolved stars in the FIR and sub-mm., The Herschel Space Telescope is well-suited to studying warm gas around evolved stars in the FIR and sub-mm. + The high spectral resolution that can be achieved with its heterodyne instrument HIFI (better than kms)) is particularly useful for this purpose. since kinematics offers a fundamental key to understanding this warm. shocked," The high spectral resolution that can be achieved with its heterodyne instrument HIFI (better than ) is particularly useful for this purpose, since kinematics offers a fundamental key to understanding this warm, shocked" +pericentric radius.,pericentric radius. +" The total energy radiated during the fallback is given by GAL;MM/2r,. where AA/ is the fallback mass."," The total energy radiated during the fallback is given by $GM_H\Delta M/2r_c$, where $\Delta M$ is the fallback mass." + This energy can be less than the οποιον released in the subsequent viscous accretion stage discussed below., This energy can be less than the energy released in the subsequent viscous accretion stage discussed below. + Nevertheless. since the lallback stage is relatively short-lived. it dominates (he early Iuminositv of a disruption event. (," Nevertheless, since the fallback stage is relatively short-lived, it dominates the early luminosity of a disruption event. (" +"2) The viscous accretion stage (Cannizzo.Lee.&Goodman1990}:; The torus formed from returning debris gradually spreads inward and outward [rom r=r. wider (he action ol viscosity. and gives rise to a mass accretion rate (and a luminosity) evolving with time approximately as ~/.7,","2) The viscous accretion stage \citep{can90}: The torus formed from returning debris gradually spreads inward and outward from $r = r_c$ under the action of viscosity, and gives rise to a mass accretion rate (and a luminosity) evolving with time approximately as $\sim +t^{-1.2}$." + The energy radiated during this stage is given bv (1/2r.)]. where rj; is the radius of the last stable circular orbit (=3 Schwarzschild radii for a non-spinuning black hole).," The energy radiated during this stage is given by $GM_{\rm +H}\Delta +M[(1/2r_{ms}) -(1/2r_c)]$ , where $r_{ms}$ is the radius of the last stable circular orbit $=3$ Schwarzschild radii for a non-spinning black hole)." + The accretion occurs on a viscous time scale. which is tvpically very long compared to the fallback time (Cannizo et al.," The accretion occurs on a viscous time scale, which is typically very long compared to the fallback time (Cannizo et al." + 1990; Ulmer 1999: Appendix A of the present paper)., 1990; Ulmer 1999; Appendix A of the present paper). + Therefore. this stage is expected to last a long time. up to hundreds of vears. depending on the magnitude of the viscosity in the disk. and (he Iuminosityv is significantly lower than that associated with the fallback stage (Appendix A)).," Therefore, this stage is expected to last a long time, up to hundreds of years, depending on the magnitude of the viscosity in the disk, and the luminosity is significantly lower than that associated with the fallback stage (Appendix \ref{appa}) )." + In the case of NGC 5905. the X-ray luminosity was seen {ο rise rapidly during the first epoch of observations at /=1990.54 vr. indicating that the flare probably began. around that time (see Table 1 and Fig. 1)).," In the case of NGC 5905, the X-ray luminosity was seen to rise rapidly during the first epoch of observations at $t = 1990.54$ yr, indicating that the flare probably began around that time (see Table 1 and Fig. \ref{fig1}) )." + The Iuminositv then dropped by more (han a factor of 100 between /=1990.54 vr and /=1996.89 vr., The luminosity then dropped by more than a factor of $100$ between $t = 1990.54$ yr and $ t = 1996.89$ yr. + Such a rapid decline indicates Chat the observed outburst of NGC 5905 could not have been due to the accretion phase. but nist have corresponded to the fallback stage Gf it indeed was a tidal disruption event).," Such a rapid decline indicates that the observed outburst of NGC 5905 could not have been due to the accretion phase, but must have corresponded to the fallback stage (if it indeed was a tidal disruption event)." + Therefore. in this paper we assume that the flare in NGC 5905 corresponds to the fallback stage of tidal disruption.," Therefore, in this paper we assume that the flare in NGC 5905 corresponds to the fallback stage of tidal disruption." + Let us assume that the center of the star follows a nearly parabolic orbit (.e.. the binding energv of the star to the black hole is close to zero). and for definiteness letus assume that the pericenter of the orbit is at rp=rp. ie. that the parameter 7 defined below in equation (8)) is equal to unity.," Let us assume that the center of the star follows a nearly parabolic orbit (i.e., the binding energy of the star to the black hole is close to zero), and for definiteness letus assume that the pericenter of the orbit is at $r_P = r_T$, i.e. that the parameter $\eta$ defined below in equation \ref{omgs}) ) is equal to unity." + Since the specific energy at the center of the star is E=05/2—GMj/rp0. the orbital velocity of the star at pericenter is ep=(26Mgj/rp)?e(rg/rp)7. and the spread in the specific energy of the disrupted debris. 2.4. is governed by the variation of the black hole gravitational potential across the star. and (he spin-up of the star as a result ol the tidal interaction (Rees1988).," Since the specific energy at the center of the star is $E_c = v_P^2/2 - G M_H/r_T = 0$, the orbital velocity of the star at pericenter is $v_P = (2 G M_H / +r_T)^{1/2} = c\, (r_H / r_T)^{1/2}$, and the spread in the specific energy of the disrupted debris, $2\Delta E$, is governed by the variation of the black hole gravitational potential across the star, and the spin-up of the star as a result of the tidal interaction \citep{ree88}." +". If A4;9M,. we have where & depends on the spin-up state of the star."," If $M_H \gg M_\star$, we have where $k$ depends on the spin-up state of the star." + If the star is spun up to the break-up spin angular velocity. we have fx 3.," If the star is spun up to the break-up spin angular velocity, we have $k \approx 3$ ." + On the other hand. if the spin-up ellect is negligible. then we have &zz1 ," On the other hand, if the spin-up effect is negligible, then we have $k \approx 1$ " +rom L1551 IRS5.,from L1551 IRS5. + The ceutroid positions. aud background subracted count-rates cau be found in Table 1..," The centroid positions, and background subtracted count-rates can be found in Table \ref{tab:source}." + The xositiou of the brighter of fjo two against the molecular outflow is visibile in Fie. 3.., The position of the brighter of the two against the molecular outflow is visibile in Fig. \ref{fig:image}. + Neitrer of these sources cau ο associated with any visile object in the deep aand Z-band images at tlose positions., Neither of these sources can be associated with any visible object in the deep and $I$ -band images at these positions. + Both \? aud ο tests sLow hat the οΕς ον rol these ποιαος ds constaut to a hieh (>D0 ) xobabilitv level., Both $\chi^2$ and K-S tests show that the X-ray emission from these sources is constant to a high $\ge 90\%$ ) probability level. + The spectra of these two sources are sieuificautlv harder than the s)octrunm of the ποος associated with the L1554 IRS5 jc(the spectrum of the xiehter of the two is showi iu Fie. 5)).," The spectra of these two sources are significantly harder than the spectrum of the source associated with the L1551 IRS5 jet (the spectrum of the brighter of the two is shown in Fig. \ref{fig:irs5bisspec}) )," + aud can both JC Saistactorily described with an absorbed power-law spectrum. with iudices varviie hetween 1.2 and 2.5.," and can both be satisfactorily described with an absorbed power-law spectrum, with indices varying between 1.2 and 2.5." + The absoràiug coluun deusitv is iu both cases moderate. with Ag betwee 1c5 and &8 maenitueles.," The absorbing column density is in both cases moderate, with $A_V$ between $\simeq 5$ and $\simeq 8$ magnitudes." + The resultiug column deusities are thus sinular to wlat is expected for the Li551 molecular cloud at these positions (Saudqvist&Bernes.195 n)., The resulting column densities are thus similar to what is expected for the L1551 molecular cloud at these positions \citealp{sb80}) ). + Given the A-rav spectra characteristics. as we Las the lack of anv visible caucdiate counterpart i our deep {-xuid nuages. we consider it ikelv that these ποιασος nre rot associated with the molecular L1551 IRS5 outflow. eve1i though they are positionally coiicideut with (parts of) 1.," Given the X-ray spectral characteristics, as well as the lack of any visible candidate counterpart in our deep $I$ -band images, we consider it likely that these sources are not associated with the molecular L1551 IRS5 outflow, even though they are positionally coincident with (parts of) it." + Rather. they are most likely to be extra-ealactic N-rav sources (plausibly active ealactic nuclei) shining tliouel the L1551 cloud.," Rather, they are most likely to be extra-galactic X-ray sources (plausibly active galactic nuclei) shining through the L1551 cloud." + Typical acive galactic uuclei soul have. on the basis oft1011) veh FXΕΥ: ratio. optical magutudes VZz19. which would become 1ZTx2 whe ithe intervening column density is faken 1ito account.," Typical active galactic nuclei would have, on the basis of their high $F_{\rm X}/F_V$ ratio, optical magnitudes $V \ga 19$, which would become $V \ga 24$ when the intervening column density is taken into account." + Therefore tlicr optical counterpar sare not expected to be visible. on the optical images preseued here. agaiuts the ckerounud of the molecular outflow ClUSSION.," Therefore their optical counterparts are not expected to be visible, on the optical images presented here, againts the background of the molecular outflow emission." + The Spectra could in priucipe be fit also with a thernal spectrum. with a very veh resuling teniperatire (TE100 MIS).," The spectra could in principle be fit also with a thermal spectrum, with a very high resulting temperature $T \ga 100$ MK)." + While this temperature would LO lucoupatidle with coronal Xoostellar origin duriug nm cherectic flare. the lack «Mf auv visible counter down to aut maenitudes (even though the absor colunu is ouly a few maeuitiuOS} and the cousaut curve ofthe sources nike this last hypothesis ulikely.," While this temperature would not be incompatible with coronal protostellar origin during an energetic flare, the lack of any visible counterpart down to faint magnitudes (even though the absorbing column is only a few magnitudes) and the constant light curve of the sources make this last hypothesis unlikely." + The presence of two sereuci1ος X-ray sources in PN image shown in Fie., The presence of two serendipitous X-ray sources in the PN image shown in Fig. + 3 at flux levels of order 101 erg 7 D is fully in line wih the expectec 11111001) density of backeround sources determined on the! basis of the logN5 relationship for X-ray sources (seο(00 citealpliaa| 20013). which predics that at this fux lini 100 to 200 sources per square degree should be preseu iu any eiveu X-rav observation.," \ref{fig:image} at flux levels of order $10^{-14}$ erg $^{-2}$ $^{-1}$ is fully in line with the expected number density of background sources determined on the basis of the $\log N \log S$ relationship for X-ray sources (see \\citealp{haa+2001}) ), which predicts that at this flux limit 100 to 200 sources per square degree should be present in any given X-ray observation." + The area covered by N-ray nuage of Fie., The area covered by X-ray image of Fig. + 3 is &0.02 square dee. so that the expected uunuber of serendipitous sources is 2 to [.," \ref{fig:image} is $\simeq 0.02$ square deg, so that the expected number of serendipitous sources is 2 to 4." + IIubble Space Telescope (IST) observations (Fridlund&Liseau. 1998)) indicate the presence of a uuuber of shocks along the extent of the IRS5 jet., Hubble Space Telescope (HST) observations \citealp{fl98}) ) indicate the presence of a number of shocks along the extent of the IRS5 jet. + The jet is observed to end m a “working surface” against the ambicut media at zLO arcsec roni the presuned 1ocation of the source powering it (soο 1l aud 2 oπαλαιά & Liseau. 1998))., The jet is observed to end in a “working surface” against the ambient medium at $\simeq 10$ arcsec from the presumed location of the source powering it (see 1 and 2 of \citealp{fl98}) ). +" This «lxick feature ds designuated ""knot D in the nomenclature o [Neckel&Staude(1O87) aud Liseau(199 D.", This shock feature is designated “knot D” in the nomenclature of \citet{nec87} and \citet{fl94}. +. We have measured tjo ratio tows the working surface (knot D) of he jet., We have measured the ratio towards the working surface (knot D) of the jet. + Asstis a type D pure recombinaion spectra (which 15 justified since woe also detect || 5007 COLLISn at tUs position see low). we fixd Ay to he G mae. cepeudineg on which extinction law is apλαο.," Assuming a type B pure recombination spectrum (which is justified since we also detect ] 5007 emission at this position – see below), we find $A_V$ to be 4–6 mag, depending on which extinction law is applied." + We also find that the exduction Is duücreasing 11 the «lirection towards IRS5 along the jet (coufirniue the resIt of Stockeetal. 1988))., We also find that the extinction is increasing in the direction towards IRS5 along the jet (confirming the result of \citealp{shs+88}) ). + The absorbing colin deitv. for the IRS5 X-ray spectugu. ds thus compatible wih the absorbing column deusity measured toward the visible jet (and in particular toward the shock feature). making the association between the X-ray cussion and the jet plausible.," The absorbing column density, for the IRS5 X-ray spectrum, is thus compatible with the absorbing column density measured toward the visible jet (and in particular toward the shock feature), making the association between the X-ray emission and the jet plausible." + Since as mentioned above the IRS protostellay svstem is hidden behind a very thick laver of asorbiue material. correspouding to lyZ150 mae. it can be exeuded that the N-rav photons eiven the small absorbing colununu deusitv aud the lack of high-cucrey photons in the sSpectruni) Clute from (or close to) the photosxiiere/celiromosphliere of the protostars powering the jet.," Since as mentioned above the IRS5 protostellar system is hidden behind a very thick layer of absorbing material, corresponding to $A_V \ga 150$ mag, it can be excluded that the X-ray photons – given the small absorbing column density and the lack of high-energy photons in the spectrum) – emanate from (or close to) the photosphere/chromosphere of the protostars powering the jet." + We therefore draw the conclusion that this source is the result of thermal eiuissiou im the shocks whose recolubinaion light is seen along the jet iu the visual waveleugth regiae., We therefore draw the conclusion that this source is the result of thermal emission in the shocks whose recombination light is seen along the jet in the visual wavelength regime. +The Lyman-alpha forest is perceived as being simple. and in this simplicity. promises to become a key to many unsolved problems in cosmology.,"The Lyman-alpha forest is perceived as being simple, and in this simplicity promises to become a key to many unsolved problems in cosmology." + In the most recent demonstration of the power of simplicity. Croft et shorteiteCWBOL presented. a measurement of the matter linear power spectrum on scales which are nonlinear today a measurement not casily reproducible by other means. such as galaxy surveys at low recshift.," In the most recent demonstration of the power of simplicity, Croft et \\shortcite{CWB01} presented a measurement of the matter linear power spectrum on scales which are nonlinear today – a measurement not easily reproducible by other means, such as galaxy surveys at low redshift." + Not onlv was the phenomenon that they modeled simple. but also the method that they used to recover the linear power spectrum was simple — perhaps. excessively simple.," Not only was the phenomenon that they modeled simple, but also the method that they used to recover the linear power spectrum was simple – perhaps excessively simple." + For example. Croft ct shorteiteCWDOL— considered. only one prior. cosmological model in deriving the correction function that translates the observed Lux power spectrum into a linear power spectrum.," For example, Croft et \\shortcite{CWB01} considered only one prior cosmological model in deriving the correction function that translates the observed flux power spectrum into a linear power spectrum." + In this paper our purpose is to check whether their method. is reliable by sampling over a range of prior cosmological models., In this paper our purpose is to check whether their method is reliable by sampling over a range of prior cosmological models. + We also attempt to estimate systematic errors and their covariance., We also attempt to estimate systematic errors and their covariance. + We begin in §2 by making sure that we are able to reproduce Croft ct results., We begin in 2 by making sure that we are able to reproduce Croft et results. + In 83 we give our results., In 3 we give our results. + We close in Ed with an optimistic conclusion., We close in 4 with an optimistic conclusion. + Since our goal is to evaluate the accuracy of the Croft ct WDOLI. method. we apply their method to a range of cosmological models.," Since our goal is to evaluate the accuracy of the Croft et \\shortcite{CWB01} method, we apply their method to a range of cosmological models." + We adopt the same linear transfer function. but we vary the amplitude and the tilt. ancl we experiment with different ecometrics and different Llubble constants.," We adopt the same linear transfer function, but we vary the amplitude and the tilt, and we experiment with different geometries and different Hubble constants." + In refbandpower— we also report the οσοι of varving the linear power spectrum over narrow intervals of wavenumber., In \\ref{bandpower} we also report the effect of varying the linear power spectrum over narrow intervals of wavenumber. + We use a standard Particle-Alesh method to simulate the distribution the matter at z=2.72., We use a standard Particle-Mesh method to simulate the distribution the matter at $z=2.72$. + Following Croft ct shorteiteCΑΝΘΗ we assume that the underlving barvon density follows that of the dark matter.," Following Croft et \\shortcite{CWB01} + we assume that the underlying baryon density follows that of the dark matter." +" At small scales the barvon density is smoothed out compared to the dark matter density. but the scale at whieh this occurs. the ""filtering scale. is much smaller than the range of scales of interest"," At small scales the baryon density is smoothed out compared to the dark matter density, but the scale at which this occurs, the “filtering” scale, is much smaller than the range of scales of interest" +The Local Bubble (LB) or Local Hot Bubble and its environment are sketched in Figure 1..,The Local Bubble (LB) or Local Hot Bubble and its environment are sketched in Figure \ref{fig:schematic}. + The Local Bubble. a &10° pe? region of X-ray emissive. presumably hot (~105 Ix) plasma. is nestled wilhin a rarefied cavity in (he Galactic disk called the Local Cavity. (INXnapp1983:Snowdenοἱal.19983:Sfeiret 1999).," The Local Bubble, a $\sim10^6$ $^{3}$ region of X-ray emissive, presumably hot $\sim10^6$ K) plasma, is nestled within a rarefied cavity in the Galactic disk called the Local Cavity, \citep{knapp,mccammon_etal,snowden_etal_98,sfeir_etal}." +. Within the Local Bubble. lie a number of cool (~LO! K) clouds. including the complex of parsec-scale clouds surrounding (he Sun (Frisch1986:Lallement&Berlin1992:Gryetal.1995).," Within the Local Bubble, lie a number of cool $\sim10^4$ K) clouds, including the complex of parsec-scale clouds surrounding the Sun \citep{frisch_86,lallement_bertin,gry_etal}." +. Estimates of (he number of clouds per line of sight range from ~2 to ~6. with ~2 coming from (he ratio of the typical observed absorbing column density (Hutchinsonοἱal.19983). (o the absorbing column density of the local cloud (Lallementοἱal.1995).. and ~6 coming from the number ol clouds along the € CMa line of sight (Gryetal.1995)..," Estimates of the number of clouds per line of sight range from $\sim2$ to $\sim6$, with $\sim2$ coming from the ratio of the typical observed absorbing column density \citep{hutchinson_etal} + to the absorbing column density of the local cloud \citep{lallement_etal}, and $\sim6$ coming from the number of clouds along the $\epsilon$ CMa line of sight \citep{gry_etal}." + Bevond the Local Bubble. in the direction of the Galactic center. lies a superbubble named Loop I. which was blown by the stars and supernovae in the Sco Cen association (Egger1993)..," Beyond the Local Bubble, in the direction of the Galactic center, lies a superbubble named Loop I, which was blown by the stars and supernovae in the Sco Cen association \citep{egger}." + The Local Bubble is larger aud more energetic than a supernova remnant. vel smaller and less energetic (han a superbubble.," The Local Bubble is larger and more energetic than a supernova remnant, yet smaller and less energetic than a superbubble." + Such bubbles are important as most of the hol eas in the Galactic disk resides within them., Such bubbles are important as most of the hot gas in the Galactic disk resides within them. + Like the distribution of small versus large stellar associations. (he population of bubbles is likely to be larger than the population of superbubbles.," Like the distribution of small versus large stellar associations, the population of bubbles is likely to be larger than the population of superbubbles." + Nonetheless. because its solver N-rav photons from its relatively cooler plasma are more easily absorbed. à bubble like the Local Bubble would be much more diffieult. to detect [rom a ereat distance (han would an energetic superbubble like Loop I. Thus. many other Local Bubble analogs may reside within the Galaxy. unknown to us because thev are obscured by the neutral and molecular material of the Galactic disk.," Nonetheless, because its softer X-ray photons from its relatively cooler plasma are more easily absorbed, a bubble like the Local Bubble would be much more difficult to detect from a great distance than would an energetic superbubble like Loop I. Thus, many other Local Bubble analogs may reside within the Galaxy, unknown to us because they are obscured by the neutral and molecular material of the Galactic disk." + In this sense. we are forlimate to have a local specimen (o examine.," In this sense, we are fortunate to have a local specimen to examine." + At this time. our understanding of the Local Bubble is chielly phenomenological.," At this time, our understanding of the Local Bubble is chiefly phenomenological." + To some degree. the Local Bubble is defined as the source of soft. N-ravs (~1 keV) produced between us and (he nearest opaque material.," To some degree, the Local Bubble is defined as the source of soft X-rays $\sim \frac{1}{4}$ keV) produced between us and the nearest opaque material." + Its physical presence has been surnised [rom the anti-correlation between soft X-ray intensities and neutral hyclrogen column densities (associated with the larger Local Cavity). detections of N-ravs originating in the foreground of opaque clouds. relative constaucies between Be (0.07 to 0.11 keV). D (0.13 to 0.19 keV) and C (0.16 to 0.28 keV) band surface brightnesses across the skv (implving very little absorption as the effective absorption cross sections vary significantly between Che bands). and consistency among two decades of X-ray observations.," Its physical presence has been surmised from the anti-correlation between soft X-ray intensities and neutral hydrogen column densities (associated with the larger Local Cavity), detections of X-rays originating in the foreground of opaque clouds, relative constancies between Be (0.07 to 0.11 keV), B (0.13 to 0.19 keV) and C (0.16 to 0.28 keV) band surface brightnesses across the sky (implying very little absorption as the effective absorption cross sections vary significantly between the bands), and consistency among two decades of X-ray observations." + Fundamental characteristics of the LB. such as ils presumed. temperature ancl size. cannot be determined directly. but can only be estimated when additional constraints (such as lonizational equilibrium. constancy of emissivity. and [filling factor) are assumed.," Fundamental characteristics of the LB, such as its presumed temperature and size, cannot be determined directly, but can only be estimated when additional constraints (such as ionizational equilibrium, constancy of emissivity, and filling factor) are assumed." + Given these assumptions. the estimated temperature has been derived [vom the ratio of fIuxes," Given these assumptions, the estimated temperature has been derived from the ratio of fluxes" +with an intrinsic scatter of 0.3 dex in logA.,with an intrinsic scatter of $0.3$ dex in $\log M\bh$. +" Subsequently. eiven the stellar mass of the spheroidal component οutes: (=1.2) of cach progenitor of a mucreine pa. we use equation (2.2.0)) to estimate the central BIT mass M4; (/=1.2) iu the progenitor at redshift 2. by asstune that the scatter of the correlation follows a normal distribution and adopting a πα] evolution correction of A,x(1|:)9952010).."," Subsequently, given the stellar mass of the spheroidal component $M_{*,{\rm bulge},i}$ $(i=1,2)$ of each progenitor of a merging pair, we use equation \ref{eq:bhbulge}) ) to estimate the central BH mass $M\bh{_{,i}}$ $i=1,2$ ) in the progenitor at redshift $z$, by assuming that the scatter of the correlation follows a normal distribution and adopting a small evolution correction of $M\bh \propto (1+z)^{0.68}$." + Note that the following clemeuts are involved to estimate the distribution of AM.quac: (a) The bulge to total stellar mass ratio (D/T): given the stellar mass Af. of a ealaxy. the mass AL.ule can be estimated according to the morphology of the ealaxy. as the D/T ratios are differcut for galaxies with different morphologics2009).," Note that the following elements are involved to estimate the distribution of $M\bulge$: (a) The bulge to total stellar mass ratio (B/T): given the stellar mass $M_*$ of a galaxy, the mass $M\bulge$ can be estimated according to the morphology of the galaxy, as the B/T ratios are different for galaxies with different morphologies." +. Based on the detailed analysis of sample of nearby galaxies. it has been found that B/T=a0.22 aud 0.05 with variances of 0.05 aud 0.02 for Sa-Sb aud Sc-Sd. respectively2009).," Based on the detailed analysis of a sample of nearby galaxies, it has been found that $B/T=0.22$ and $0.05$ with variances of $0.05$ and $0.02$ for Sa-Sb and Sc-Sd, respectively." +. We assuue that B/PT=1 for elliptica and SO ealaxies aud D/T=0 for inveeular galaxies. respectively. (," We assume that $B/T=1$ for elliptical and S0 galaxies and $B/T=0$ for irregular galaxies, respectively. (" +b) Distribution of morphological combinations of nicrgius galaxw pairs: it is possible that the two progenitors of a iereie galaxy pair have differen morplologics.,b) Distribution of morphological combinations of merging galaxy pairs: it is possible that the two progenitors of a merging galaxy pair have different morphologies. + Currently detailed statistics on the morphological combinations of the pairs are no available. although there are quite a. umuber of coustraiuts on the mereer rates of red galaxies. blue ealaxies aud mined ones2008).," Currently detailed statistics on the morphological combinations of the pairs are not available, although there are quite a number of constraints on the merger rates of red galaxies, blue galaxies and mixed ones." +. Tere we simply assume that the morphological types of the two progenitors are independent of cach other. and consequcutly the fraction of the merger rates of the airs With auv specific morphological combination to the otal mmerecr rates onv depends ou he fraction of these vpes to the total uuuber of galaxiss," Here we simply assume that the morphological types of the two progenitors are independent of each other, and consequently the fraction of the merger rates of the pairs with any specific morphological combination to the total merger rates only depends on the fraction of these types to the total number of galaxies." + This assumption appears cousistent wih the current observatious that the yactions of differeut norphological vpes for galaxies m airs are snailar to those for field eaaxies2005).. (, This assumption appears consistent with the current observations that the fractions of different morphological types for galaxies in pairs are similar to those for field galaxies. ( +c) Stellar mass functions of galaxies with different norphological tvpes: the galaxy Iuninositv fuuctiou (LE) or four spectral tvpes of galaxies over :—01.2 was previously estinated (see Table 3 of 2006)).,c) Stellar mass functions of galaxies with different morphological types: the galaxy luminosity function (LF) for four spectral types of galaxies over $z\sim 0.2-1.2$ was previously estimated (see Table 3 of ). + These four spectral types roughly correspond o the morphological types E/S0. Si-Sb. Sc-Sd aud Dx. respectively.," These four spectral types roughly correspond to the morphological types E/S0, Sa-Sb, Sc-Sd and Irr, respectively." + For cach type of galaxies. the mass-to-light ratio can be estimated through their average colors1995).. aud their LFs can thus © converted to the stellar mass functions.," For each type of galaxies, the mass-to-light ratio can be estimated through their average colors, and their LFs can thus be converted to the stellar mass functions." + According to hese mass functions. the fraction of cach type of galaxies o the total galaxies can be obtained at any given M. over D0021.2.," According to these mass functions, the fraction of each type of galaxies to the total galaxies can be obtained at any given $M_*$ over $z\sim 0.2-1.2$." + For galaxies at redshifts +<<0.2. we adopt he stellar mass functions for different morphological vpes given by and estimate the fraction of cach type to the total at any given AZ.," For galaxies at redshifts $z<0.2$, we adopt the stellar mass functions for different morphological types given by and estimate the fraction of each type to the total at any given $M_*$." + Ta our calculations below. for cach merecr generated as that described in Section ??.. we randomly set the morphological type to cach progenitor according to the fractious of cach type of galaxies to the total at Af. and M». respectively.," In our calculations below, for each merger generated as that described in Section \ref{subsec:mrg}, we randomly set the morphological type to each progenitor according to the fractions of each type of galaxies to the total at $M_{*,1}$ and $M_{*,2}$, respectively." +" For those nreeular or purely disk-like ealaxics. we set the initial mass of thei MBIIS to be 10141, or zero."," For those irregular or purely disk-like galaxies, we set the initial mass of their MBHs to be $10^5\msun$ or zero." + Here. these two cüffereut initial values do not lead to significantly differcut results.," Here, these two different initial values do not lead to significantly different results." + During the merger of late-type eas-rich galaxies (Sa-Sb. Sc-Sd. or hr) with other galaxies. significant nuclear activities may bo triggered rapidly.," During the merger of late-type gas-rich galaxies (Sa-Sb, Sc-Sd, or Irr) with other galaxies, significant nuclear activities may be triggered rapidly." + The reason lies iu the act that late-tvpe galaxies contain siguificaut amount of eascous materials which could lose angular momentum and sink under dvuanücal friction during the ealaxy ucrecr., The reason lies in the fact that late-type galaxies contain significant amount of gaseous materials which could lose angular momentum and sink under dynamical friction during the galaxy merger. + Early-tyvpe gas-poor (ved/clliptical) galaxies may vc able to capture some eas from gas-rich encounters during the mereime process. but the time for the eas o reach the center is likely to be comparable to the nereine timescale (see Section 2.3)).," Early-type gas-poor (red/elliptical) galaxies may be able to capture some gas from gas-rich encounters during the merging process, but the time for the gas to reach the center is likely to be comparable to the merging timescale (see Section \ref{sub:Devol}) )." + Therefore. the imclear activities in these galaxies may start onlv after he merecrs have almost completed.," Therefore, the nuclear activities in these galaxies may start only after the mergers have almost completed." + Ii addition. the host ealaxies of all the confirmed dACNs selected through double-peaked narrow lines contain stellar disks2010). which would sugeest that they are iiereiug relmnauts of late-type galaxies.," In addition, the host galaxies of all the confirmed dAGNs selected through double-peaked narrow lines contain stellar disks, which would suggest that they are merging remnants of late-type galaxies." + Based on the above arguments. we assume that the unclear activity is trigecred in cach eas-rich componoeut with a central AIBIT once dts separation with its colupalion becomes smaller than a threshold D..," Based on the above arguments, we assume that the nuclear activity is triggered in each gas-rich component with a central MBH once its separation with its companion becomes smaller than a threshold $D_{\rm c}$." + Ou the other hand. we assune that the nuclear activity cannot be trigeered iu any eas-poor conponentof a iicreiue pair prior to the completion of the merger (see also discussions iu Section ??7)).," On the other hand, we assume that the nuclear activity cannot be triggered in any gas-poor componentof a merging pair prior to the completion of the merger (see also discussions in Section \ref{sec:results}))." + The plivsical size of a galaxy is characterized by its haltlieht (or effective) radius ry., The physical size of a galaxy is characterized by its half-light (or effective) radius $r_{\rm h}$. + Once the separation of the componeut 7 (1 or2) of a pair to the other componcut j (2 or 1) is smaller thau the hal-lieht raius of Compoint j (o. my j). the center of conponenut íi qmay be sigwificautly perturbed.," Once the separation of the component $i$ (1 or2) of a pair to the other component $j$ (2 or 1) is smaller than the half-light radius of component $j$ (i.e., $r_{{\rm h},j}$ ), the center of component $i$ may be significantly perturbed." + Tere we asstme the tweshold D. fY component / to be D;= where A is a fudge actor of order unuity.," Here we assume the threshold $D_{\rm c}$ for component $i$ to be $D_{{\rm c},i}= Kr_{{\rm h},j}$, where $K$ is a fudge factor of order unity." +" For major Kryjmcrecrs. nuclear activiticS can be trigeeredao m both compoieuts only if both componcuts are gas-ricl aud their sexuatioün D. having the range 1x5 5/3). equation (3)) can be simplified to give the condition for the thin-dise approximation (Franketal.2002). as in which the local speed of sound. c.. has been detined by cz=OD/Op.," Along with the definition of a polytropic equation of state \citep{sc39}, $P=K\rho^\gamma$ (with the polytropic exponent, $\gamma$, having the range $1 \le \gamma \le 5/3$ ), equation \ref{hybal}) ) can be simplified to give the condition for the thin-disc approximation \citep{fkr02} as in which the local speed of sound, $c_{\mathrm s}$, has been defined by $c_{\mathrm s}^2 = \partial P/\partial\rho$." + This detinition. as well as the form of 44 in equation (4)). will be instrumental in determining the mass density balance (the continuity condition) in a conserved fractal accretion dise.," This definition, as well as the form of $H$ in equation \ref{tdcon}) ), will be instrumental in determining the mass density balance (the continuity condition) in a conserved fractal accretion disc." + For an infinitesimal volume of the fractal medium. cV. this balance will be given by Making note of the connection that dV=//rdrdo for the axisymmetric thin disc flow. a more informative form of equation (5)) can be derived as in which Y is the surface density. defined by X—p// (Franketal.2002).," For an infinitesimal volume of the fractal medium, ${\mathrm d}V$, this balance will be given by Making note of the connection that ${\mathrm d}\overline{V}=H\overline{r}\,{\mathrm d}\overline{r}\, +{\mathrm d}\phi$ for the axisymmetric thin disc flow, a more informative form of equation \ref{balan}) ) can be derived as in which $\Sigma$ is the surface density, defined by $\Sigma \simeq \rho H$ \citep{fkr02}." +. Using the thin-dise approximation. as given by equation CE). one can recast equation (6)) further as where o=2A(1/2).," Using the thin-disc approximation, as given by equation \ref{tdcon}) ), one can recast equation \ref{sigcon}) ) further as where $\sigma =2\Delta -(1/2)$." + The foregoing expression gives the mass density balance equation (the continuity equation) for the axisymmetric fractal flow., The foregoing expression gives the mass density balance equation (the continuity equation) for the axisymmetric fractal flow. +" Similarly. in the infinitesimal volume. dV. the balance of momentum density will imply with v being the velocity vector. F. and F4 being. respectively. the gravitational and centrifugal forces acting on the mass contained in the infinitesimal volume. dV. and Fy, being the total surface force due to the pressure acting on the full surface bounding the volume. dV."," Similarly, in the infinitesimal volume, ${\mathrm d}V$, the balance of momentum density will imply with ${\mathbf v}$ being the velocity vector, ${\mathbf F}_{\mathrm g}$ and ${\mathbf F}_{\mathrm{cf}}$ being, respectively, the gravitational and centrifugal forces acting on the mass contained in the infinitesimal volume, ${\mathrm d}V$, and ${\mathbf F}_{\mathrm p}$ being the total surface force due to the pressure acting on the full surface bounding the volume, ${\mathrm d}V$ ." + The first two forces have radial components only. and their magnitudes are given by and respectively. with A in the latter being the constant specitic angular momentum of the conserved dise flow 1996)..," The first two forces have radial components only, and their magnitudes are given by and respectively, with $\lambda$ in the latter being the constant specific angular momentum of the conserved disc flow \citep{c89,skc90,skc96}. ." +" On the other hand. Fy, has η. ὁ and 2 components."," On the other hand, ${\mathbf F}_{\mathrm p}$ has $r$, $\phi$ and $z$ components." + However. only the radial component is relevant for the axisymmetric thin-disc flow.," However, only the radial component is relevant for the axisymmetric thin-disc flow." + Any volume element. dV. experiences a force. cV(V?). due to the pressure exerted on it by the surrounding medium 1987).," Any volume element, ${\mathrm d}V$, experiences a force, $-{\mathrm d}V({\mathbf \nabla}P)$, due to the pressure exerted on it by the surrounding medium \citep{ll87}." +. Translating this effect onto an intinitesimal volume element of the fractal medium. the magnitude of the radial component of the force. Ες. can be set down as Now going back to the left-hand side of equation (8)). the total change of radial momentum is extracted as a result that could be derived by invoking the continuity condition. as it is given by equation (5)).," Translating this effect onto an infinitesimal volume element of the fractal medium, the magnitude of the radial component of the force, ${\mathbf F}_{\mathrm p}$ , can be set down as Now going back to the left-hand side of equation \ref{mombal}) ), the total change of radial momentum is extracted as a result that could be derived by invoking the continuity condition, as it is given by equation \ref{balan}) )." + And so. making use of equations (9)). CO» CL ED andtl2p in equation (8)). it becomespossible to obtain the finalmomentum balance condition for the conserved fractal dise flowas," And so, making use of equations \ref{radgrav})), \ref{radcent}) ), \ref{radpres}) ) and \ref{lhsmombal}) ) in equation \ref{mombal}) ), it becomespossible to obtain the finalmomentum balance condition for the conserved fractal disc flowas" +opens the possibility of using most realistic and sophisticated profiles like the Einasto profile for lensing studies and marks a route to obtain a satisfactory solution to the cusp-core problem.Acknowledgements:,opens the possibility of using most realistic and sophisticated profiles like the Einasto profile for lensing studies and marks a route to obtain a satisfactory solution to the cusp-core problem.: +: The authors wish to thank H. Morales and R. Carboni for eritical reading., The authors wish to thank H. Morales and R. Carboni for critical reading. + This research has made use of NASA's Astrophysics Data System Bibliographic Services., This research has made use of NASA's Astrophysics Data System Bibliographic Services. + The Mellin transform-method (222) uses the Mellin integral transform for the integral evaluation.," The Mellin transform-method \citep{0853125287,1996MER.16..05,159829184X} + uses the Mellin integral transform for the integral evaluation." + The Mellin transform of a function f(=) is an integral transform defined by: if the integral exits., The Mellin transform of a function $f\left(z\right)$ is an integral transform defined by: if the integral exits. + It is clear from the definition that the Mellin transform does not exist for all functions such as the polynomials. the integral does not converge.," It is clear from the definition that the Mellin transform does not exist for all functions such as the polynomials, the integral does not converge." + The Mellin transform when it does exits it converges in à vertical strip in the complex z-plane., The Mellin transform when it does exits it converges in a vertical strip in the complex -plane. + This strip ts called the (SOA)., This strip is called the (SOA). + The inverse Mellin transform ts defined by: where the contour of integration C is a vertical line in the complex z-plane and must be placed in the SOA of f (z)., The inverse Mellin transform is defined by: where the contour of integration $C$ is a vertical line in the complex -plane and must be placed in the SOA of $f\left(z\right)$ . + Given two functions f(z) and e(2) the Mellin convolution ts defined by: It is well know that the Laplace or Fourier transform of the product of two different functions ts the convolution of the respectively transform., Given two functions $f\left(z\right)$ and $g\left(z\right)$ the Mellin convolution is defined by: It is well know that the Laplace or Fourier transform of the product of two different functions is the convolution of the respectively transform. + In the case of the Mellin transform we have: if z=| this formula is know as the Parseval's theorem for the Mellin transform., In the case of the Mellin transform we have: if $z=1$ this formula is know as the Parseval's theorem for the Mellin transform. + The most important feature of the Mellin transform-method ts that using the equation (A4)) integrals of the type. can be written as an inverse Mellin transform.," The most important feature of the Mellin transform-method is that using the equation \ref{eq:central_feature_mellin}) ) integrals of the type, can be written as an inverse Mellin transform." + With the requirement that f and g should be of the hypergeometric type and consequently their Mellin transforms can be written as products with the form Pa+Au or [D(à+Au]! with the A's being real numbers. the resulting integrals are of the Mellin-Barnes type and then can be written in terms of the Fox H-functionfor A#] or the Meijer G-function for A=| (see Appendix Appendix B:)).," With the requirement that $f$ and $g$ should be of the hypergeometric type and consequently their Mellin transforms can be written as products with the form $\Gamma\left(a+Au\right)$ or $\left[\Gamma\left(a+Au\right)\right]^{-1}$ with the $A$ 's being real numbers, the resulting integrals are of the Mellin-Barnes type and then can be written in terms of the Fox H-functionfor $A\neq1$ or the Meijer G-function for $A=1$ (see Appendix \ref{sec:B}) )." +radiative evolution of the lobe we ignore the details of how velativistic particles are injected iuto the lobe.,radiative evolution of the lobe we ignore the details of how relativistic particles are injected into the lobe. + One inodel for the injection is that the particles ire accelerated in the shock at the hot spots., One model for the injection is that the particles are accelerated in the shock at the hot spots. + The accelerated particles cüffuse across the head region where thev are subject to svuchrotron losses., The accelerated particles diffuse across the head region where they are subject to synchrotron losses. +" Since the pressure in the head region remains approxinatelv constant as sugeested frou, observations. the accelerated particles are subject to severe adiabatic losses as they euter the lobe whose pressure is a decreasing fiction of time (Blundell.Rawlnes&Willott19001."," Since the pressure in the head region remains approximately constant as suggested from observations, the accelerated particles are subject to severe adiabatic losses as they enter the lobe whose pressure is a decreasing function of time \citep{betal99}." + As a result. the radio power cleclines more rapidly than that inferred frou observatious.," As a result, the radio power declines more rapidly than that inferred from observations." + One possible remedy for this euliauced loss is that particle re-acceleratiou is ongoing in the lobe (Manolakou&Iirk2002)., One possible remedy for this enhanced loss is that particle re-acceleration is ongoing in the lobe \citep{mk02}. +. This would lead to simular results to that obtained by Kaiser&Best(2007). based ou the time-independent mjectiou., This would lead to similar results to that obtained by \citet{kb07} based on the time-independent injection. + Tere without eoiug into a specific injection model. we adopt the similar asstuption that the injection is time independent. with a power-law euergv distribution.," Here without going into a specific injection model, we adopt the similar assumption that the injection is time independent, with a power-law energy distribution." + The evolution of the emitting plasima im the lobes can )o characterized by three separate phases: 1) the initial nili-up phase in which the total euergv iu the lobe increases with time due to the injection of both kinetic energv bv relativistic particles aud magnetic energv. 2) he adiabatic phase. aud 3) the ICS phase.," The evolution of the emitting plasma in the lobes can be characterized by three separate phases: 1) the initial build-up phase in which the total energy in the lobe increases with time due to the injection of both kinetic energy by relativistic particles and magnetic energy, 2) the adiabatic phase, and 3) the ICS phase." +" The relevant nues t,. fy aud f£, can be estimated in a specific model or the lobe pressure pj."," The relevant times $t_a$, $t_b$ and $t_c$ can be estimated in a specific model for the lobe pressure $p_l$." + We follow the procedure iu Dluudell.Rawhues&Willott(1999) by settiug the wressure to that downstream of the bow shock. eiviug ριντ377.," We follow the procedure in \citet{betal99} by setting the pressure to that downstream of the bow shock, giving $p_l\propto t^{-(4+\beta)/(5-\beta)}$." + Wo also ignore the large-scale ordered uaenetie fields aud set the magnetic pressure fo jy., We also ignore the large-scale ordered magnetic fields and set the magnetic pressure to $p_l$. + The adiabatie expansion pV=coust gives CL|33/T5j) (GNiuseretal.1997)., The adiabatic expansion $p_lV^{\Gamma}={\rm const}$ gives $\alpha_V=(4+\beta)/\Gamma(5-\beta)$ \citep{ketal97}. +. One has where one assumes that Bsy=By/(50uT). νι=v/(lGIIz) and 9=3/2.," One has where one assumes that $B_{50}=B_0/(50\,{\rm nT})$, $\nu_1=\nu/(1\,\rm GHz)$ and $\beta=3/2$." +" That fj,zf, implies thatsvuchnrotrou losses are dominant only in the very carly. build-up plase of the evolution."," That $t_b\gg t_a$ implies thatsynchrotron losses are dominant only in the very early, build-up phase of the evolution." + For ligh-power jets. bv substituting (19)) for (2)). one estimates the characteristic size at which the ICS losses dominate.," For high-power jets, by substituting \ref{eq:tc}) ) for \ref{eq:Dt2}) ), one estimates the characteristic size at which the ICS losses dominate." +" This corresponds to a break or knee at Since in the adiabatic regime. the particle spectrmu relmains the sue as the injection spectrum. the total spectral power for DD_c$ ), the total power is $P_\nu\propto U^{(2+p)/4}_B\sim D^{-\delta}$ , with an index The index is similar to that found in \citet{kb07} (their Eq 7)." + The approximation is obtained when p=2and ο)=3/2., The approximation is obtained when $p=2$ and $\beta=3/2$. +" As a result. the P, D power-law in this regine is significautly steeper than (29))."," As a result, the $P_\nu$ $D$ power-law in this regime is significantly steeper than \ref{eq:PD1}) )." +" Figure 2 shows three P, D tracks at 1.1GIIz. with three different input powers."," Figure \ref{fig:PD1} shows three $P_\nu$ $D$ tracks at $1.4\,\rm GHz$, with three different input powers." + Here both the initial size and the core radius are taken to be 2 kpc., Here both the initial size and the core radius are taken to be 2 kpc. + The tracks are obtained using the analytical solutious (20)) aud (21)) with 0—0.5. 7=0.5. p.=αντ«107?kem7. j—23/2. aud P=1/3 (which is appropriate for relativistic plastuas).," The tracks are obtained using the analytical solutions \ref{eq:Nad}) ) and \ref{eq:NSC}) ) with $\theta=0.5$, $\eta=0.5$, $\rho_c=1.7\times10^{-22}\,{\rm kg}\,{\rm m}^{-3}$, $\beta=3/2$, and $\Gamma=4/3$ (which is appropriate for relativistic plasmas)." + We assume the particle spectruuu to be the typical one from the standard diffusive shock acceleration. characterised by a power-law with au iudex p=2d aud the lower- aud upper-cutoff. (+1.η) (c£.," We assume the particle spectrum to be the typical one from the standard diffusive shock acceleration, characterised by a power-law with an index $p=2.1$ and the lower- and upper-cutoff, $(\gamma_1,\gamma_m)=(5,10^7)$ (cf." +Eq 19).,Eq \ref{eq:ql}] ]). + The maguetic field at the hot spots is asstuned to be By=30uT (Blundell.Rawlings 1999)..," The magnetic field at the hot spots is assumed to be $B_0=30\,\rm nT$ \citep{betal99}. ." + Since the initial particlespectruni is assuned to be zero. the spectral power. P. increases rapidly to the phase when the spectral power reaches," Since the initial particlespectrum is assumed to be zero, the spectral power, $P_\nu$ , increases rapidly to the phase when the spectral power reaches" +"inaterial deusities p=3.3 ο ci? for MesSiO, and 3.7 ecu 7 for MgFeSiO,. we fiud opacities at V of kpc7 cup | for MeoSiO , aud ~3032 cu? ο1 for MeFeSiO| (with gii=38lpe. where Qui is the dust absorption cocfücient aud e isf the erain radius).","material densities $\rho =3.3$ g $^{-3}$ for $_2$ $_4$ and 3.7 g $^{-3}$ for $_4$ , we find opacities at $V$ of $\kappa_V \simeq 7$ $^2$ $^{-1}$ for $_2$ $_4$ and $\simeq 3032$ $^2$ $^{-1}$ for $_4$ (with $\kappa_V = 3 Q_{\rm abs}/4 \rho a$, where $Q_{\rm abs}$ is the dust absorption coefficient and $a$ is the grain radius)." +" Additionally. if we infer from the SN 1961V light curve that the outburst cuded sometime in 1962. then the expansion at 2000 kins | from this eud date to the aid- of theSpitzer obscrvatious. i.c.. carly 2006. leads to an iuner radius for the dust sphere of Ry,&2.7«Lot cni"," Additionally, if we infer from the SN 1961V light curve that the outburst ended sometime in 1962, then the expansion at 2000 km $^{-1}$ from this end date to the mid-date of the observations, i.e., early 2006, leads to an inner radius for the dust sphere of $R_{\rm in} \simeq 2.7 \times 10^{17}$ cm." +" Tf we also asstune that the outburst comuucieect. roughly. at the end of 1960. then it effectively lasted for ~2 yr. and the shell thickness AR~1.3&1019 cu. or ARBy,~0.05. ("," If we also assume that the outburst commenced, roughly, at the end of 1960, then it effectively lasted for $\sim$ 2 yr, and the shell thickness $\Delta R \simeq 1.3 \times 10^{16}$ cm, or ${\Delta R}/R_{\rm in} \simeq 0.05$. (" +"As has shown. the thickuess of observed LBV nebulae. e.g. in the LMC. is generally Dl05:Cn vet. as poiut out. the DUSTY inodels are relatively inseusitive at these radii to the choice of shell thickness. aud we find little difference in the results if we set ARR,> 0.05.)","As has shown, the thickness of observed LBV nebulae, e.g, in the LMC, is generally $>$; yet, as point out, the DUSTY models are relatively insensitive at these radii to the choice of shell thickness, and we find little difference in the results if we set ${\Delta R}/R_{\rm in} > 0.05$ .)" +" Tf the mass of the gaseous nebular shell is Aag210AL.. (see above). then. assuniug a dust-to-2as ratio of L/100. the shells dust mass is Miu2OLAL... which. for optical depth Mh=BALastbaIz aud Roya=Ru results iu Tyoc0Q001 and z0.6. IU,respectively Gvlich correspond in DUSTY to 0.133 aud 1.0823. respectively)."," If the mass of the gaseous nebular shell is $M_{\rm shell} \simeq 10\ M_{\odot}$ (see above), then, assuming a dust-to-gas ratio of 1/100, the shell's dust mass is $M_{\rm dust} \simeq 0.1\ M_{\odot}$, which, for optical depth $\tau_V = 3M_{\rm dust}\kappa_V/4{\pi}R^2_{\rm shell}$ and $R_{\rm shell} = R_{\rm in}$, results in $\tau_V \simeq 0.004$ and $\simeq 0.6$, respectively (which correspond in DUSTY to 0.133 and 1.083, respectively)." + FinalEma we assume for the DUSTY ioceling a dust erain size distribution (with iudex q= 3.5) and that the density distribution in the spherical shell around the ceutral source varies Xr7.," Finally, we assume for the DUSTY modeling a dust grain size distribution (with index $q=3.5$ ) and that the density distribution in the spherical shell around the central source varies $\propto r^{-2}$." +" If we represent Object 7 in DUSTY as à Dig=30000 I blackbody with huuinositv Lz10° L.. then the ust tempcratures at the imucr aud outer edges of the shell are approximately 119) and 127 Ik. respectively. for the Mgo»SiO, model. and approximately 196 aud 115 I. respectively. for the MeFeSiO, model."," If we represent Object 7 in DUSTY as a $T_{\rm eff} = 30000$ K blackbody with luminosity $L \approx 10^6\ L_{\odot}$ , then the dust temperatures at the inner and outer edges of the shell are approximately 149 and 127 K, respectively, for the $_2$ $_4$ model, and approximately 196 and 115 K, respectively, for the $_4$ model." + Clearly. the values of zr for amorphous silicates in the shell are significantly smaller thin those ποπιο from our asstumed range in extinction. ly= 1.52.3 mae (and are far smaller than what asstuned for their primary scenario).," Clearly, the values of $\tau_V$ for amorphous silicates in the shell are significantly smaller than those stemming from our assumed range in extinction, $A_V=1.8$ –2.3 mag (and are far smaller than what assumed for their primary scenario)." + As we have already cluphasized. above. it is not necessary to prestuue that any nebula around SN 1961V is particularly dusty.," As we have already emphasized, above, it is not necessary to presume that any nebula around SN 1961V is particularly dusty." +" For this reason. we further assiune that the additional optical depth arises aloug the line-ofsight to SN 1961V. within the host ealaxyv. aud. therefore. we apply the ""LMC average” extinction law frou(2001)."," For this reason, we further assume that the additional optical depth arises along the line-of-sight to SN 1961V within the host galaxy, and, therefore, we apply the “LMC average” extinction law from." +. Iu Figure |. we show our dust models. relative to the served flux at V for Object 7 aud the upper limits ou he mid-IR enmüssion from a dust shell.," In Figure \ref{figmir} we show our dust models, relative to the observed flux at $V$ for Object 7 and the upper limits on the mid-IR emission from a dust shell." +" The prediction of the emission from the lower-optical-depth MeoS1O0, dust model is comfortably within the observed upper inits. while. adauittedly. the MeFeSiO inodoel predicts hat SN 1961V. should have Όσοι detected at 21 sau. although it would escape detection in all of the IRAC xus (whereas all of the dust models by exceed the observed limits. at least at 8 gan. if not iu all of the IRAC bands)."," The prediction of the emission from the lower-optical-depth $_2$ $_4$ dust model is comfortably within the observed upper limits, while, admittedly, the $_4$ model predicts that SN 1961V should have been detected at 24 $\mu$ m, although it would escape detection in all of the IRAC bands (whereas all of the dust models by exceed the observed limits, at least at 8 $\mu$ m, if not in all of the IRAC bands)." + The situation for this atter mocdelis further ageravated. of course. 1f we assume hat Object 7 has Tig=10000 1. increasing the overall wcL-IR dhunuinositv from the dust shell.," The situation for this latter model is further aggravated, of course, if we assume that Object 7 has $T_{\rm eff}=40000$ K, increasing the overall mid-IR luminosity from the dust shell." + Reeardless of he stars effective temperature. one could sidestep the ack of detected 21 gan emission. however. by presunming. or instance. that the amorphous silicates iu the shell are less Fe-vich. which is certainly possible.," Regardless of the star's effective temperature, one could sidestep the lack of detected 24 $\mu$ m emission, however, by presuming, for instance, that the amorphous silicates in the shell are less Fe-rich, which is certainly possible." + Another oossibilitv is that the dust mass in the shell is less than what we have asstuned. lowering the overall huuinositv of he chussion.," Another possibility is that the dust mass in the shell is less than what we have assumed, lowering the overall luminosity of the emission." + Furthermore. the geometry of the ejected natter from Object 7 112v be aspherical. asvinnetric. or oth2001).," Furthermore, the geometry of the ejected matter from Object 7 may be aspherical, asymmetric, or both." +. In iu eveut. we have shown. using both observatious of other SN imupostors and what we consider to be a more realistic model of any dusty ejecta around the star. that the lack of mud-IR Cluission frou SN 1961V. alone. particularly across all of theSpitzer bands. is not a valid areuueut to climinate the possibility altogether that it is a SN impostor.," In any event, we have shown, using both observations of other SN impostors and what we consider to be a more realistic model of any dusty ejecta around the star, that the lack of mid-IR emission from SN 1961V alone, particularly across all of the bands, is not a valid argument to eliminate the possibility altogether that it is a SN impostor." + Based on our analysis of the available data. we cousider SN 1961V (still) to be a SN impostor aud that Object Tds the survivor of this event.," Based on our analysis of the available data, we consider SN 1961V (still) to be a SN impostor and that Object 7 is the survivor of this event." + All of the areuineuts we have mace above. as part of this analysis. support this conclusion.," All of the arguments we have made above, as part of this analysis, support this conclusion." + We have also attempted to dispel several erroneous suppositious about the nature of this event., We have also attempted to dispel several erroneous suppositions about the nature of this event. + The survivor is clearly observed iu very recent vears to exist., The survivor is clearly observed in very recent years to exist. + The star quite plausibly las the propertics of a quiescent. massive LBV.," The star quite plausibly has the properties of a quiescent, massive LBV." + The star has uot vet exploded and is not a radio SN., The star has not yet exploded and is not a radio SN. + The star is smrounded bv a civetunstellar shell or nebula. however. this shell is not nearly as dusty as required by and previous investigators.," The star is surrounded by a circumstellar shell or nebula, however, this shell is not nearly as dusty as required by and previous investigators." + We find that the visual extinction to Object 7 is in the ranee Ay=1.5 2.3 ae. and we sugeest that most of this extinction is arising frou 1ο oejuterstellar median along our Luc-ofsight within the ost galaxy. rather than from the shell itself.," We find that the visual extinction to Object 7 is in the range $A_V=1.8$ –2.3 mag, and we suggest that most of this extinction is arising from the interstellar medium along our line-of-sight within the host galaxy, rather than from the shell itself." + As a result. jerefore. the shell need uot be nearly as Iuuinous an IR cutter as jg Car.," As a result, therefore, the shell need not be nearly as luminous an IR emitter as $\eta$ Car." + This conclusion is further supported by je nid-IR observations of other SN iupostors., This conclusion is further supported by the mid-IR observations of other SN impostors. + The positional proximity of Object 7 to SN 1961V. aud ie positional offset between SN 1961V aud the radio source centroid. are both imescapable facts.," The positional proximity of Object 7 to SN 1961V, and the positional offset between SN 1961V and the radio source centroid, are both inescapable facts." + The ouly conceivable way to counter the former fact is to couclude wat Object 7 is either a physical or an optical double o the progenitor of an actual SN., The only conceivable way to counter the former fact is to conclude that Object 7 is either a physical or an optical double to the progenitor of an actual SN. + This. of course. is xossible.," This, of course, is possible." + The uncertainty alone in the absolute position. WL. corresponds to ~5 pc. certainly allowing for the oossibilitv. iu the relatively crowded cluster euvironmoeut of SN 1961V. that Object 7 is merely a ueighhor to he progenitor.," The uncertainty alone in the absolute position, $0{\farcs}1$, corresponds to $\sim 5$ pc, certainly allowing for the possibility, in the relatively crowded cluster environment of SN 1961V, that Object 7 is merely a neighbor to the progenitor." + Also. the probability of core-collapse SNe or high-mass stars in binarics is relatively bhügh2009).," Also, the probability of core-collapse SNe for high-mass stars in binaries is relatively high." +. Although. if Object 7 the binary colupanion to the star that exploded. we iuüeht expect Object 7 to have been stripped or otherwise affected o» what would have been a very powerful explosion. xotentiallv leading to an unusual brightuess or color.," Although, if Object 7 the binary companion to the star that exploded, we might expect Object 7 to have been stripped or otherwise affected by what would have been a very powerful explosion, potentially leading to an unusual brightness or color." + This is not supported by the available photometry or inferred huninositv of Object 7., This is not supported by the available photometry or inferred luminosity of Object 7. + Tustead. it appears to ave the properties of a “run-ofthe-uull.” evolved. high-nass star.," Instead, it appears to have the properties of a “run-of-the-mill,” evolved, high-mass star." + Nonetheless. the positional offset between SN 1961V aud the radio centroid is insurnmountable — these wo are not one and the same. which is essentially at thejeart ofthe case that has been made for SN 1961V. beine a true SN.," Nonetheless, the positional offset between SN 1961V and the radio centroid is insurmountable — these two are not one and the same, which is essentially at theheart of the case that has been made for SN 1961V being a true SN." + No need exists for the supposed core-collapse explosion “hybrid” of à SN IEP aud SNUn., No need exists for the supposed core-collapse explosion “hybrid” of a SN II-P and SNIIn. + Furthermore. we disagree with the statement made by that SN 1961V is somehow unique among the impostors.," Furthermore, we disagree with the statement made by that SN 1961V is somehow unique among the impostors." +"In particular, the CART algorithm, the C4.5 algorithm with confidence values of 0.25 and 0.1 and the Random Forest algorithm with 10 and 50 trees were considered.","In particular, the CART algorithm, the C4.5 algorithm with confidence values of 0.25 and 0.1 and the Random Forest algorithm with 10 and 50 trees were considered." +" For all test cases, a ten-fold cross validation strategy was used."," For all test cases, a ten-fold cross validation strategy was used." +" The compiled 75,000 sample set (Set 3) was divided into 10 complimentary subsets and the learning algorithm was executed for 10 times."," The compiled 75,000 sample set (Set 3) was divided into 10 complimentary subsets and the learning algorithm was executed for 10 times." +" In each run, one of the ten subsets was used for testing and the other nine subsets were put together to form the training set."," In each run, one of the ten subsets was used for testing and the other nine subsets were put together to form the training set." + The presented results are the computed averages across all ten trials., The presented results are the computed averages across all ten trials. +" By this approach, every sample is part of the test set at least once."," By this approach, every sample is part of the test set at least once." + The resulting confusion matrices when considering the 13 band parameters are shown in Figure 6.., The resulting confusion matrices when considering the 13 band parameters are shown in Figure \ref{resultsGoldSubI}. + These tables correlate the actual morphological classes with those outputted by the classifier., These tables correlate the actual morphological classes with those outputted by the classifier. +" For instance, in the first row, the percentages of elliptical galaxies that were classified as elliptical (E), spiral (S) and unknown (U) are shown."," For instance, in the first row, the percentages of elliptical galaxies that were classified as elliptical (E), spiral (S) and unknown (U) are shown." +" Decision trees output a single morphology type for every input, therefore the percentages in each row add up to100%."," Decision trees output a single morphology type for every input, therefore the percentages in each row add up to." +. This corresponds to all of the input samples of a particular class., This corresponds to all of the input samples of a particular class. + The global accuracy percentage was then calculated by comparing the total number of correctly classified samples with the total number of inputted tests., The global accuracy percentage was then calculated by comparing the total number of correctly classified samples with the total number of inputted tests. +" In all decision tree algorithms tested, the global accuracy is always above with the highest being achieved by the 50 tree random forest technique."," In all decision tree algorithms tested, the global accuracy is always above with the highest being achieved by the 50 tree random forest technique." + All confusion matrices result to have the highest values in the diagonal., All confusion matrices result to have the highest values in the diagonal. + This indicates that the majority of samples were classified correctly., This indicates that the majority of samples were classified correctly. +" The random forest algorithm with 50 trees did prove to be the most accurate and did manage to correctly classify of all ellipticals, of all spirals and of all unknown objects."," The random forest algorithm with 50 trees did prove to be the most accurate and did manage to correctly classify of all ellipticals, of all spirals and of all unknown objects." + The slightly less than optimal classification percentages for unknown objects can be due to a number of factors., The slightly less than optimal classification percentages for unknown objects can be due to a number of factors. +" First of all, the number of training samples with unknown morphology might have not been enough for the algorithm to learn how to identify such samples and secondly, objects that mislead humans might actually have very similar properties to spiral or elliptical galaxies and are ultimately also classified correctly by the algorithm."," First of all, the number of training samples with unknown morphology might have not been enough for the algorithm to learn how to identify such samples and secondly, objects that mislead humans might actually have very similar properties to spiral or elliptical galaxies and are ultimately also classified correctly by the algorithm." +" The membership functions derived by the fuzzy inference system for the DeVaucouleurs fit axis ratio, exponential fit axis ratio and concentration parameters in the band, are shown in Figure 7.."," The membership functions derived by the fuzzy inference system for the DeVaucouleurs fit axis ratio, exponential fit axis ratio and concentration parameters in the band, are shown in Figure \ref{fisMembershipFunctions}." +" For such a model, subtracting clustering was used."," For such a model, subtracting clustering was used." + The results obtained after testing are presented in Figure 8.., The results obtained after testing are presented in Figure \ref{resultsGoldSubFisI}. +" Clearly, the developed model is capable of describing elliptical and spiral galaxies but suffers to accurately detect galaxies tagged to have an unknown type."," Clearly, the developed model is capable of describing elliptical and spiral galaxies but suffers to accurately detect galaxies tagged to have an unknown type." +Note that here is an offset of the zero point between tle relativistic and nonrelativistie Fermi levels given by Ej(relativistic)=Ey(nourelativistic)+c. where the offset is negligible when particles are extremely relaivistic.,"Note that there is an offset of the zero point between the relativistic and nonrelativistic Fermi levels given by $E_f({\rm relativistic}) = E_f({\rm nonrelativistic}) + m c^2$, where the offset is negligible when particles are extremely relativistic." + Again in the nonrelativisic regime. relic neutrinos are expected lobe moderately cdegeerate.," Again in the nonrelativistic regime, relic neutrinos are expected to be moderately degenerate." + Due to the change of dispersion relation of individual particles caused by 1he relativistic-to-Donreativistic transition. the «egree of degeneracy changes slightly. but thüs elTe4 appears minor.," Due to the change of dispersion relation of individual particles caused by the relativistic-to-nonrelativistic transition, the degree of degeneracy changes slightly, but this effect appears minor." + Next we compare the kiuetic euergy leve of boutd neutrinos in he cluster and that of uubound neulrinos to see if relic uettrinos are col eiougli πε) that tley Cal fall to tve cluster., Next we compare the kinetic energy level of bound neutrinos in the cluster and that of unbound neutrinos to see if relic neutrinos are cold enough so that they can fall to the cluster. + The Ferini leve xd gravitationaly luduced kinetic elerey at tle cluster core zwe of 10.1 eV or above as seen in .18.., The Fermi level and gravitationally induced kinetic energy at the cluster core are of $10^{-4}$ eV or above as seen in \ref{neu.EfEk}. + On the other hand. uubouud ‘ell€ neutrinos wlich uneergo adiabatic expansion have (je iperature given by eq(31)).," On the other hand, unbound relic neutrinos which undergo adiabatic expansion have the temperature given by \ref{Tnonrela}) )." +" For Α1659 al 2=0.18 and for in=1.6 eV. the kinetic euergy of Uulx=xl relies will be 3.65x10 ""eV. wl1C1 is well below the ene‘oy level of the particles iu the Hs “core."," For A1689 at $z=0.18$ and for $m=1.6$ eV, the kinetic energy of unbound relics will be $3.65\times 10^{-8}$ eV, which is well below the energy level of the particles in the cluster core." + So it is possible that the relic eutrinos can fall into the cluster core., So it is possible that the relic neutrinos can fall into the cluster core. + Tve cluster also has lot plasma. whic may affect the fermion degeueracy.," The cluster also has hot plasma, which may affect the fermion degeneracy." + Here we briefly argle hat the effect of hot Ρο will be -—inor., Here we briefly argue that the effect of hot plasma will be minor. + First of all. hot plasina aud neutrinos (or weakly inte‘acting fermions in general) interact oy through gravity aud the plasina. temperature las uot]ing to do with the velocity clispersion of eutrinos. which 7is determined by tle eucircles mass at a gl'en r.," First of all, hot plasma and neutrinos (or weakly interacting fermions in general) interact only through gravity and the plasma temperature has nothing to do with the velocity dispersion of neutrinos, which is determined by the encircles mass at a given $r$." + What matters is tle plasina's contri utioutothee 'àirclec inass (or eucircled gravitational eerey ifthe plasiua is relativistic)., What matters is the plasma's contribution to the encircled mass (or encircled gravitational energy if the plasma is relativistic). + The raio of gas nass a total mass has been estimated to be aOluw by X-‘ay observaions (Anclerso&Maclejski2001)., The ratio of gas mass and total mass has been estimated to be about by X-ray observations \citep{Anderson04}. +. They interact. with fermious only Irouel yewLoulan gravity. because the plasiua is uot hot eiough to be relativistic or the kinetic eerev oO Sa plasna pa‘ticle is negligible compared to the rest-inass energy.," They interact with fermions only through Newtonian gravity, because the plasma is not hot enough to be relativistic or the kinetic energy of a plasma particle is negligible compared to the rest-mass energy." + Therefore iuiless the plasma particles have exceptioually high concentration near tle 3D center of the cluster. their effect [9] the οιcircled mass siould be minor compared to that by the dark matter particles.," Therefore unless the plasma particles have exceptionally high concentration near the 3D center of the cluster, their effect on the encircled mass should be minor compared to that by the dark matter particles." + Howevel. all extreme ugh conceutration is uot expected uuless the plasuia temperature profile has a si180larity heal the center.," However, an extreme high concentration is not expected unless the plasma temperature profile has a singularity near the center." + Since the X-ray. emission is integrated along the light of sight. X-ray observations alone wil not be capabe of pin-poiutiug the plasma temperature near the 3D center of tle cluster.," Since the X-ray emission is integrated along the light of sight, X-ray observations alone will not be capable of pin-pointing the plasma temperature near the 3D center of the cluster." + This degenerate [ermion/ueutrino hypothesis shouk be tested observationally with coming censiv profiles of otler clusters obtained by οavitational lensiug., This degenerate fermion/neutrino hypothesis should be tested observationally with future-coming density profiles of other clusters obtained by gravitational lensing. + Those profiles should e inodeled by the fixed set of j»article properties. (η.. aud by a varie| set of tle central deusity. p(Q).," Those profiles should be modeled by the fixed set of particle properties, $(m,g)$, and by a varied set of the central density, $\rho(0)$." + Mo«leliο multiple cluser profiles nay further e«yustrain the particle propeδν., Modeling multiple cluster profiles may further constrain the particle properties. +" There may be a room fo"" inprovemenut in the pheromenological equation of sate (PEOS).", There may be a room for improvement in the phenomenological equation of state (PEOS). + Tle PEOS used i1 this paper. (2)). overestimates the degereracy pressure. pp. siuce pp here is the Zero-lemperaure degeueracy pressure for a given numer censity. η. regardless of the temperature ol fermious or regardless of the degree of degeneracy.," The PEOS used in this paper, \ref{peos}) ), overestimates the degeneracy pressure, $p_D$, since $p_D$ here is the zero-temperature degeneracy pressure for a given number density, $n$, regardless of the temperature of fermions or regardless of the degree of degeneracy." + Fo| the same observed deusity. profile. the," For the same observed density profile, the" +As is obvious from Figures 6 to 10.. the binary velocity dispersion. Le. the second order velocity. moment fre. depends most sensitively on the inner eutolf radius min and the exponent 5 in the distribution of the semi-major axis αν and to a lesser degree on the primary mass ÀJ and the exponent .r in the Salpeter IME adopted as the distribution of the secondary mass ne.,"As is obvious from Figures \ref{sigaminps} to \ref{siggam}, the binary velocity dispersion, i.e. the second order velocity moment $\tilde{\mu}_2$, depends most sensitively on the inner cutoff radius $r_{\rm min}$ and the exponent $\gamma$ in the distribution of the semi-major axis $a_p$ and to a lesser degree on the primary mass $M$ and the exponent $x$ in the Salpeter IMF adopted as the distribution of the secondary mass $m_2$." +" As the stars in a binary. svsteni are allowed to approach each other more closcly in other words. às Main is lowered their orbital velocities rise rapicly. boosting the velocity dispersion of the binary population as a whole to values as high as 10 km/s for rji,=1i.. as can be seen in Figure 6.."," As the stars in a binary system are allowed to approach each other more closely – in other words, as $r_{\rm min}$ is lowered – their orbital velocities rise rapidly, boosting the velocity dispersion of the binary population as a whole to values as high as 10 km/s for $r_{\rm min}=1~{\rm R}_\odot$, as can be seen in Figure \ref{sigaminps}." + Since the bright giant stars that one is most likely to observe have radii of the order of 10 I... the velocity. dispersion is limited to values below 4 kms. The value of the outer cut-olf radius. rax. does not. strongly alfect the value of the binary. dispersion.," Since the bright giant stars that one is most likely to observe have radii of the order of 10 ${\rm +R}_\odot$, the velocity dispersion is limited to values below 4 km/s. The value of the outer cut-off radius, $r_{\rm max}$, does not strongly affect the value of the binary dispersion." + Higher μις values mean that more stars orbit on wide and consequently slow orbits. causing the dispersion to be a bit. lower.," Higher $r_{\rm +max}$ values mean that more stars orbit on wide and consequently slow orbits, causing the dispersion to be a bit lower." + A higher value of causes stars to move on more tightly bound orbits. hus boosting their velocities.," A higher value of $\gamma$ causes stars to move on more tightly bound orbits, thus boosting their velocities." + This is clear from Figure 10.., This is clear from Figure \ref{siggam}. + Η ο. the exponent of the Salpeter INL. is mace larger. the secondary masses will tend to be lower which also causes the wimaryv's orbital velocity and hence the velocity. dispersion of the binary population as a whole to be lower (see Figure 11)).," If $x$, the exponent of the Salpeter IMF, is made larger, the secondary masses will tend to be lower which also causes the primary's orbital velocity and hence the velocity dispersion of the binary population as a whole to be lower (see Figure \ref{sigx}) )." + WAZ is raised. the center of mass will be closer to he primary. causing its orbital velocity to drop slowly. as is observed in Figure S.. Larger values for mo will produce jeavier secondary stars.," If $M$ is raised, the center of mass will be closer to the primary, causing its orbital velocity to drop slowly, as is observed in Figure \ref{sigM}.. Larger values for $m_2$ will produce heavier secondary stars." + A slowly rising velocity dispersion ensues. as can be seen in Figure 9..," A slowly rising velocity dispersion ensues, as can be seen in Figure \ref{sigm2}." + Phe same exercise was done with a uniform distribution for the eccentricity., The same exercise was done with a uniform distribution for the eccentricity. + The outcome was essentially identical: the binary velocity dispersion dilfered at most by 0.1 kms. Hence. our results do not depend critically on the adopted distribution for the eccentrieltvy.," The outcome was essentially identical: the binary velocity dispersion differed at most by 0.1 km/s. Hence, our results do not depend critically on the adopted distribution for the eccentricity." + The values for the binary velocity. dispersion obtained here are about the same as those obtained by Llargreaves although these authors use Gaussian distributions for the ellipticity. secondary mass ancl period. making it clifficult to directly compare the results.," The values for the binary velocity dispersion obtained here are about the same as those obtained by Hargreaves although these authors use Gaussian distributions for the ellipticity, secondary mass and period, making it difficult to directly compare the results." + Mateo (1993).. emploving a Monte Carlo simulation with a uniformly clistributed ellipticity and secondary mass and a power law distribution for the period. find higher velocity dispersions.," Mateo \cite{mat}, employing a Monte Carlo simulation with a uniformly distributed ellipticity and secondary mass and a power law distribution for the period, find higher velocity dispersions." + However. it is mentioned by Hargreaves and by Olszewski that the values published by Mateo are overestimated due to a coding error.," However, it is mentioned by Hargreaves and by Olszewski that the values published by Mateo are overestimated due to a coding error." + The corrected Mateo values however are in good agreement with the results obtained. by other authors and with those presented here., The corrected Mateo values however are in good agreement with the results obtained by other authors and with those presented here. + In the following. we will adopt the model with as our “standard” model.," In the following, we will adopt the model with as our “standard” model." +" Its velocity dispersion is km/s and its kurtosis amounts to £14,=N6.80."," Its velocity dispersion is $\sigma_{\rm b} += 2.87$ km/s and its kurtosis amounts to $\xi_{4, \rm{b}} = 86.89$." + Vhe LOSVD that would actually be observed. is. the convolution of the binary LOSVD (describing the motion of stars in binary svstems) and the intrinsic LOSVD of the ealaxy (determined by the stars’ orbital motions through the galaxy)., The LOSVD that would actually be observed is the convolution of the binary LOSVD (describing the motion of stars in binary systems) and the intrinsic LOSVD of the galaxy (determined by the stars' orbital motions through the galaxy). +" Lowe denote the intrinsic galaxy LOSVD hy yile,) and the binary LOSVD by ορ).then the observed"," If we denote the intrinsic galaxy LOSVD by $\varphi_{\rm i}(v_p)$ and the binary LOSVD by $\varphi_{\rm + b}(v_p)$ ,then the observed" +"The Fermi--LAT (?) is a pair conversion telescope designed to cover the energy band from 20 MeV to greater than 300 GeV. It is the product of an international collaboration between NASA and DOE in the U.S. and many scientific institutions across France, Italy, Japan, and Sweden."," The -LAT \citep{2009ApJ...697.1071A} is a pair conversion telescope designed to cover the energy band from 20 MeV to greater than 300 GeV. It is the product of an international collaboration between NASA and DOE in the U.S. and many scientific institutions across France, Italy, Japan, and Sweden." + The y-ray emission of 345 was identified based on correlations found between the optical variability and major y- ray events observed by LAT between August 2008 and April 2010.," The $\gamma$ -ray emission of $\,$ 345 was identified based on correlations found between the optical variability and major $\gamma$ -ray events observed by LAT between August 2008 and April 2010." +" The y-ray counterpart of 3345 was localized to R.A. 16543""0.245, Dec. +39°448’222.7”(?).."," The $\gamma$ -ray counterpart of 345 was localized to R.A. $^\mathrm{h}$ $^\mathrm{m}$ $^\mathrm{s}$, Dec. $+$ \citep{Schinzel_2010A}." +" For this paper a light curve for which the y-ray monitoring data was split into regular time intervals, each integrating over periods of 7 days and an energy range of GGeV, was obtained in the fashion described in ?.."," For this paper a light curve for which the $\gamma$ -ray monitoring data was split into regular time intervals, each integrating over periods of 7 days and an energy range of GeV, was obtained in the fashion described in \citet{Schinzel_2010A}." + The position of the y-ray counterpart was fixed to the radio localization of 3345., The position of the $\gamma$ -ray counterpart was fixed to the radio localization of 345. + For the spectral shape of the y-ray emission of 3345 a power-law was used with the spectral index fixed to its 20 month average value of T22.45?., For the spectral shape of the $\gamma$ -ray emission of 345 a power-law was used with the spectral index fixed to its 20 month average value of $\Gamma=2.45$. +", The particular time binning of 7 days in this case provides the best trade-off between time resolution and signal to noise.", The particular time binning of 7 days in this case provides the best trade-off between time resolution and signal to noise. +" This yielded a light curve with 81 significant detections and five 2c upper limit time intervals 22454756, 2454826, 2454903, 2454945, 2455155), in total this covers a time period of 602 days (20 months)."," This yielded a light curve with 81 significant detections and five $\sigma$ upper limit time intervals 2454756, 2454826, 2454903, 2454945, 2455155), in total this covers a time period of 602 days (20 months)." +" In order to homogenize the light curve, 2σ upper limits were used as values with their error estimate for that interval replaced with half the difference between that upper limit and its value determined through the unbinned spectral likelihood analysis."," In order to homogenize the light curve, $\sigma$ upper limits were used as values with their error estimate for that interval replaced with half the difference between that upper limit and its value determined through the unbinned spectral likelihood analysis." + This method was applied for the calculation of the variability index in ? and ?.., This method was applied for the calculation of the variability index in \citet{Schinzel_2010A} and \citet{2010ApJS..188..405A}. +" Following the onset of a new period of flaring activity in 2008, a dedicated monthly monitoring campaign was initiated, using the VLBA to monitor the radio emission of 3345 at 43.2, 23.8, and GGHz (VLBA project codes: BS193, BS194)."," Following the onset of a new period of flaring activity in 2008, a dedicated monthly monitoring campaign was initiated, using the VLBA to monitor the radio emission of 345 at 43.2, 23.8, and GHz (VLBA project codes: BS193, BS194)." +" In this paper only the GGHz observations are discussed, while the analysis of 15.4 and GGHz data is continued."," In this paper only the GHz observations are discussed, while the analysis of 15.4 and GHz data is continued." + The observations were made with a bandwidth of MMHz (total recording bit rate ss!)., The observations were made with a bandwidth of MHz (total recording bit rate $^{-1}$ ). +" A total of 12 VLBA observations were completed, with about 4.5 hours at GGHz spent on 3345 during each observation."," A total of 12 VLBA observations were completed, with about 4.5 hours at GHz spent on 345 during each observation." +" Scans on were interleaved with observations of (amplitude check, EVPA calibrator), (D-term calibrator), and (amplitude check, EVPA calibrator)."," Scans on were interleaved with observations of (amplitude check, EVPA calibrator), (D-term calibrator), and (amplitude check, EVPA calibrator)." + The VLBA data were correlated at the NRAO VLBA hardware correlator and starting from December 2009 the new VLBA-DiFX correlator was employed., The VLBA data were correlated at the NRAO VLBA hardware correlator and starting from December 2009 the new VLBA-DiFX correlator was employed. + Analysis was done with NRAO's Astronomical Image Processing System (AIPS) and Caltech's Difmap (?) software for imaging and modeling., Analysis was done with NRAO's Astronomical Image Processing System (AIPS) and Caltech's Difmap \citep{1995BAAS...27..903S} software for imaging and modeling. + Corrections were applied for the parallactic angle and for Earth’s orientation parameters used by the VLBA correlator., Corrections were applied for the parallactic angle and for Earth's orientation parameters used by the VLBA correlator. + Fringe fitting was used to calibrate the observations for group delay and phase rate., Fringe fitting was used to calibrate the observations for group delay and phase rate. + A summary of all the observations is presented in Table 1.., A summary of all the observations is presented in Table \ref{tab:obssummary}. +" Here, the data from the 12 epochs of this dedicated monitoring campaign are presented, combined with 20 VLBA observations from the blazar monitoring program of Marscher et al. ("," Here, the data from the 12 epochs of this dedicated monitoring campaign are presented, combined with 20 VLBA observations from the blazar monitoring program of Marscher et al. (" +"VLBA project codes BM256, $1136) availableonline?.","VLBA project codes BM256, S1136) available." +". The combined data (see Table 1)) cover a period from January 2008 to March 2010, with observations spaced roughly at monthly intervals or shorter."," The combined data (see Table \ref{tab:obssummary}) ) cover a period from January 2008 to March 2010, with observations spaced roughly at monthly intervals or shorter." +" The brightness distribution of the radio emission was modelfitted by multiple Gaussian components providing positions, flux densities and sizes of distinct emitting regions in the jet."," The brightness distribution of the radio emission was modelfitted by multiple Gaussian components providing positions, flux densities and sizes of distinct emitting regions in the jet." + Fig., Fig. + 1 illustrates the observed radio structure and the Gaussian modelfit representation., \ref{fig:map} illustrates the observed radio structure and the Gaussian modelfit representation. +" In the following, we interpret the eastern-most Gaussian modelfit component obtained from the VLBI map, hereafter labeled as QO (see Fig. 1)),"," In the following, we interpret the eastern-most Gaussian modelfit component obtained from the VLBI map, hereafter labeled as Q0 (see Fig. \ref{fig:map}) )," +" as the base (or ""core"") of the radio jet at GGHz.", as the base (or “core”) of the radio jet at GHz. + The remaining features can signify perturbations or shocks developing in the jet., The remaining features can signify perturbations or shocks developing in the jet. + Locations and proper motions of these jet features are then determined with respect to QO., Locations and proper motions of these jet features are then determined with respect to Q0. +" To find the best description of the observed brightness distribution, compact emission in the nuclear region (<00.15mmas from QO) was modeled using four different approaches: 1) single circular Gaussian, 2) single elliptical Gaussian, 3) two circular Gaussians, 4) three circular Gaussians."," To find the best description of the observed brightness distribution, compact emission in the nuclear region $\leq$ mas from Q0) was modeled using four different approaches: 1) single circular Gaussian, 2) single elliptical Gaussian, 3) two circular Gaussians, 4) three circular Gaussians." +" In the following discussion, these modelfitting approaches are designated 1C, 1E, 2C and 3C, respectively."," In the following discussion, these modelfitting approaches are designated 1C, 1E, 2C and 3C, respectively." +the adopted indices windows: examples of our best and worst S/N spectra are overplotted.,the adopted indices windows; examples of our best and worst S/N spectra are overplotted. + We also measured two additional indices. centred around the calcium H and K lines and the Hy line (see also Fig. 3..," We also measured two additional indices, centred around the calcium H and K lines and the $_{\beta}$ line (see also Fig. \ref{fig_spindex}," + bottom panels): The H and K line strengths depend mostly on temperature and on the calcium abundance. while the Πρ line strength depends on temperature and of course on the hydrogen abundance.," bottom panels): The H and K line strengths depend mostly on temperature and on the calcium abundance, while the $_{\beta}$ line strength depends on temperature and of course on the hydrogen abundance." + We used these two indices to reject a few remaining c outliers (at most 2—3 stars per cluster)., We used these two indices to reject a few remaining $\sigma$ outliers (at most 2–3 stars per cluster). + Since we used the indices only in a relative sense. we did not need to compare our measurements with the literature. therefore we defined our own narrow and conservative windows (see Fig. 3..," Since we used the indices only in a relative sense, we did not need to compare our measurements with the literature, therefore we defined our own narrow and conservative windows (see Fig. \ref{fig_spindex}," + lower panels) in order to minimize the spread due to disturbing features containing other elements and to maximize our ability to pinpoint outliers., lower panels) in order to minimize the spread due to disturbing features containing other elements and to maximize our ability to pinpoint outliers. + In our wavelength region. we measured two different CN band indices. $3839 for the CN band around and S4142 for the much weaker one around 42002," In our wavelength region, we measured two different CN band indices, S3839 for the CN band around and S4142 for the much weaker one around 4200." +003)., Fig. + Fig. 4 shows a comparison between the two., \ref{fig_cncn2} shows a comparison between the two. + The correlation appears weak for the metal-poor clusters (NGC 6752. NGC 288. NGC 1851). in spite. of the higher S/N of the spectra. because these double-metal molecular bands are weaker.," The correlation appears weak for the metal-poor clusters (NGC 6752, NGC 288, NGC 1851), in spite of the higher S/N of the spectra, because these double-metal molecular bands are weaker." + A clear correlation appears for the most metal-rich clusters (47 Tuc. NGC 6352. NGC 5927. and NGC 6388). although it is not as striking for NGC 6388. given the low S/N and paucity of stars.," A clear correlation appears for the most metal-rich clusters (47 Tuc, NGC 6352, NGC 5927, and NGC 6388), although it is not as striking for NGC 6388, given the low S/N and paucity of stars." + The slope of the relation between S4142 and $3839 appears to be roughly the same for all clusters (dotted line in Fig. 4)).," The slope of the relation between S4142 and S3839 appears to be roughly the same for all clusters (dotted line in Fig. \ref{fig_cncn2}) )," + while the zeropoint varies slightly from cluster to cluster., while the zeropoint varies slightly from cluster to cluster. + As expected. Fig.," As expected, Fig." + 4 clearly shows that S4142 is less sensitive to the CN variations. because generally its spread is just slightly larger than the median errorbar shown in the right corner of each panel.," \ref{fig_cncn2} clearly shows that S4142 is less sensitive to the CN variations, because generally its spread is just slightly larger than the median errorbar shown in the lower-right corner of each panel." + This is especially true for the clusters., This is especially true for the metal-poor clusters. + On the other hand. the spread of 83839 ts always larger than its median errobar. even for the metal-poor clusters.," On the other hand, the spread of S3839 is always larger than its median errobar, even for the metal-poor clusters." + For this reason. we will be relying on $3839 measurements for CN. and we will set aside the less reliable S4142 ones 2003).," For this reason, we will be relying on S3839 measurements for CN, and we will set aside the less reliable S4142 ones ." +. At a fixed overall abundance. it is well known that the CN-band and CH-band are stronger in stars with lower temperature and gravity.," At a fixed overall abundance, it is well known that the CN-band and CH-band are stronger in stars with lower temperature and gravity." + To eliminate this dependency. different authors use different proxies for temperature and gravity. such as colours or nagnitudes or some combination of the Balmer indices2006).," To eliminate this dependency, different authors use different proxies for temperature and gravity, such as colours or magnitudes or some combination of the Balmer indices." + The indices are then corrected by fitting the lower envelope of the distribution in the chosen plane. and the new indices are generally indicated as 083839(CN) and 0CH4300.," The indices are then corrected by fitting the lower envelope of the distribution in the chosen plane, and the new indices are generally indicated as $\delta$ S3839(CN) and $\delta$ CH4300." + Most of the cited authors find generally no significant trend for S3839(CN). but they do always correct the CH4300 index. usually with a second-order polynomial.," Most of the cited authors find generally no significant trend for S3839(CN), but they do always correct the CH4300 index, usually with a second-order polynomial." + Give the diversity of shapes and slopes. we prefer to use to correct for the curvatureinduced," Given the diversity of shapes and slopes, we prefer to use to correct for the curvatureinduced" +relation J~AL?oE with the model of galaxy formation.,relation $J\sim M^{5/3}$ with the model of galaxy formation. + Thev explained it as a consequence of the tidial torque model., They explained it as a consequence of the tidial torque model. + Sistero(1983). incorporated (he rotational velocity of the Universe., \citet{Sistero83} incorporated the rotational velocity of the Universe. + A similar approach was presented bv Carrasco(1982) who explained this relation as a consequence of mechanical equilibrium between the gravitational and rotational energy. while Li(1998) proposed more general relation for J(M) ancl explained it as a result of the influence of the global rotation of the Universe on the structure formation.," A similar approach was presented by \citet{Carrasco82} who explained this relation as a consequence of mechanical equilibrium between the gravitational and rotational energy, while \citet{Li98} proposed more general relation for $J(M)$ and explained it as a result of the influence of the global rotation of the Universe on the structure formation." + Our finding is in agreement wilh prediction of the Li model (Li1993:Goclowskietal.2005).," Our finding is in agreement with prediction of the Li model \citep{Li98,Godlowski05}." +. In our opinion the observed relation between (he richness of galaxy. cluster and the alignment is due to (dal torque. as suggested by Catelan&Thenuns(1996).," In our opinion the observed relation between the richness of galaxy cluster and the alignment is due to tidal torque, as suggested by \citet{Catelan96}." +. Moreover. the analvsis of the linear tidal torque theory is pointing in the same direction 2006a.b).," Moreover, the analysis of the linear tidal torque theory is pointing in the same direction \citep{Noh06a,Noh06b}." +. Thev noticed the connection of the alignment with the considered scale of structure., They noticed the connection of the alignment with the considered scale of structure. + We [ound a strong correlation between. DM. (vpe and the velocity. dispersion., We found a strong correlation between $BM$ type and the velocity dispersion. + The velocily dispersion decreases wilh 2 tvpe., The velocity dispersion decreases with $BM$ type. + We found only weak correlation between ihe alignment and. BAL tvpe. claimed by Arval and Saurer 2007).," We found only weak correlation between the alignment and $BM$ type, claimed by Aryal and Saurer \citep{Aryal04,Aryal05a,Aryal06,Aryal07}." +. Our sample of clusters is an order of magnitude greater (han that one analvzed bv them., Our sample of clusters is an order of magnitude greater than that one analyzed by them. + Moreover (his weak correlation is found only in the case of using supergalactic coordinate svstem as the reference svstem., Moreover this weak correlation is found only in the case of using supergalactic coordinate system as the reference system. + The correlation between the alignment. and velocity. dispersion of galaxies belonging to clusters was found by Plionisetal.(2003)., The correlation between the alignment and velocity dispersion of galaxies belonging to clusters was found by \citet{Plionis03}. +. In our data this effect is statistically insignificant Gt is at 1.560 level).," In our data this effect is statistically insignificant (it is at $1,5\sigma$ level)." + Moreover. it is noted only in the case of A sample. not in D sample restricted to galaxies brighter than ma+3.," Moreover, it is noted only in the case of $A$ sample, not in $B$ sample restricted to galaxies brighter than $m_3+3$." + In PF Catalogue the position angles of brighter galaxies. which is the brightest member. the second. third ancl tenth brightest galaxy are distributed randomly (Pankoetal.2009).. while the present analvsis of all galaxies in cluster shows an anisotropic distribution.," In PF Catalogue the position angles of brighter galaxies, which is the brightest member, the second, third and tenth brightest galaxy are distributed randomly \citep{Panko09}, while the present analysis of all galaxies in cluster shows an anisotropic distribution." + II brighter galaxies are located more centrally. ancl dimmer ones are located outside rich," If brighter galaxies are located more centrally, and dimmer ones are located outside rich" + With the launch of the Wilkinson Microwave Anisotropy Probe (WMAD) in 2003. the CAMB has been measured in highly detailed full-skv maps (Bennettetal.2003:Spergel2007:Hinshawetal.2009:Jarosik 2011).. which have been examined in great. detail over (he past lew vears (Cruzetal.2005:deOliveira-Costa2004:Land&/Magueijo2005:LLoftuftοἱal.2009:HansenetNim&Naselskv2010:Bennett 2011).," With the launch of the Wilkinson Microwave Anisotropy Probe (WMAP) in 2003, the CMB has been measured in highly detailed full-sky maps \citep{Bennett2003,Spergel:2006,WMAP5,WMAP7}, which have been examined in great detail over the past few years \citep{Cruz2005,deOliveira2004,Land2005a,Hoftuft:2009,Hansen:2008,KimNaselsky:2010,Bennett:2010}." +. In particular. the angular (vo-point correlation function C(8) has been studied: it is defined as (he average product between the temperature of (wo points angle 9 apart ]lere 7(€2) is the fluctuation around the mean of the temperature in direction Q on the sky.," In particular, the angular two-point correlation function $C(\theta)$ has been studied; it is defined as the average product between the temperature of two points angle $\theta$ apart Here $T(\hat{\Omega})$ is the fluctuation around the mean of the temperature in direction $\hat\Omega$ on the sky." + Several anomalies have been claimed in (he angular correlation function. especially the missing power on large angular scales (lor a review. see Copiοἱal. (2010))).," Several anomalies have been claimed in the angular correlation function, especially the missing power on large angular scales (for a review, see \cite{CHSS_review}) )." + Specilicallv. the angularcorrelation function is very nearly zero ad scales above 607: such a low correlation has," Specifically, the angularcorrelation function is very nearly zero at scales above $60\degr$ ; such a low correlation has" +The debiased NEO distribLion we use lias a [ull suite of high-speed impactors: more thau half the impactors are moving faste rihan tee = 19.3 km/s when they hit the Moon.,The debiased NEO distribution we use has a full suite of high-speed impactors; more than half the impactors are moving faster than $v_{med}$ = 19.3 km/s when they hit the Moon. + This has serious üunplicatious [for the calculate projectile diameters that created lunar craters since the higher speeds we calculate mean tha typical iupactor diameters are sinaller than previously derived., This has serious implications for the calculated projectile diameters that created lunar craters since the higher speeds we calculate mean that typical impactor diameters are smaller than previously derived. + Strictly speaking. our results aj»ply ouly when the NEO orbital distribution is valid. which," Strictly speaking, our results apply only when the NEO orbital distribution is valid, which" +the information obtained by every additional observation for the purpose of estimating the parameters of the model behind the observations.,the information obtained by every additional observation for the purpose of estimating the parameters of the model behind the observations. + The formulation of our problem is much more specific and simple - we want to optimize our chances to ’catch’ the transit using well-scheduled follow-up observations., The formulation of our problem is much more specific and simple - we want to optimize our chances to 'catch' the transit using well-scheduled follow-up observations. +" While every RV measurement contributes in some way to the orbital solution, the contribution of an individual photometric measurement to the transit solution boils down to the binary question whether it is in the transit or not."," While every RV measurement contributes in some way to the orbital solution, the contribution of an individual photometric measurement to the transit solution boils down to the binary question whether it is in the transit or not." +" Thus, ABE uses an elaborate merit function that quantifies the amount of information in the RV measurements."," Thus, ABE uses an elaborate merit function that quantifies the amount of information in the RV measurements." +" ABE can probably be applied to our problem as well, but we feel it would be redundant due to the simpler nature of the problem."," ABE can probably be applied to our problem as well, but we feel it would be redundant due to the simpler nature of the problem." + We speculate that the two approaches would yield very similar results., We speculate that the two approaches would yield very similar results. + Our experience shows that the MH algorithm and the ITP tend to find all possible periods that fit the data., Our experience shows that the MH algorithm and the ITP tend to find all possible periods that fit the data. +" Because of the low cadence of measurements, some hypothetical models may fit the data simply because the “transits” occur during ’gap’ intervals, when no observations were made."," Because of the low cadence of measurements, some hypothetical models may fit the data simply because the “transits” occur during 'gap' intervals, when no observations were made." +" Thus, the follow-up prediction function, when generalized to a broader model space of periodic variables, will allow constructing a follow-up strategy that will complement the low-cadence observations in a way that will optimize the period coverage."," Thus, the follow-up prediction function, when generalized to a broader model space of periodic variables, will allow constructing a follow-up strategy that will complement the low-cadence observations in a way that will optimize the period coverage." +" MCMC methods, such as the MH algorithm, can be very demanding in terms of processing time."," MCMC methods, such as the MH algorithm, can be very demanding in terms of processing time." +" Therefore, improving the efficiency and automatizing the strategy in order to explore large data bases is crucial to its usefulness."," Therefore, improving the efficiency and automatizing the strategy in order to explore large data bases is crucial to its usefulness." +" Thus, we are examining the idea of reducing the amount of model parameters that the MH algorithm explores to three main parameters: the transit period, duration, and mid-transit epoch, while marginalizing over the other two parameters: the transit depth and mean magnitude out of transit."," Thus, we are examining the idea of reducing the amount of model parameters that the MH algorithm explores to three main parameters: the transit period, duration, and mid-transit epoch, while marginalizing over the other two parameters: the transit depth and mean magnitude out of transit." + The marginalization will hopefully shorten the computing time., The marginalization will hopefully shorten the computing time. +" Another idea worth examining is using a BLS-like algorithm, which will scan the (P,Τε,w) space and calculate the likelihood of each configuration, from which it will build, in a Bayesian fashion, the ITP function."," Another idea worth examining is using a BLS-like algorithm, which will scan the $P,T_c,w$ ) space and calculate the likelihood of each configuration, from which it will build, in a Bayesian fashion, the ITP function." +" Such scanning is obviously a compromise, since it is discrete and finite by nature, and the coverage of the parameter space may be lacking."," Such scanning is obviously a compromise, since it is discrete and finite by nature, and the coverage of the parameter space may be lacking." +" However, the gain in computation time compared to a Monte Carlo approach might be worth the price."," However, the gain in computation time compared to a Monte Carlo approach might be worth the price." +" At this stage the simulations we have presented in this paper are a feasibility test, based on Epoch Photometry."," At this stage the simulations we have presented in this paper are a feasibility test, based on Epoch Photometry." +" The encouraging preliminary results we present here lead us to believe that the strategy can be beneficial for successor, (Eyeretal.2009)..Gaia,,"," The encouraging preliminary results we present here lead us to believe that the strategy can be beneficial for successor, \citep{2009sf2a.conf...45E}.," +" whose expected launch is planned to 2012, will measure about a billion stars in our Galaxy and in the Local Group, and will perform, besides ultraprecise astrometry, also spectral and photometric observations."," whose expected launch is planned to 2012, will measure about a billion stars in our Galaxy and in the Local Group, and will perform, besides ultraprecise astrometry, also spectral and photometric observations." +" is supposed to improve on the accuracy of using larger mirrors, more efficient cameras and detectors and better software to reduce the data."," is supposed to improve on the accuracy of using larger mirrors, more efficient cameras and detectors and better software to reduce the data." +" In its photometric mission, will scan the whole sky, with a photometric precision of 1 mmag for the brightest stars, and up to 20 mmag at a magnitude of 20 (Eyeretal.2009).."," In its photometric mission, will scan the whole sky, with a photometric precision of 1 mmag for the brightest stars, and up to $20$ mmag at a magnitude of $20$ \citep{2009sf2a.conf...45E}." + main exoplanets search programme is focused on detection through astrometric motion measurements., main exoplanets search programme is focused on detection through astrometric motion measurements. +" The strategy we propose here may be generalized to direct follow-up efforts of Gaia""s photometry, aimed to detect transiting exoplanets."," The strategy we propose here may be generalized to direct follow-up efforts of 's photometry, aimed to detect transiting exoplanets." + This research was supported by The Israel Science Foundation and The Adler Foundation for Space Research (grant No., This research was supported by The Israel Science Foundation and The Adler Foundation for Space Research (grant No. + 119/07)., 119/07). +was decomposed into the stellar disk. gaseous clisk and clark halo contributions Vai. Voc and Vinge via The shape of the stellar disk contribution is derived from the NIR photometry presented in. Vacluvescu et al. (,"was decomposed into the stellar disk, gaseous disk and dark halo contributions $V_{\rm disk}$ , $V_{\rm gas}$ and $V_{\rm halo}$ via The shape of the stellar disk contribution is derived from the NIR photometry presented in Vaduvescu et al. (" +2005).,2005). + From the W-banc photometric profile the contribution of the stellar disk was derived. using the task ROTMOD in GIPSY with the assumption of a vertical sech? distribution having a scale height zo.=f/6 (van der Ixruüit Searle 1981)., From the K-band photometric profile the contribution of the stellar disk was derived using the task ROTMOD in GIPSY with the assumption of a vertical $^{2}$ distribution having a scale height $z_0=h/6$ (van der Kruit Searle 1981). + Its amplitude is scaled: using a constant mass-to-light. CAZ/L) ratio., Its amplitude is scaled using a constant mass-to-light $M/L$ ) ratio. + From the photonietric profile we can exclude any significant contribution from a bulge. because 33741 even shows a brightness deficit at small radii. extrapolating the exponential fit to the inner region.," From the photometric profile we can exclude any significant contribution from a bulge, because 3741 even shows a brightness deficit at small radii, extrapolating the exponential fit to the inner region." + The gaseous disk contribution was clerived [ron the LU observations presented here. multiplving the neutral hyelrogen surface density by 1.33 to account lor primordial lle.," The gaseous disk contribution was derived from the HI observations presented here, multiplying the neutral hydrogen surface density by 1.33 to account for primordial He." + The stellar AZ/L ratio being one of the largest: uncertainties in the rotation curve fits. we describe here the attempts we mace to put some strong a-priori constraints.," The stellar $M/L$ ratio being one of the largest uncertainties in the rotation curve fits, we describe here the attempts we made to put some strong a-priori constraints." + Unfortunately. with the present data this was not possible to achieve.," Unfortunately, with the present data this was not possible to achieve." + Attempts were mace using the measured. (D-Ix) colour and the predictions of stellar population synthesis models. of Bell de Jong (2001)., Attempts were made using the measured (B-K) colour and the predictions of stellar population synthesis models of Bell de Jong (2001). + We find a predicted K-band stellar ALL ratio of 0.8., We find a predicted K-band stellar $M/L$ ratio of 0.3. + We also tried. to constrain the stellar AIL ratio by using the predictions of Bell et al. (, We also tried to constrain the stellar $M/L$ ratio by using the predictions of Bell et al. ( +2003).,2003). + They only give values based on the observed. B-V ancl lt colours., They only give values based on the observed B-V and B-R colours. + By taking the latter value from LEDA (Lyon-Meudon Extragalactic Database) we obtain a Ix-band stellar AL/L vatio of 0.7., By taking the latter value from LEDA (Lyon-Meudon Extragalactic Database) we obtain a K-band stellar $M/L$ ratio of 0.7. + Another attempt at constraining the stellar AZ/L ratio was made through an estimate of the lower limit of the stellar mass by comparing UBY photometry (NED) plus JIx magnitudes (Vacuveseu et al., Another attempt at constraining the stellar $M/L$ ratio was made through an estimate of the lower limit of the stellar mass by comparing UBV photometry (NED) plus JK magnitudes (Vaduvescu et al. + 2005) with several libraries of SEDs computed. with the spectral synthesis code CRASLL (Silva et al., 2005) with several libraries of SEDs computed with the spectral synthesis code GRASIL (Silva et al. + 1998)., 1998). + Phe observed SED can be well reproduced bv several cüllerent star formation histories., The observed SED can be well reproduced by several different star formation histories. + There are no dillieulties in. producing an amount of about 107. M. or more in stars as predicted in the cored and in the NEW mass niodels., There are no difficulties in producing an amount of about $10^7$ $_\odot$ or more in stars as predicted in the cored and in the NFW mass models. +" Instead. in order to obtain significantly. lower masses. Less 5210"" ALL. and a good Lit to the observed SED. there are some requirements to be fulfilled: a peculiar SER. a delaved formation for 10 Gyr aid most of the stars formed in the last 0.5 Gar."," Instead, in order to obtain significantly lower masses, i.e. $\leq 5 \times 10^6$ $_\odot$, and a good fit to the observed SED, there are some requirements to be fulfilled: a peculiar SFR, a delayed formation for 10 Gyr and most of the stars formed in the last 0.5 Gyr." + In any case. also accepting this fact. by. adopting a standard Salpeter IATL extenelec from O.1 to LOO M.. we never found. that the observed SED implies stellar masses lower than ~5OPAL..," In any case, also accepting this fact, by adopting a standard Salpeter IMF extended from 0.1 to 100 $_{\odot}$, we never found that the observed SED implies stellar masses lower than $\sim 5 \times 10^6 M_\odot$." +" These results. combined with the estimates from the stellar population svnthesis models. induced us to consider in the rotation curve fits a minimum Ix-band. ΑΙ, ratio of 0.3. corresponding to a stellar mass of ~710A7. at a distance of 3 Alpe."," These results, combined with the estimates from the stellar population synthesis models, induced us to consider in the rotation curve fits a minimum K-band $M/L$ ratio of 0.3, corresponding to a stellar mass of $\sim 7 \times 10^6 M_\odot$ at a distance of 3 Mpc." + We remind. however. that the stellar ML ratio coming out of the fits is mostly constrained. by the innermost two/three data points of the rotation curve. which are also the most alfected by non-circular motions. in proportion to the rotation velocity.," We remind, however, that the stellar $M/L$ ratio coming out of the fits is mostly constrained by the innermost two/three data points of the rotation curve, which are also the most affected by non-circular motions, in proportion to the rotation velocity." + In the specific example shown in Fig., In the specific example shown in Fig. + 18 the stellar mass is 6.10A7..," \ref{grasil} the stellar mass is $\sim 6 \times 10^6 +M_\odot$." + Ehe spectrophotomoetric determination of the stellar. disk. mass does not. help in discriminating between cored and NEW halos. and it is not decisive against MOND.," The spectrophotometric determination of the stellar disk mass does not help in discriminating between cored and NFW halos, and it is not decisive against MOND." + In any case. the small stellar mass found. with these estimates (of the order of 10 M.) is an advantage for our aims: uncertainties in the stellar AZ/L do not have a great inlluence on the derived dark matter halo profile.," In any case, the small stellar mass found with these estimates (of the order of $10^7$ $_{\odot}$ ) is an advantage for our aims: uncertainties in the stellar $M/L$ do not have a great influence on the derived dark matter halo profile." + Concerning the dark matter halo. several alternatives were investigated.," Concerning the dark matter halo, several alternatives were investigated." + In numerous previous studies dark halos with a central constant-density core provided the best fits to the rotation curve., In numerous previous studies dark halos with a central constant-density core provided the best fits to the rotation curve. + An example of such a cored halo is the Burkert halo (Burkert 1995. Salucci Burkert 2001): its density. distribution is given hy were po (the central density) and rise (the core radius) are the two free parameters.," An example of such a cored halo is the Burkert halo (Burkert 1995, Salucci Burkert 2001); its density distribution is given by were $\rho_0$ (the central density) and $r_{\rm core}$ (the core radius) are the two free parameters." + Then. another fit to the observed. rotationcurve was performed using the Navarro. Frenk and White halo (NEW). the result of an analytical fit to the density distribution of dark matter halos in CDM cosmological simulations.," Then, another fit to the observed rotationcurve was performed using the Navarro, Frenk and White halo (NFW), the result of an analytical fit to the density distribution of dark matter halos in CDM cosmological simulations," +"Hence, time delay for a round trip is The solution to this equation (41) is then given by for the following (i): D=2 In this case the integral in the equation (41) becomes so that the time delay for a round trip can be given as If, however,ro<> lore=(ra/ro)>>1 so that, after neglecting the higher order terms like 1/z?, 1/2, ... etc.","Hence, time delay for a round trip is Let us consider The solution to this equation (41) is then given by for the following (i): $D=2$ In this case the integral in the equation (41) becomes so that the time delay for a round trip can be given as If, however,$r_0<>1$ or $x=(r_2/r_0)>>1$ so that, after neglecting the higher order terms like $1/x^3$ $1/x^5$ , ... etc." + we get so that, we get so that +dust. and. f;(¢.¢) is the size distribution fuuction of dust species j in the ISM at a time f£.,"dust, and $f_{j}(a,t)$ is the size distribution function of dust species $j$ in the ISM at a time $t$." + We note Κα/Mw) is a timescale of sweeping whole ISAL by SNe., We note that $(M_{\rm swept}\gamma_{\rm SN}(t)/M_{\rm ISM}(t))^{-1}$ is a timescale of sweeping whole ISM by SNe. + The IME-averaged ass of dust species ; with radii between « and 0|Aa injected from SNe ID iuto the ISM with nuuber deusitv rysypsx is defined. by AMuxaj)=(αλλα.," The IMF-averaged mass of dust species $j$ with radii between $a$ and $a+\Delta a$ injected from SNe II into the ISM with number density $n_{\rm ISM, SN}$ is defined by $\overline{\Delta M_{\rm SN,d,j}}(a)=\overline{{\cal M}_{\rm d,j}^{n_{\rm SN}}}(a)\Delta a$." + The first term on the rieht-haud side is MT.the injection rate of dust from SNe IL, The first term on the right-hand side is the injection rate of dust from SNe II. + The second term is the destruction rate of iuterstellu dust by SN blast waves. aud the third teri is the rate at which the interstellar dust is incorporated into stars.," The second term is the destruction rate of interstellar dust by SN blast waves, and the third term is the rate at which the interstellar dust is incorporated into stars." + We quantity the properties of dark matter halos. asstuuine a dvuauicallv equilibrium state.," We quantify the properties of dark matter halos, assuming a dynamically equilibrium state." + The radius of dark matter halo. ra. is estimated in terms of the mass of dark halo. M. aud the redshift of virialization. t4. as where po)—Πρ.P/8zG* mysis the criticalpc density. of. the Universe at ;=0. 8.Cua) is the overdensity of a dark matter halo vilialized at τω. aud G is the eravitational coustaut.," The radius of dark matter halo, $r_{\rm vir}$, is estimated in terms of the mass of dark halo, $M_{\rm vir}$, and the redshift of virialization, $z_{\rm vir}$ as where $\rho_{{\rm c}0}\equiv3H_{0}^{2}/8\pi G$ is the critical density of the Universe at $z=0$, $\delta_{c}(z_{\rm vir})$ is the overdensity of a dark matter halo vilialized at $z_{\rm vir}$, and $G$ is the gravitational constant." + We assume dark matter halos απ. singular isothermal spleres aud rotating uniforni gas disks in their eravitational potentials., We assume dark matter halos as singular isothermal spheres and rotating uniform gas disks in their gravitational potentials. + Cosmological N-body sinnulatious show that structures of dark matter halos are well described by the NEW profile (Navarroctal.1996)., Cosmological N-body simulations show that structures of dark matter halos are well described by the NFW profile \citep{Nav96}. +.. Moetal.(1998) studied a simple disk wodel in the eravitational potential of the singular isothermal sphere and more realistic disk aodel in the eravitational poteutial of the NEW halo profile., \citet{Mo98} studied a simple disk model in the gravitational potential of the singular isothermal sphere and more realistic disk model in the gravitational potential of the NFW halo profile. +" We adopt a radius of the disk. πωςCOLS, (Ferraraetal2000:Tirashita&Ferrara 2002).. bv considering the conservation of augular momentum aud assuniug a typica value for the spin parameter A=0.0L from the paper bv Ferraraetal.(2000) who cstimate the radius of the disk as rai=L5Amay dn a modifie isothermal halo."," We adopt a radius of the disk, $r_{\rm disk}\simeq0.18r_{\rm vir}$ \citep{Fer00,Hir02}, by considering the conservation of angular momentum and assuming a typical value for the spin parameter $\lambda=0.04$ from the paper by \citet{Fer00} who estimate the radius of the disk as $r_{\rm disk}=4.5 \lambda r_{\rm vir}$ in a modified isothermal halo." + lu our one-zoue model. we need a vina temperature for the initial eas temperature ac a dvianuical timescale of eas in the disk.," In our one-zone model, we need a virial temperature for the initial gas temperature and a dynamical timescale of gas in the disk." +" Cas collapsed at τν iu the dark matter halo of Mg has a virial temperature. Zj4,. defined as where Ap ds the Boltzimaun constant. ji is the mean inolecular weight. and yp is themass of a lydrogen atom."," Gas collapsed at $z_{\rm vir}$ in the dark matter halo of $M_{\rm vir}$ has a virial temperature, $T_{\rm vir}$, defined as where $k_{\rm B}$ is the Boltzmann constant, $\mu$ is the mean molecular weight, and $m_{\rm H}$ is themass of a hydrogen atom." + The initial value for the temperature of gas. T. is assumed to be Tj.," The initial value for the temperature of gas, $T$, is assumed to be $T_{\rm vir}$." + A circular velocity. ος. is defined as and we also define a rotation timescale. fey. as Note that the rotation timescale of the eas disk. tay. depend oulv on virialization redshift. =... as We must estimate the iuuber deusitv of the hydrogen gas. nq. because it affects both the chemical reaction rate aud the cooling rate.," A circular velocity, $v_{\rm c}$, is defined as and we also define a rotation timescale, $t_{\rm cir}$, as Note that the rotation timescale of the gas disk, $t_{\rm cir}$, depend only on virialization redshift, $z_{\rm vir}$, as We must estimate the number density of the hydrogen gas, $n_{\rm H}$, because it affects both the chemical reaction rate and the cooling rate." +" The cooling time of halo gas is much shorter than the IIubble timescale for the objects of iuterest iu this paper (Ta,2100004) (e.g.IIutehiugsοἳal. 2002).", The cooling time of halo gas is much shorter than the Hubble timescale for the objects of interest in this paper $T_{\rm vir}\gtrsim10000K$ ) \citep[e.g.][]{Hut02}. +. It is widely uuderstood that most :—10 ealaxies were not clear disk ealaxics: numerical sinulatious that proceed from cosmological initial conditions (:~[00 200) clearly reveal that they possess highly aireeular structures whose SE rates are not casily quautifiable. that filamentary accretion and frequent mergers are still clawning the halo at this epoch. and that turbuleut flows arise in the center of the halo that preveut coherent disks forming on the spatial scales of ealaxies (Jolinsonetal.2008:(πας2010:Wiseetal. 2010).," It is widely understood that most $z\sim10$ galaxies were not clear disk galaxies; numerical simulations that proceed from cosmological initial conditions $z\sim100-200$ ) clearly reveal that they possess highly irregular structures whose SF rates are not easily quantifiable, that filamentary accretion and frequent mergers are still churning the halo at this epoch, and that turbulent flows arise in the center of the halo that prevent coherent disks forming on the spatial scales of galaxies \citep{Joh08, Gre10, Wis10}." +. We asstuue that a significant fraction of barvous finally collapses to a disk iu the dark matter halo potential for simplicity., We assume that a significant fraction of baryons finally collapses to a disk in the dark matter halo potential for simplicity. + Ini seiii- models.it is assunned that the cooled halo οasx settles iuto the disk (e.g.Colectal. 2000)..," In semi-analytic models,it is assumed that the cooled halo gas settles into the disk \citep[e.g.][]{Col00}. ." + We make similar assuniptiou i our model. but iore detailed treatiuent for Ilo formation. dust evolution and star formation iu the gas," We make similar assumption in our model, but more detailed treatment for ${\rm H}_{2}$ formation, dust evolution and star formation in the gas" +where©. is a constant of order unity (seeDavisοἱal.1985:WetherillKenvon&Li1993;BenzAsphaug1999.andreferences therein).,"where$\beta_e$ is a constant of order unity \citep[see][and references therein]{dav85, ws93, kl98, ben99}." +. For a singlee KBO. the amount of mass accreted in collisions with all other KBOs duringe a lime interval 9/ is The amount of mass lost is KBOs with y>n lose mass and reach zero mass on a removal timescale With these definitions. the evolution of an ensemble of IKRDOs depends on the relative velocily V. the size distribution. ancl (he disruption energy.," For a single KBO, the amount of mass accreted in collisions with all other KBOs during a time interval $\delta t$ is The amount of mass lost is KBOs with $\dot{m_l} > \dot{m_a}$ lose mass and reach zero mass on a removal timescale With these definitions, the evolution of an ensemble of KBOs depends on the relative velocity $V$, the size distribution, and the disruption energy." + Because (he disruption energy scales wilh size. larger objects are harder to disrupt than smaller objects.," Because the disruption energy scales with size, larger objects are harder to disrupt than smaller objects." + To produce a break in the size distribution. we need a ‘break radius. rj. where and /y is some reference time.," To produce a break in the size distribution, we need a `break radius,' $r_b$, where and $t_0$ is some reference time." + We choose /y = 1 Gyr as a reasonable e-folding time lor the decline in the INDO space density., We choose $t_0$ = 1 Gyr as a reasonable e-folding time for the decline in the KBO space density. + To apply the analylic model to the ABO size distribution. we use parameters appropriate for the outer solar svstem.," To apply the analytic model to the KBO size distribution, we use parameters appropriate for the outer solar system." + We adopt / = ¢/2. with e = 0.04 for classical IKRDOs and € = 0.2 for PIutinos.," We adopt $i$ = $e$ /2, with $e$ = 0.04 for classical KBOs and $e$ = 0.2 for Plutinos." + This simplification ignores the richness of INDO orbits. bul gives representative results without extra parameters.," This simplification ignores the richness of KBO orbits, but gives representative results without extra parameters." + We assume a total mass in INDOs. Mypo. in an annulus with αμ = 40 AU and da = 10 AU.," We assume a total mass in KBOs, $M_{KBO}$, in an annulus with $a_0$ = 40 AU and $\delta a$ = 10 AU." + A mininunm mass solar nebula has νο 10 AL the curent Ixuiper Bellhas νο = 0.050.20 34. (Stein.1996a:Lun&JewittBernsteinοἱal. 2003)..," A minimum mass solar nebula has $M_{KBO} \sim$ 10 $M_{\oplus}$; the current Kuiper Belthas $M_{KBO}$ = 0.05–0.20 $M_{\oplus}$ \citep{ste96a,luu02,ber03}. ." + This range in initial INDO mass provides a representative range for the normalization constants. ng and nj. in our model size distribution.," This range in initial KBO mass provides a representative range for the normalization constants, $n_S$ and $n_L$ , in our model size distribution." +he slower scatter decrease in smaller mass bins.,the slower scatter decrease in smaller mass bins. + With this xhaviour we can deduce an explanation for the weak scatter decrease in the small merger number range and the stronger decrease in the limit of large merger number: the probability or having minor mergers is higher at the high mass end than or the low mass end. where major mergers dominate.," With this behaviour we can deduce an explanation for the weak scatter decrease in the small merger number range and the stronger decrease in the limit of large merger number: the probability for having minor mergers is higher at the high mass end than for the low mass end, where major mergers dominate." + We know from observations as well as from simulations that new galaxies form. during the structure formation process., We know from observations as well as from simulations that new galaxies form during the structure formation process. + To make our simple model more realistic we now consider different replenishment scenarios., To make our simple model more realistic we now consider different replenishment scenarios. + We assume again a certain initial number of objects Nin with a log-normal or à Schechter distribution and. perform the same iterative random merging procedure as described. in section ?7.. Llo, We assume again a certain initial number of objects $N_{\mathrm{ini}}$ with a log-normal or a Schechter distribution and perform the same iterative random merging procedure as described in section \ref{depletion}. +wever. we now refill the pool after. merger events with new objects from an external unchanged reservoir.," However, we now refill the pool after merger events with new objects from an external unchanged reservoir." + We define the refilleratio NuewINSS to be the number of objects added from the refill pool Nye. per number of merger events Novent Within one merging generation., We define the refill-ratio $N_{\mathrm{new}}/N_{\mathrm{event}}$ to be the number of objects added from the refill pool $N_{\mathrm{new}}$ per number of merger events $N_{\mathrm{event}}$ within one merging generation. +" The definition of one merging generation is the same as before but after the n-th merging generation the sample always contains more than N(v)=Ninf2"" objects depending on the relillratio Nye. (Neveu.", The definition of one merging generation is the same as before but after the $n$ -th merging generation the sample always contains more than $N(n) = N_{ini}/2^n$ objects depending on the refill-ratio $N_{\mathrm{new}}/N_{\mathrm{event}}$ . + At first we consider a refill-ratio of NassANuai=1. be. for cach merger event one new object is added randomly from the refill pool and the total number of objects in the sample stavs constant.," At first we consider a refill-ratio of $N_{\mathrm{new}}/N_{\mathrm{event}} = 1$, i.e. for each merger event one new object is added randomly from the refill pool and the total number of objects in the sample stays constant." + We also consider a refill-ratio of INSINsa= 1/3. Le. one new object for every events. motivated by κοΝΤ simulations (see section ??)).," We also consider a refill-ratio of $N_{\mathrm{new}}/N_{\mathrm{event}} = 1/3$ , i.e. one new object for every events, motivated by $\Lambda$ CDM simulations (see section \ref{CDMmerging}) )." + For the initial log-normal distribution. we consider a refill. pool identical to the initial distribution as well as a pool of smaller mass galaxies with mean black hole masses logMSfAl.))~3.3 and the same initial scatter.," For the initial log-normal distribution, we consider a refill pool identical to the initial distribution as well as a pool of smaller mass galaxies with mean black hole masses $\langle \log (M_{\bullet}/M_{\odot}) \rangle \sim 3.3$ and the same initial scatter." + For the initial Schechter distribution we use either the initial Schechter distribution itself as a. refillpool or we use the Sehechter distribution containing only bulges at the low mass end with Εμμ=158;1071.58107731.., For the initial Schechter distribution we use either the initial Schechter distribution itself as a refill-pool or we use the Schechter distribution containing only bulges at the low mass end with $m_{\mathrm{bulge}} = 1.58 \times 10^8 - 1.58 \times 10^{10} M_{\odot}$. + The cases with smaller refill pools (lower galaxy masses) allow a more realistic comparison to the XCDAM-simulations presented in section ??.., The cases with smaller refill pools (lower galaxy masses) allow a more realistic comparison to the $\Lambda$ CDM-simulations presented in section \ref{CDMmerging}. + In total we have four dillerent refill-cenarios which will be investigated in the following: A general feature of all replenishment models. is. that the seatter in the Afe-Adgiuiee-relation is again reduced with increasing merger number., In total we have four different refill-scenarios which will be investigated in the following: A general feature of all replenishment models is that the scatter in the $M_{\bullet}$ $M_{\mathrm{Bulge}}$ -relation is again reduced with increasing merger number. + However. compared to the depletion scenario. more merger generations are needed. to reduce the scatter by the same amount.," However, compared to the depletion scenario, more merger generations are needed to reduce the scatter by the same amount." + In other words. for the same merger generation the scatter decrease is weaker as new objects with a larger initial scatter are added.," In other words, for the same merger generation the scatter decrease is weaker as new objects with a larger initial scatter are added." + For small refill pools and large vefill-ratios we find an interesting feature., For small refill pools and large refill-ratios we find an interesting feature. + Fig., Fig. + 13. and Fig., \ref{Repl_evol} and Fig. + 14. show the evolution of the relation for a refill-ratio of one and the small (low mass) refill. pools £:4)) for an initial log-normal ancl a Schechter distribution., \ref{Repl_evol_Schechter} show the evolution of the relation for a refill-ratio of one and the small (low mass) refill pools ) for an initial log-normal and a Schechter distribution. + The contours in the plot of the first random merging generation illustrate the distribution of the anchanged relill-pool, The contours in the plot of the first random merging generation illustrate the distribution of the unchanged refill-pool. + In both cases a double peak structure emerges., In both cases a double peak structure emerges. + This is a consequence of using a low mass refill pool and a high refill-ratio., This is a consequence of using a low mass refill pool and a high refill-ratio. + The low mass peak rellects the appearance of new objects chosen from. refill-distribution whereas the high mass peak evolves through merging from. the initial distribution. similar to the simple case (section 77).," The low mass peak reflects the appearance of new objects chosen from refill-distribution whereas the high mass peak evolves through merging from the initial distribution, similar to the simple case (section \ref{depletion}) )." + This behaviour will be discussed in section 77. in more detail., This behaviour will be discussed in section \ref{CDMmerging} in more detail. + In contrast to the depletion scenario. the replenishment models leacl to a slower decrease of the scatter in black hole mass.," In contrast to the depletion scenario, the replenishment models lead to a slower decrease of the scatter in black hole mass." +" The scatter quantification for the evolution of the A,- AMisuassrelation in Figs.", The scatter quantification for the evolution of the $M_{\bullet}$ $M_{\mathrm{bulge}}$ -relation in Figs. + 13 and 1H. (relill-ratio 1. small mean and initial los-normal cüstribution or Schechter distribution) is shown in Figs.," \ref{Repl_evol} and \ref{Repl_evol_Schechter} + (refill-ratio 1, small mean and initial log-normal distribution or Schechter distribution) is shown in Figs." + 15. ancl 16.., \ref{Repl_sigma_onecase} and \ref{Repl_sigma_onecase_Schechter}. + Phe decrease of the scatter at low merger numbers originates [rom merging of new objects from the refill-pool mainly dominated. by minor mergerswhereas thedecrease of the scatter at high merger numbers refelects merging at the high mass end (see section. ??))," The decrease of the scatter at low merger numbers originates from merging of new objects from the refill-pool mainly dominated by minor mergerswhereas thedecrease of the scatter at high merger numbers refelects merging at the high mass end (see section \ref{depletion}) )," +to the free-fall velocity. as was introduced in Nakano&Umebavashi(1986).,"to the free-fall velocity, as was introduced in \citet{nakano86}." +. In Umebavashi (L986)... the drift velocity involves both the Olumic dissipation and (the ambipolar diffusion processes.," In \citet{nakano86}, the drift velocity involves both the Ohmic dissipation and the ambipolar diffusion processes." + There are (wo important quantities which characterize these diffusion processes., There are two important quantities which characterize these diffusion processes. +" They are 7, and o, which denote the viscous damping time of the relative velocity of charged particle v to the neutral particles. and the evelotvon [requencey. of the charged particle ». respectively."," They are $\tau_\nu$ and $\omega_\nu$ which denote the viscous damping time of the relative velocity of charged particle $\nu$ to the neutral particles, and the cyclotron frequency of the charged particle $\nu$ , respectively." +" Then. 7, is expressed as ο is the reduced mass. »,. ny. and o, are. the mean number density for the charged particle p. the neutral particle n. and the mass densitv of charged. particle v. respectively."," Then, $\tau_\nu$ is expressed as where $\mu_{\rm \nu n}$ is the reduced mass, $n_\nu$, $n_{\rm n}$ , and $\rho_\nu$ are, the mean number density for the charged particle $\nu$, the neutral particle ${\rm n}$, and the mass density of charged particle $\nu$, respectively." +" The averaged momentium-transfer rate coefficient for a particle » colliding with a neutral particle is expressed by (00),4.", The averaged momentum-transfer rate coefficient for a particle $\nu$ colliding with a neutral particle is expressed by $\langle \sigma v \rangle_{\rm \nu n}$. + The monmentunm-transfer cross section of an ion with a neutral particle is given bv the Langevin rate coefficient (Osterbrock1961)., The momentum-transfer cross section of an ion with a neutral particle is given by the Langevin rate coefficient \citep{osterbrock61}. +. For an electron. it is lound experimentally by llavashi(1981) that the eross sections at low energies are much smaller than the Langevin rate coefficient and are nearly equal to a geometrical cross section.," For an electron, it is found experimentally by \citet{hayashi81} that the cross sections at low energies are much smaller than the Langevin rate coefficient and are nearly equal to a geometrical cross section." + We use (he empirical formulae for the momentum-transler rate coefficients (INamava&Nishi2000:Umebavashi.&Nakano 2000).," We use the empirical formulae for the momentum-transfer rate coefficients \citep{kamaya00,sano00}." +. According to Nakano&Umebavashi(1986).. the drift velocity can be given by where B is the mean magnetic field in the primordial cloud. the suffix . means ο direction component in local Cartesian coordinates where the z direction is taken as the direction of B.," According to \citet{nakano86}, the drift velocity can be given by where $\Vec{B}$ is the mean magnetic field in the primordial cloud, the suffix $x$ means $x$ direction component in local Cartesian coordinates where the $z$ direction is taken as the direction of $\Vec{B}$ ." +" In calculating the drift velocity ep, according to equation (5))we replace (1/0)(3xB), wilhthe mean magnetic force B?/4xP. where B is the mean field strength inthe cloud. 72 is the radius of the cloud."," In calculating the drift velocity $v_{{\rm B}x}$ according to equation \ref{eq:diffusion_velocity}) )we replace $(1/c)(\Vec{j} \times \Vec{B})_x$ withthe mean magnetic force $B^2/4 \pi R$ , where $B$ is the mean field strength inthe cloud, $R$ is the radius of the cloud." +deal with the self-consistent evaluation of the electron density ina multilevel non-LTE problem. if necessary — a problem for which MALI needs to plug-in a Newton-Raphson scheme to it. as proposed by Heinzel (1995) and Paletou (1995).,"deal with the self-consistent evaluation of the electron density in a multilevel non-LTE problem, if necessary – a problem for which MALI needs to plug-in a Newton-Raphson scheme to it, as proposed by Heinzel (1995) and Paletou (1995)." + Another important point is that. as indicated in our Fig.," Another important point is that, as indicated in our Fig." + 3. a great deal of time of our Broyden code is spent in the computation of the initial Jacobian. a task which can be performed with great advantage using parallel computing.," 3, a great deal of time of our Broyden code is spent in the computation of the initial Jacobian, a task which can be performed with great advantage using parallel computing." + The inner structure of the routine permits. indeed. parallelization with a high scalability.," The inner structure of the routine permits, indeed, parallelization with a high scalability." + As a final comment. it is also important to consider that Broyden's method can be easily implemented in already existing codes.solver. unlike with GS/SOR methods.," As a final comment, it is also important to consider that Broyden's method can be easily implemented in already existing codes, unlike with GS/SOR methods." +an upper limit of 0.05 M. for Praesepe (0.7 Gyr).,an upper limit of 0.05 $M_\odot$ for Praesepe (0.7 Gyr). + If this is lost at a constant rate. it would give 51077/7105. which is 7107!Myr.," If this is lost at a constant rate, it would give $5\,10^{-2}/7\,10^8$, which is $7\,10^{-11}~M_\odot$ /yr." +" Integrated over 710"" yr. this gives 51077Ma."," Integrated over $7\,10^7$ yr, this gives $5\,10^{-3}~M_\odot$." + In turn. the Li-dip may be explained if 0.05 M. is lost from 1.3 M (solar metallicity) stars (Schramm et al.," In turn, the Li-dip may be explained if 0.05 $M_\odot$ is lost from 1.3 $M_\odot$ (solar metallicity) stars (Schramm et al." + 1990; see also Russell 1995)., 1990; see also Russell 1995). + The proposed mechanism is related to the main instability strip. with a mass loss rate of 107!Myr.," The proposed mechanism is related to the main instability strip, with a mass loss rate of $10^{-11} M_\odot$ /yr." + Integrated over 70 Myr. this yields 7107M...," Integrated over 70 Myr, this yields $7\,10^{-4} M_\odot$." + Summarizing. an upper limit to mass lost during the 40-110 Myr epoch for a solar type star is 0.01 M4.," Summarizing, an upper limit to mass lost during the 40-110 Myr epoch for a solar type star is 0.01 $M_\odot$." + This implies a maximum mass loss rate of ~107Myr., This implies a maximum mass loss rate of $\sim 10^{-10}~M_\odot$ /yr. + On the other hand. in our approach. a is a suitable average value for the fraction of mass lost during this phase byp," On the other hand, in our approach, $\alpha$ is a suitable average value for the fraction of mass lost during this phase by." +"ollution, This average also includes (1) stars that are still in the pre-main sequence phase at the relevent epoch (M.«0.5M: Di Criscienzo et al.2009):: (", This average also includes (i) low-mass stars that are still in the pre-main sequence phase at the relevent epoch $M<0.5~M_\odot$: Di Criscienzo et al.; ( +ii) the same stars later providing the polluting material. but in earlier evolutionary phases (e.g. while they are in the Cepheids instability strip. see e.g. Neilson Lester 2009): and (11) interacting binaries (see e.g. Mennickent et al.,"ii) the same stars later providing the polluting material, but in earlier evolutionary phases (e.g. while they are in the Cepheids instability strip, see e.g. Neilson Lester 2009); and (iii) interacting binaries (see e.g. Mennickent et al." + 2010)., 2010). + All these classes of objects may have mass-loss rates (1n units of the stellar mass) that are significantly more than solar type stars of similar ages., All these classes of objects may have mass-loss rates (in units of the stellar mass) that are significantly more than solar type stars of similar ages. + The assumption of a value «~1% therefore does not appear completely implausible., The assumption of a value $\alpha \sim 1$ therefore does not appear completely implausible. + It should. however. be noticed that the chemical composition of the winds from these other classes of stars might not precisely reflect the original composition.," It should, however, be noticed that the chemical composition of the winds from these other classes of stars might not precisely reflect the original composition." + Low-mass stars should have burnt Li during the pre-main sequence phase. when they were still fully convective.," Low-mass stars should have burnt Li during the pre-main sequence phase, when they were still fully convective." + If they contributed significantly to the dilution required to explain the O-Na anticorrelation. then the Li observed in second-generation stars with a high degree of dilution should have been produced by the same polluters. and there should not be a simple Na-Li anticorrelation.," If they contributed significantly to the dilution required to explain the O-Na anticorrelation, then the Li observed in second-generation stars with a high degree of dilution should have been produced by the same polluters, and there should not be a simple Na-Li anticorrelation." + As a matter of fact. this is not at all excluded by current observations (see e.g. D'Orazi Marino 2010).," As a matter of fact, this is not at all excluded by current observations (see e.g. D'Orazi Marino 2010)." + For the other classes of objects. Luck Lambert (1992) made a chemical abundance analysis of Cepheids 11 the LMC and SMC.," For the other classes of objects, Luck Lambert (1992) made a chemical abundance analysis of Cepheids in the LMC and SMC." + The |O/Fe]. [Na/Fe]. [Mg/Fe]. and [Al/Fe] ratios are roughly solar. so that a putative wind from these stars may contribute to the dilution needed to explain the Na-O anc Mg-Al anticorrelations.," The [O/Fe], [Na/Fe], [Mg/Fe], and [Al/Fe] ratios are roughly solar, so that a putative wind from these stars may contribute to the dilution needed to explain the Na-O and Mg-Al anticorrelations." + However. these stars are depleted in C and Li. with evidence of of N-rich material.," However, these stars are depleted in C and Li, with evidence of dredge-up of N-rich material." + For interacting binaries. depletion of C and excesses of N have been found in most Algols (Parthasarathy et al.," For interacting binaries, depletion of C and excesses of N have been found in most Algols (Parthasarathy et al." + 1983: Tomkin et al., 1983; Tomkin et al. + 1993). and even O is depleted in the more massiveB Lyr (Balachandran et al.," 1993), and even O is depleted in the more massive $\beta$ Lyr (Balachandran et al." + 1986: indeed. massive binaries have been proposed as a source of the polluting material. rather than as diluters: de Mink et al.," 1986; indeed, massive binaries have been proposed as a source of the polluting material, rather than as diluters: de Mink et al." + 2009)., 2009). + If these two classes of objects were indeed the source of the diluters. we should then expect that the Na-O and the," If these two classes of objects were indeed the source of the diluters, we should then expect that the Na-O and the" +Dunn 1996).,Dunn 1996). + Fie., Fig. + 5 illustrates our result. indicating a sjenifüicaut ealaxy concentration in frout of the Coma cluster. with velocities ling in the 1500—6000 lan t range.," \ref{f:ghst} illustrates our result, indicating a significant galaxy concentration in front of the Coma cluster, with velocities lying in the $4500-6000$ km $^{-1}$ range." + The skv deusitv of the iufall zoue is shown in the luser of Fig. 5.., The sky density of the infall zone is shown in the insert of Fig. \ref{f:ghst}. + It was constructed from the number of galaxies in the L5006000 liu t velocity rauge nuns the nuuber of ealaxics iu he 850010000 zu + bin. comespondiie fo a simular differeuce in the velocity dispersion frou the cluster moan.," It was constructed from the number of galaxies in the $4500-6000$ km $^{-1}$ velocity range minus the number of galaxies in the $8500-10000$ km $^{-1}$ bin, corresponding to a similar difference in the velocity dispersion from the cluster mean." + By excising the ealaxies at velocities ower than 6010 Eni l we yocover a projected velocity cispersion of ~750 kin 1," By excising the galaxies at velocities lower than 6000 km $^{-1}$ , we recover a projected velocity dispersion of $\sim750$ km $^{-1}$." + Using the ALσ relation o: Fiuoguenov et al. (, Using the $M-\sigma$ relation of Finoguenov et al. ( +2001). we fiud that such velocity dis)orson IS muore ia accordance with mass ofthe Coma cluster.,"2001), we find that such velocity dispersion is more in accordance with mass of the Coma cluster." + The excess of galaxies exhibits a flat belavior witlii 0.5 degrees (1.3 Alpe). followed bv a decline by a factor of 5 within 1.7 degrees (2.8 Mpc} aud a subsequent drop by two orders of magnitude within 10 degrees (16.7 Alpe) The soft cuission from the Coma is detected to a 2.6 Alpe distance from the center (Bonamiecite et al.," The excess of galaxies exhibits a flat behavior within 0.8 degrees (1.3 Mpc), followed by a decline by a factor of 5 within 1.7 degrees (2.8 Mpc) and a subsequent drop by two orders of magnitude within 10 degrees (16.7 Mpc) The soft emission from the Coma is detected to a 2.6 Mpc distance from the center (Bonamente et al." + 2003) in a remarkable correspondeuce to the eaaxv filameut., 2003) in a remarkable correspondence to the galaxy filament. + Tn the abseuce of the fiugerofgod effect (decoupling of galaxies from the ΠΠολο flow). validated below bv our conclusion o- he fiαλλοανν origin of this galaxy concentration. the iufall zone is characterized by a 20 Apc projected leish.," In the absence of the finger–of–god effect (decoupling of galaxies from the Hubble flow), validated below by our conclusion on the filamentary origin of this galaxy concentration, the infall zone is characterized by a 20 Mpc projected length." + This leneth assmuption affects the density estimates. while tιο ο abundance is oulv based ou he asstuuption of collisional equilibrium.," This length assumption affects the density estimates, while the O abundance is only based on the assumption of collisional equilibrium." + We have verified he later assumption by sudviusg the ionization curves for OVII aud OVIII presented i LÀathur et al. (, We have verified the later assumption by studying the ionization curves for OVII and OVIII presented in Mathur et al. ( +2003).,2003). + We inve concluded hat the ASSIXion of pure collisional lonization is valid for οιr data. suce nsm10 5m and T»2«109 K (0.17 sev)," We have concluded that the assumption of pure collisional ionization is valid for our data, since $n_e>10^{-5}$ $^{-3}$ and $T>2\times10^{6}$ K (0.17 keV)." + An advantage of our neasurement is that we also decrinine the temperature x the contimmun., An advantage of our measurement is that we also determine the temperature by the continuum. +" Lower teur)oratures, Which at deusities jar LO? cm? result in simiar line ratios for OVII and OVIIL. fail to produce t1C 0served (II-c aud Πο-ο) yenisstrahlune flux at 0.71 sev. An important question we want to answer is whether ie detected emission. originates from a group or from a filament."," Lower temperatures, which at densities near $10^{-5}$ $^{-3}$ result in similar line ratios for OVII and OVIII, fail to produce the observed (H-e and He-e) bremsstrahlung flux at 0.7–1 keV. An important question we want to answer is whether the detected emission originates from a group or from a filament." + We cannot decide frou the electron. deusitv of i0 structure ΣΩ ο it suits both or the low ietallicity of filament we take ji.=1.1. fly1.2 and fiarvon0.16 to correspond to the first WMAP results in Spereel et al.," We cannot decide from the electron density of the structure $\sim50 (\mu_e / \mu_p) f_{\rm baryon} +\rho_{\rm crit}$ ), as it suits both (for the low metallicity of filament we take $\mu_e=1.1$, $\mu_p=1.2$ and $f_{\rm baryon}=0.16$ to correspond to the first WMAP results in Spergel et al." + 2003)., 2003). + However. he iuplied mass of the structure is comparable to the mass of the Coma cluster (sec also Bonamente et al.," However, the implied mass of the structure is comparable to the mass of the Coma cluster (see also Bonamente et al." + 2003)., 2003). + Ou the other hand the temperature of he emüssion is ~)2 keV. almost two orders of maguitiue lower than that of the Coma cluster.," On the other hand the temperature of the emission is $\sim0.2$ keV, almost two orders of magnitude lower than that of the Coma cluster." + It takes a few hundred eroups with virial temperature of 0.2 keV to make up a mass of he y.ructure. which leads to an overlapoues virial radi if we are to fit them iuto the eiven volume «of the structure.," It takes a few hundred groups with virial temperature of 0.2 keV to make up a mass of the structure, which leads to an overlapping virial radii if we are to fit them into the given volume of the structure." + Thus we conclude that the observed strucure is a filament., Thus we conclude that the observed structure is a filament. + For the Coma-ll field. where the statistics are he highest. we investigated he effect. of relaxing the asstuuption of solar abundance ratios.," For the Coma-11 field, where the statistics are the highest, we investigated the effect of relaxing the assumption of solar abundance ratios." + We rote that au assuntiou for C abnudaiice is müportant for overall fitting and a solar C value woud affect our results., We note that an assumption for C abundance is important for overall fitting and a solar C value would affect our results. + When eft free. however. the € abundance tends to eo to zero.," When left free, however, the C abundance tends to go to zero." + Also. there is no systematic doeudeuce of our results ou he asstuned € abundance as lo18o as the C/O ratio is solar or less. which is the correct asstnption from the poiut of view of chemical euricliment schemes aud observations of iietal-poor stars in our Galaxy.," Also, there is no systematic dependence of our results on the assumed C abundance as long as the C/O ratio is solar or less, which is the correct assumption from the point of view of chemical enrichment schemes and observations of metal-poor stars in our Galaxy." + Significant abundance measurements are: Ο.=OLLE0.02. NesNew=MEE 0.06. Fo/Fe..=001003 Cassmuiug Fe.ΠΠ=126<1TEE by utuuber). incicating that Fe is uuderabundaut Nod factor of three 1n respect to he soli Fe/O ratio. inplviue à donmünaut contribution «t SN IH to Fe enrichment.," Significant abundance measurements are: $_{\odot}=0.14\pm0.02$, $_{\odot}=0.14\pm0.06$ , $_{\odot}=0.04^{+0.03}_{-0.01}$ (assuming $_{\odot}/H=4.26\times10^{-5}$ by number), indicating that Fe is underabundant by a factor of three in respect to the solar Fe/O ratio, implying a dominant contribution of SN II to Fe enrichment." + Element abuudawees for tle* hot enussion obtaiiuec TOlu our NMM daa on the ceuer of Coma are 0.36+ 0.12. SifSi.0.15+£0.08. S/S.=(01x).15. Fe/Fe.=0.2y+05. also sugeesting prevalence �� SN II in Fe euricuneut. althoreh Fe abundance is a factor of 5 higher coupared to the filament.," Element abundances for the hot emission obtained from our XMM data on the center of Coma are $_{\odot}=0.36\pm0.12$ , $_{\odot}=0.45\pm0.08$, $_{\odot}=0.01\pm0.15$, $_{\odot}=0.20\pm0.03$, also suggesting prevalence of SN II in Fe enrichment, although Fe abundance is a factor of 5 higher compared to the filament." +" The filament Ne/O ratio reveals a subtle differeice With the OVI absorIOLS,", The filament Ne/O ratio reveals a subtle difference with the OVI absorbers. + Nicastro ot al.(2002) repors Ne/O-2 times solar for their N-rav absorption observations of material associated with the OVI absorbers., Nicastro et al.(2002) reports $=2$ times solar for their X-ray absorption observations of material associated with the OVI absorbers. + We observe a lower (solar) ratio at, We observe a lower (solar) ratio at + Tere. we present high-resolution Arecibo HI 21-au observations of the 2=0.2212 absorber. sppleueuted by a deep GAIRT ο]σι observation of the system.," Here, we present high-resolution Arecibo HI 21-cm observations of the $z=0.2212$ absorber, supplemented by a deep GMRT 21-cm observation of the system." + These observations enable us to directly decnuiue the kinetic temperature of the absorbing gas aid thus. to distinguish between the wari aud cold phases.," These observations enable us to directly determine the kinetic temperature of the absorbing gas and thus, to distinguish between the warm and cold phases." + We fiud. as conjectured previously. tha the bulk of the gas is indeed in the warn phase. which contains at least threc-fourthis of the total III along this li16 of sight.," We find, as conjectured previously, that the bulk of the gas is indeed in the warm phase, which contains at least three-fourths of the total HI along this line of sight." + This is the second DLA for which it has been οservatioταν established tlat a high spin temperature is due to a oxeponderance of gas iu the warm neutral iiedimu: Lane e al. (, This is the second DLA for which it has been observationally established that a high spin temperature is due to a preponderance of gas in the warm neutral medium; Lane et al. ( +2000) show that this phase contains at least two-tlires of the gas ina DLA at 2=0.0912 (also. coiucidentallv. t«wvurds OI 363).,"2000) show that this phase contains at least two-thirds of the gas in a DLA at $z=0.0912$ (also, coincidentally, towards OI 363)." + The rest of the paper is oreaused as follows: he GAIRT and Areciνο Observations aud data analysis are described in Sect. 2.., The rest of the paper is organised as follows: the GMRT and Arecibo observations and data analysis are described in Sect. \ref{sec:obs}. + Sect., Sect. + 3 presents the absorption spectra: the spin teiiperature of fie absorber and the temperatures of the differeut absorone components are also estimated here., \ref{sec:anal} presents the absorption spectra; the spin temperature of the absorber and the temperatures of the different absorbing components are also estimated here. + Finally. Sect.," Finally, Sect." + 1 discusses our results both in the coutex of observations © ‘the +=0.2212 DLA at other wavelengths. aud with resect to their general nuplicatiouns for the nature of systems which eive rise to damped Lyianu-a absorption.," \ref{sec:dis} discusses our results both in the context of observations of the $z = 0.2212$ DLA at other wavelengths, and with respect to their general implications for the nature of systems which give rise to damped $\alpha$ absorption." + The 2=0.2212 absorber towards OI 363 was observed ou a umber of occasions in February. April and Aueust 2000. using the 305-1 Areciho radio telescope.," The $z = 0.2212$ absorber towards OI 363 was observed on a number of occasions in February, April and August 2000, using the 305-m Arecibo radio telescope." +" observations were doue in total power mode. with he ""L-wide receiver. using 9level sampling for the o-correlation spectrometer."," All observations were done in total power mode, with the “L-wide” receiver, using 9–level sampling for the auto-correlation spectrometer." + Two orthogonal circular avization channels were observed sinnltaueoisly., Two orthogonal circular polarization channels were observed simultaneously. +" The first two sessions (n Februuy and April 200) used deidwidths of 3.125 aud 6.25 MIIZ. coutred at a iecliocentrie redshift of 2=0.2212. aud divided 1ito 2018 chanels,"," The first two sessions (in February and April 2000) used bandwidths of 3.125 and 6.25 MHz, centred at a heliocentric redshift of $z = 0.2212$, and divided into 2048 channels." + This vielded velocity resohtions of 0.3935 and το respectively., This yielded velocity resolutions of $0.3935$ and $0.79$ respectively. + OI 363 has substantial coutinuunu flix deusitv 2 Jv) at L baud aud the bandpass is heuce dominated by systenatics due to standing wave patterns., OI 363 has substantial continuum flux density $\sim 2$ Jy) at L band and the bandpass is hence dominated by systematics due to standing wave patterns. +" To improve he bandpass caibration. the observations were carried out in a ""double switched” mode."," To improve the bandpass calibration, the observations were carried out in a “double switched” mode." + OI 363 was observed fut. followed bv an observation of blaul slaw.," OI 363 was observed first, followed by an observation of blank sky." + Next. a similar position-switched observation was made for a rearby source. OE371 (B 0712|318. fttx deusitv ~ 1.1 Jy).," Next, a similar position-switched observation was made for a nearby source, OI 371 (B 0742+318, flux density $\sim$ 1.4 Jy)." + OI 363 and OI 371 have verv similar declinatious aud contiunuu fux «ensitioes: the observations were so timed hat the alt-az track of the feed was almost the same for all phases of the observing cvele., OI 363 and OI 371 have very similar declinations and continuum flux densities; the observations were so timed that the alt-az track of the feed was almost the same for all phases of the observing cycle. + Each of these pliases was ~| nüuutes lone (with 5-second data records) aud his evele was repeated ou cach observing dav for as long as the sources were visible from Arecibo., Each of these phases was $\sim 4$ minutes long (with 5-second data records) and this cycle was repeated on each observing day for as long as the sources were visible from Arecibo. + All observations were carried out at nieht. to minimise solar effects.," All observations were carried out at night, to minimise solar effects." + The otal on-source time for OI 363 was about 9 hours., The total on-source time for OI 363 was about 9 hours. + A second set of observations was carried out iu Augus 2000. with the aln of better resolving he narroy* absorption coniponents seen in the initial Arecibo observations.," A second set of observations was carried out in August 2000, with the aim of better resolving the narrow absorption components seen in the initial Arecibo observations." + Far smaller baudwidths of 0.781 and 0.195 MIIZ were hence used. again divided into 2018. chaunels. and with two polarizatious at cach setting.," Far smaller bandwidths of 0.781 and 0.195 MHz were hence used, again divided into 2048 channels, and with two polarizations at each setting." +" This gave velocity resolutions of ~0.099 aud ~0.025 respectively,", This gave velocity resolutions of $\sim 0.099$ and $\sim 0.025$ respectively. + These observations were carried out in the standard on-off position switching mode (ic. a single blank sky spectrum was used to calibrate the baudpass). since the wider of the two banchwidths (0.781 AIIIZ) was narrower in frequency than oue cvcle of the standing wave ripple (which is ~1 MIITIZ at AÀrecibo).," These observations were carried out in the standard on-off position switching mode (i.e. a single blank sky spectrum was used to calibrate the bandpass), since the wider of the two bandwidths (0.781 MHz) was narrower in frequency than one cycle of the standing wave ripple (which is $\sim 1$ MHz at Arecibo)." + Each on-off evcle was of five minutes duration. sub-divided iuto Ἱποσο records.," Each on-off cycle was of five minutes duration, sub-divided into 1-second records." + The total ou-source time was ~ 35 niuutes., The total on-source time was $\sim$ 35 minutes. + The data for both sets of observations were reduced using the Arecibo software packageANALYZ., The data for both sets of observations were reduced using the Arecibo software package. + For the February aud April observations. cach fourte 4.oeetruna was initially iuspected for raijo frequency interference (REIT).," For the February and April observations, each four-minute spectrum was initially inspected for radio frequency interference (RFI)." + If interference was seen. the individal 5-sec records of the fom-1uinute rum were passed trough a standard REI excision program. and all recuds wit[um strong (>100) features were removed.," If interference was seen, the individual 5-sec records of the four-minute run were passed through a standard RFI excision program, and all records with strong $ > 10 \sigma$ ) features were removed." + Each fouruimute spectrun was also inspected for the presence of standing waves., Each four-minute spectrum was also inspected for the presence of standing waves. + It was found that the fluctuations Ol Caci stc ]xsition-switched spectrum were indeed cdominaed N PAanding waves across the bandpass., It was found that the fluctuations on each such position-switched spectrum were indeed dominated by standing waves across the bandpass. + Ilowever. when an OL 363 spectra was divided by the correspouci18o cAectzum of ΟΙ 371 using the formula. the resultant spectruni contain OSSCLLlalv Cassia noise.," However, when an OI 363 spectrum was divided by the corresponding spectrum of OI 371 using the formula, the resultant spectrum contained essentially Gaussian noise." + This ratio of the two spectra was aso bandpass corrected and had no relmmaiine effects from the aziuth/zeuith-auele dependence of gain, This ratio of the two spectra was also bandpass corrected and had no remaining effects from the azimuth/zenith-angle dependence of gain. + It was then multiplied by the flux deusitv of ΟΙ 371 (take itobe 1.1 Jy at 1160 MIIz) to convert the spectrum iuto Jy., It was then multiplied by the flux density of OI 371 (taken to be $1.4$ Jy at 1160 MHz) to convert the spectrum into Jy. + The basic data editiue for the August spectrum was carried out in a similar manner., The basic data editing for the August spectrum was carried out in a similar manner. + Tere. lowever. the individual five-ninute spectra were obtained by the formula The spectra were then corrected for the System Equivalent Flux Deusity (SEFD) v/s Zenith angle dependence. to obtain the fal spectra in Jv.," Here, however, the individual five-minute spectra were obtained by the formula The spectra were then corrected for the System Equivalent Flux Density (SEFD) v/s Zenith angle dependence, to obtain the final spectra in Jy." + For all data sets. the above procedure was carried out separately for the two polarizations.," For all data sets, the above procedure was carried out separately for the two polarizations." + Individual four- and fiveauinute spectra were averaged together (using the appropriate weights) to produce the final spectrum for cach bandwidth., Individual four- and five-minute spectra were averaged together (using the appropriate weights) to produce the final spectrum for each bandwidth. + A linear baseliue was thei fitted to these spectra (excluding the location of the Lue) aud, A linear baseline was then fitted to these spectra (excluding the location of the line) and +that will evolve into sdBs within a Hubble time.,that will evolve into sdBs within a Hubble time. + We have assumed that the core-envelope structure is retained and used the results of, We have assumed that the core-envelope structure is retained and used the results of. +" The primary masses in these systems range from [Figure1.21l.—3Mo, the secondary masses range from 0.1—0.6Mo, and the initial periods range from 10— 350d. In many cases, the CE phase was sufficient to remove the primary’s envelope and drive the system to merger so that the tidal readjustment phase described above was not required."," The primary masses in these systems range from $1.2 - 3~M_{\sun}$, the secondary masses range from $0.1 - 0.6~M_{\sun}$, and the initial periods range from $10 - 350$ d. In many cases, the CE phase was sufficient to remove the primary's envelope and drive the system to merger so that the tidal readjustment phase described above was not required." +" For each value of acg roughly the same number of proto-sdBs were formed, except for ασε=0.5 which produced fewer sdB progenitors."," For each value of $\alpha_{CE}$ roughly the same number of proto-sdBs were formed, except for $\alpha_{CE} = 0.5$ which produced fewer sdB progenitors." +" In this case many binaries merge before the primary’s envelope is removed, producing an RGB star that is too massive to evolve directly to the sdB stage."," In this case many binaries merge before the primary's envelope is removed, producing an RGB star that is too massive to evolve directly to the sdB stage." +" A full exploration of the parameter space and formation rate requires further work, but we note that our preliminary investigation suggests that a diverse population of initial binaries will evolve into singleton sdBs and that this result holds for a wide range of values for acg and 7."," A full exploration of the parameter space and formation rate requires further work, but we note that our preliminary investigation suggests that a diverse population of initial binaries will evolve into singleton sdBs and that this result holds for a wide range of values for $\alpha_{CE} $ and $\eta$." +" Furthermore, since both members of the initial binary are of relatively low mass, their formation is favored by the observed Initial Mass Function."," Furthermore, since both members of the initial binary are of relatively low mass, their formation is favored by the observed Initial Mass Function." + The time required to form a singleton sdB with this channel varies widely., The time required to form a singleton sdB with this channel varies widely. +" In one extreme, a binary consisting of stars with masses of 3Mo and 0.35Mo with a 90 d period merged after only 380 Myr, implying that if the merger product maintains its core-envelope structure, this system could form an sdB within ~0.5 Gyr of its birth."," In one extreme, a binary consisting of stars with masses of $3~M_{\sun}$ and $0.35~M_{\sun}$ with a 90 d period merged after only 380 Myr, implying that if the merger product maintains its core-envelope structure, this system could form an sdB within $\sim 0.5$ Gyr of its birth." +" On the other hand, some systems take more than a Hubble time to coalesce and, if the merged star mixes it could take an additional 6 Gyr to evolve to the sdB stage."," On the other hand, some systems take more than a Hubble time to coalesce and, if the merged star mixes it could take an additional 6 Gyr to evolve to the sdB stage." +" From our grid of models, the mean amount of time for a system to merge into a proto-sdB was 5.5 Gyr."," From our grid of models, the mean amount of time for a system to merge into a proto-sdB was 5.5 Gyr." +" More work is needed to study the chemical stratification of the merger product, but the time it takes the merged star to become an sdB is bracketed by the 140 Myr and 3-5 Gyr time scales for the non-mixed and completely mixed cases, respectively."," More work is needed to study the chemical stratification of the merger product, but the time it takes the merged star to become an sdB is bracketed by the 140 Myr and 3-5 Gyr time scales for the non-mixed and completely mixed cases, respectively." + This channel may also explain a conundrum among the presently observed sdB + G or K dwarf binaries. (, This channel may also explain a conundrum among the presently observed sdB + G or K dwarf binaries. ( +"We will use *MS"" as shorthand notation for G and K dwarfs.)",We will use “MS” as shorthand notation for G and K dwarfs.) +" predicted that all such systems form as the result of a CE phase and should have periods S20 d. These authors also predict long period (P=40 d), post-Roche lobe overflow sdB + G or K binaries, but in these systems the companions are subgiants or giants (i.e., more massive stars at a later evolutionary state)."," \citet{Han:2003} predicted that all such systems form as the result of a CE phase and should have periods $\la 20$ d. These authors also predict long period $(P\ga40$ d), post-Roche lobe overflow sdB + G or K binaries, but in these systems the companions are subgiants or giants (i.e., more massive stars at a later evolutionary state)." +" The short period, sdB+MS binaries should be easy to find because their large velocity variations can easily be discerned within a single observing run, but none have been reported."," The short period, sdB+MS binaries should be easy to find because their large velocity variations can easily be discerned within a single observing run, but none have been reported." +" The observational evidence suggests that the presence of a G or K dwarf companion indicates a wide (P>100 d) binary (see,e.g.,heatetal.|2011,andreferences therein), despite the suggestion o (2002) that radial velocity observations should reveal such sdB--MS systems to be close."," The observational evidence suggests that the presence of a G or K dwarf companion indicates a wide $P>100$ d) binary \citep[see, e.g.,][and references therein]{Copperwheat:2011}, despite the suggestion of \citet{Heber:2002} that radial velocity observations should reveal such sdB+MS systems to be close." +" Our own experiments withBSE,, including various modifications to the mass loss, angular momentum loss, and stable mass transfer criterion ofwhichmimictheresultsof 2003)., (somefail to produce long period sdB4-MS [Hanbinaries."," Our own experiments with, including various modifications to the mass loss, angular momentum loss, and stable mass transfer criterion \citep[some of which mimic the results of][]{Han:2003}, fail to produce long period sdB+MS binaries." +"et al]But if these sdB4-MS binaries are instead viewed as the binary remnants of original hierarchical triple systems, in which the inner binary has evolved to become a singleton sdB as outlined above, then the remaining outer binary (presently seen as was never “close” (i.e., tidally and is thus sdB+MS)irrelevant to the production of theinteracting) sdB. For stability of the hierarchical triple, the ratio of the semi-major axis of the outer binary to that of the inner, sdB forming binary must be greater than 20log(1-4-ma3/mp), where ma is the mass of the outer star, mg is the mass of the inner binary, and we have assumed circular orbits (Harrington[1975)."," But if these sdB+MS binaries are instead viewed as the binary remnants of original hierarchical triple systems, in which the inner binary has evolved to become a singleton sdB as outlined above, then the remaining outer binary (presently seen as sdB+MS) was never “close” (i.e., tidally interacting) and is thus irrelevant to the production of the sdB. For stability of the hierarchical triple, the ratio of the semi-major axis of the outer binary to that of the inner, sdB forming binary must be greater than $\sim 20 \log(1 + m_{3}/m_{B})$, where $m_{3}$ is the mass of the outer star, $m_{B}$ is the mass of the inner binary, and we have assumed circular orbits \citep{Harrington:1975}." +". Furthermore, as mass is lost by the inner binary to form the sdB, the orbit of the outer binary will expand adiabatically to a;=ai(Mi/Myg), where a is the semi-major axis and M is the total mass of the system and the subscripts 7 and f correspond the value before and after mass loss respectively (Eggletonetal.|1989;Debes&Sigurdsso 2002)."," Furthermore, as mass is lost by the inner binary to form the sdB, the orbit of the outer binary will expand adiabatically to $a_{f} = a_{i} (M_{i}/M_{f})$, where $a$ is the semi-major axis and $M$ is the total mass of the system and the subscripts $i$ and $f$ correspond the value before and after mass loss, respectively \citep{Eggleton:1989, Debes:2002}." +". If we apply these constraints to the illustrative case described above and assume that this binary is orbited by a 0.8Mo K dwarf, theminimum orbital period of the resulting sdB + K dwarf binary is 1360 d. When we consider the entire grid of models discussed above, the shortest possible period for a sdB + 0.8 Mo K dwarf binary is 185 d. Furthermore, we note that the outer star might promote the merger of the inner binary via the Kozai mechanism."," If we apply these constraints to the illustrative case described above and assume that this binary is orbited by a $0.8~M_{\sun}$ K dwarf, the orbital period of the resulting sdB + K dwarf binary is 1360 d. When we consider the entire grid of models discussed above, the shortest possible period for a sdB + 0.8 $M_{\sun}$ K dwarf binary is 185 d. Furthermore, we note that the outer star might promote the merger of the inner binary via the Kozai mechanism." +" This triple-star channel, involving the new H-merger channel described above, can produce long period sdB+MS binaries, so previous studies of the sdB--MS binary population that do not"," This triple-star channel, involving the new H-merger channel described above, can produce long period sdB+MS binaries, so previous studies of the sdB+MS binary population that do not" +above two im units of the continu (um order to avoid the contribution of blends).,above two in units of the continuum (in order to avoid the contribution of blends). + The FWIIM was «eterminued by a Caussian fit to the entire luie. profile., The FWHM was determined by a Gaussian fit to the entire line profile. + The EWs were calculated 1 wointcerating the li1ο flux iu fje Interval 1613.1780A., The EWs were calculated by integrating the line flux in the interval 4643–4780. +.. οne can note that the mean EW of A L686 increased rom 313 to 313 f£Toni 1995 (2)ctober to 1996 September., One can note that the mean EW of $\lambda$ 4686 increased from 313 to 343 from 1995 October to 1996 September. + This 10 Increase lav be exlated by zu dutrinsic EW variabilitv and/or x long-teru chauges in the stellar coΠα flux., This 10 increase may be explained by an intrinsic EW variability and/or by long-term changes in the stellar continuum flux. + As can be seen in Figure So pancl)). the data obtained in 1996 September eenerallv show time-dependent variations.," As can be seen in Figure \ref{f8} ), the data obtained in 1996 September generally show time-dependent variations." + This is especially clear for the skewness time series. with the timescale of the variations beime of the same order of magnitude as the variations of the contiwu flux shown in the uppermost part of Figure 8.. namely. in the range 57 days (note that. unlike the EW. the skewuess is inscusitive to chanecs in the coutiuuuai flux level).," This is especially clear for the skewness time series, with the timescale of the variations being of the same order of magnitude as the variations of the continuum flux shown in the uppermost part of Figure \ref{f8}, namely, in the range 5–7 days (note that, unlike the EW, the skewness is insensitive to changes in the continuum flux level)." + On the other hand. however. aud although this may be duced by the paucity of the data. no clear time-dependent behavior is noticeable in the 1995 October dataset pancl)).," On the other hand, however, and although this may be induced by the paucity of the data, no clear time-dependent behavior is noticeable in the 1995 October dataset )." + NMiedziclski (1996a) reported on a spectroscopic patter of variability of verv imuch reminiscent of the oue presented bv the apparcutly single WN 5 star that dixplavs phase-locked (although strouely epoch- spectral variations according to 7 zz 3.77 davs (Moreletal.1998.. ancl references therein).," Niedzielski (1996a) reported on a spectroscopic pattern of variability of very much reminiscent of the one presented by the apparently single WN 5 star that displays phase-locked (although strongly epoch-dependent) spectral variations according to $\cal P$ $\approx$ 3.77 days \cite{Morel98a}, and references therein)." + The results of our iuvestigation of the spectral variability of are broadly consistent with this sugecstion., The results of our investigation of the spectral variability of are broadly consistent with this suggestion. + Iu particular. as eeneral features of the spectroscopic pattern of variability. one can note in both objects the substantial variations of the absorption conipoueut of the optical P Cyreni profiles (readilv observable in AALGOL 1620. where the absorption trough occasionally disappears: Fig.5)) or the coherent time-dependent changes in the global line-profile properties (c.g. skewness: Fig.5)).," In particular, as general features of the spectroscopic pattern of variability, one can note in both objects the substantial variations of the absorption component of the optical P Cygni profiles (readily observable in $\lambda$$\lambda$ 4604, 4620 where the absorption trough occasionally disappears; \ref{f5}) ) or the coherent time-dependent changes in the global line-profile properties (e.g., skewness; \ref{f8}) )." + Similarities cau also be found with131. another very rare example of sinele-line WR star dispaving cyclical variatious (Moreletal. 1999)).," Similarities can also be found with, another very rare example of single-line WR star displaying cyclical variations \cite{Morel98b}) )." + Evidence was also preseutec by NMiedziclski (1996a) for cvclical (according to 7 zz 2.667 davs). correlated changes iu the EWs of A1686 axl A51I12.," Evidence was also presented by Niedzielski (1996a) for cyclical (according to ${\cal P}$ $\approx$ 2.667 days), correlated changes in the EWs of $\lambda$ 4686 and $\lambda$ 5412." + The data preseuted in the present paper do not. however. support a claim of such periodicity.," The data presented in the present paper do not, however, support a claim of such periodicity." + In articular. a period search iu our EW data (but also in «mr centroid. PFWIIM. aud skewness data: Fig.8)) vields no significaut signal at the," In particular, a period search in our EW data (but also in our centroid, FWHM, and skewness data; \ref{f8}) ) yields no significant signal at the" +generated. assuming LOO equally spaced. phase bins and. 30 second exposure Lengths.,"generated, assuming 100 equally spaced phase bins and 30 second exposure lengths." + ὃν fitting racdial-velocity. curves to this fake data. we obtained a systemic velocity of Lt km +.," By fitting radial-velocity curves to this fake data, we obtained a systemic velocity of –14 km $^{-1}$." + Fig., Fig. + 10. shows the result. of the radial-velocity curve [fit (solid. line) to the svnthetie trailed spectrum. and. the truce motion of the centre-of-mass of the secondary. star (dashed. lino) for comparison.," \ref{fig:rvcurve} shows the result of the radial-velocity curve fit (solid line) to the synthetic trailed spectrum, and the true motion of the centre-of-mass of the secondary star (dashed line) for comparison." +. nsPhe value of 5 = lt km lcis significantly.lp dillerent from the true value of 5 = 0 km used in the model. anc brings our systemic velocity of 7 km + into agreement with the value of 7.8 + F4 km ! obtained by 7.," The value of $\gamma$ = –14 km $^{-1}$ is significantly different from the true value of $\gamma$ = 0 km $^{-1}$ used in the model, and brings our systemic velocity of 7 km $^{-1}$ into agreement with the value of –7.8 $\pm$ 1.4 km $^{-1}$ obtained by \citet{schwope97}." + Εις shows that a knowledge of the intensity distribution across the secondary is required. to. accurately determine the svstenic velocity (as also found by 2))., This shows that a knowledge of the intensity distribution across the secondary is required to accurately determine the systemic velocity (as also found by \citealt{schwope97}) ). + This may have implications for the accurate determinations of 7s used in CV age tests (o... 7. and ?)).," This may have implications for the accurate determinations of $\gamma$ 's used in CV age tests (e.g., \citealt*{vanparadijs96} and \citealt{north02}) )." +" Since LIU Aer is an eclipsing svstem. its inclination has been reasonably constrained. by. previous studies. inclucing estimates of. 7 SO X5"" () obtained. [rom fits to polarisation curves. and; = 85.67 (2) (rom modelling the"," Since HU Aqr is an eclipsing system, its inclination has been reasonably constrained by previous studies, including estimates of $i$ = $^{\circ}\pm$ $^{\circ}$ \citep{glenn94} obtained from fits to polarisation curves, and $i$ = $^{\circ}$ \citep{schwope01} from modelling the" +"Usiug the fact that wire41.47)=uGed)+1. and that the right-haud term of the first equation of (3.38)) is bounded. we apply the BAZO theory for parabolic equation to (3.38)) aud hence we obtain.for some positive Constant c>0: However. the L? theory for parabolic equation applied to (3.38)) gives. lor some positive coustant Com: Finally. the above two inequalities give: (Estimate of υπ. Let w2v,. we write down the equation satisfied by w: Usingthe L? theory for parabolie equatious (with various values of p) to (3.38)). (3.10)) aud (3.13)). we deduce. for some other positive constant c> 0. that: Applying the parabolie Ixozono-Taniuchi inequality (3.1)) to the function c. using iu particular (3.12)) (3.11)). (3.£3))","Using the fact that $u(x+1,t)=u(x,t)+1$, and that the right-hand term of the first equation of \ref{kimi1}) ) is bounded, we apply the $BMO$ theory for parabolic equation to \ref{kimi1}) ) and hence we obtain,for some positive constant $c_{1}>0$: However, the $L^{p}$ theory for parabolic equation applied to \ref{kimi1}) ) gives, for some positive constant $c_{2}>0$: Finally, the above two inequalities give: (Estimate of $\|v_{x}\|_{W^{2,1}_{2}}$ Let $w=v_{x}$, we write down the equation satisfied by $w$ : Usingthe $L^p$ theory for parabolic equations (with various values of $p$ ) to \ref{kimi1}) ), \ref{kimi2}) ) and \ref{kimi3}) ), we deduce, for some other positive constant $c>0$ that: Applying the parabolic Kozono-Taniuchi inequality \ref{prop1_eq})) to the function $v_{x}$ , using in particular \ref{1612}) \ref{theeq}) \ref{kimi3})" +"Usiug the fact that wire41.47)=uGed)+1. and that the right-haud term of the first equation of (3.38)) is bounded. we apply the BAZO theory for parabolic equation to (3.38)) aud hence we obtain.for some positive Constant c>0: However. the L? theory for parabolic equation applied to (3.38)) gives. lor some positive coustant Com: Finally. the above two inequalities give: (Estimate of υπ. Let w2v,. we write down the equation satisfied by w: Usingthe L? theory for parabolie equatious (with various values of p) to (3.38)). (3.10)) aud (3.13)). we deduce. for some other positive constant c> 0. that: Applying the parabolie Ixozono-Taniuchi inequality (3.1)) to the function c. using iu particular (3.12)) (3.11)). (3.£3)).","Using the fact that $u(x+1,t)=u(x,t)+1$, and that the right-hand term of the first equation of \ref{kimi1}) ) is bounded, we apply the $BMO$ theory for parabolic equation to \ref{kimi1}) ) and hence we obtain,for some positive constant $c_{1}>0$: However, the $L^{p}$ theory for parabolic equation applied to \ref{kimi1}) ) gives, for some positive constant $c_{2}>0$: Finally, the above two inequalities give: (Estimate of $\|v_{x}\|_{W^{2,1}_{2}}$ Let $w=v_{x}$, we write down the equation satisfied by $w$ : Usingthe $L^p$ theory for parabolic equations (with various values of $p$ ) to \ref{kimi1}) ), \ref{kimi2}) ) and \ref{kimi3}) ), we deduce, for some other positive constant $c>0$ that: Applying the parabolic Kozono-Taniuchi inequality \ref{prop1_eq})) to the function $v_{x}$ , using in particular \ref{1612}) \ref{theeq}) \ref{kimi3})" +pressure depends on the gas opacity. which in turn depends on the ionization balance.,"pressure depends on the gas opacity, which in turn depends on the ionization balance." + The effects of X-ray ionization on the radiation force due to lines is calculated using the procedure outlined by ?.., The effects of X-ray ionization on the radiation force due to lines is calculated using the procedure outlined by \cite{stevens90}. + In this procedure. the “force multiplier” of ὁ (the ratio of the full radiation force to that due solely to electron scattering) is suppressed by a factor which depends on the ionization parameter and temperature.," In this procedure, the “force multiplier” of \cite{castor75} + (the ratio of the full radiation force to that due solely to electron scattering) is suppressed by a factor which depends on the ionization parameter and temperature." + The effects of heating by radiation are also taken into account by these calculations., The effects of heating by radiation are also taken into account by these calculations. + Specifically. PKOA calculated the gas temperature assuming that the gas is optically thin to its own cooling radiation.," Specifically, PK04 calculated the gas temperature assuming that the gas is optically thin to its own cooling radiation." + Thus the net cooling rate depends on the density. the temperature. the ionization parameter. and the characteristic temperature of the X-ray radiation.," Thus the net cooling rate depends on the density, the temperature, the ionization parameter, and the characteristic temperature of the X-ray radiation." + In this case it is possible to fit analytical formulae to the heating and cooling rate obtained from detailed photoionization calculations for various gas parameters., In this case it is possible to fit analytical formulae to the heating and cooling rate obtained from detailed photoionization calculations for various gas parameters. + PKO4 used a fit to photoionization calculations obtained by ? who included Compton heating/cooling. X-ray photoionization heating/recombination cooling. bremsstrahlung and line cooling.," PK04 used a fit to photoionization calculations obtained by \cite{blondin94} who included Compton heating/cooling, X-ray photoionization heating/recombination cooling, bremsstrahlung and line cooling." + The hydrodynamical simulations described above provide the time-dependent density and velocity structure of the disk wind., The hydrodynamical simulations described above provide the time-dependent density and velocity structure of the disk wind. + To compute synthetic spectra from these. we have performed radiative transfer simulations using the Monte Carlo code described. in Papers I and II.," To compute synthetic spectra from these, we have performed radiative transfer simulations using the Monte Carlo code described in Papers I and II." + For the radiative transfer. simulations. the Monte Carlo code was modified to accept a generalized axisymmetric wind with density and velocity specified via input data.," For the radiative transfer simulations, the Monte Carlo code was modified to accept a generalized axisymmetric wind with density and velocity specified via input data." + As for the yarametrized wind models adopted in Papers I and IT. these inpu data define a 2D grid of wind properties (in this case. with oroperties depending on polar coordinates + and 0).," As for the parametrized wind models adopted in Papers I and II, these input data define a 2D grid of wind properties (in this case, with properties depending on polar coordinates $r$ and $\theta$ )." + The mass density in each wind grid cell is assumed to be uniform and aken from the hydrodynamical model., The mass density in each wind grid cell is assumed to be uniform and taken from the hydrodynamical model. + The three components of velocity θε co and 0.) at every point in the wind are obtained by linear interpolation (in. + and 0) between the values which are provided at the boundaries of each wind grid cell.," The three components of velocity $v_{r}$, $v_{\theta}$ and $v_{\phi}$ ) at every point in the wind are obtained by linear interpolation (in $r$ and $\theta$ ) between the values which are provided at the boundaries of each wind grid cell." +" This interpolation 1s necessary since use of the Sobolev approximation or line transitions requires that the velocity is everywhere a smooth ""unction.", This interpolation is necessary since use of the Sobolev approximation for line transitions requires that the velocity is everywhere a smooth function. + In certain regions. particularly close to the disk plane where he transition between the disk atmosphere and the outflow lies. the ivdrodynamical simulations predict rather high densities.," In certain regions, particularly close to the disk plane where the transition between the disk atmosphere and the outflow lies, the hydrodynamical simulations predict rather high densities." + In some cases. this makes certain grid cells very optically thick.," In some cases, this makes certain grid cells very optically thick." + Physically. any X-ray photons which penetrate deep within these optically hick layers will be thermalized and contribute to heating of the disk atmosphere.," Physically, any X-ray photons which penetrate deep within these optically thick layers will be thermalized and contribute to heating of the disk atmosphere." + In the parametrized models considered in Paper IT. this sink of X-ray photons was roughly accounted for by assuming that all Monte Carlo quanta which reach the .ry-plane in the simulation strike the optically thick disk and are then lost.," In the parametrized models considered in Paper II, this sink of X-ray photons was roughly accounted for by assuming that all Monte Carlo quanta which reach the $xy$ -plane in the simulation strike the optically thick disk and are then lost." + That approach neglects reflection by the disk but avoids the need to track the Tonte Carlo quanta as they propagate through very optically thick material., That approach neglects reflection by the disk but avoids the need to track the Monte Carlo quanta as they propagate through very optically thick material. + In the more realistic model considered here. however. here is no sharply-detined boundary between the disk atmosphere and the wind.," In the more realistic model considered here, however, there is no sharply-defined boundary between the disk atmosphere and the wind." + Thus reflection by the dense material at the very base of the outflow is automatically included in the simulations., Thus reflection by the dense material at the very base of the outflow is automatically included in the simulations. + However. this introduces additional computational challenges.," However, this introduces additional computational challenges." +" In articular, quanta occasionally propagate deep into the optically hick regions where they interact many times and have very low orobability of reemerging without being thermalized (and therefore ost to the X-ray regime since the expected temperature of the disk atmosphere is relatively low)."," In particular, quanta occasionally propagate deep into the optically thick regions where they interact many times and have very low probability of reemerging without being thermalized (and therefore lost to the X-ray regime since the expected temperature of the disk atmosphere is relatively low)." + To deal with these quanta. a cut is introduced whereby the flight paths of Monte Carlo quanta which propagate sufficiently deep into the base of the wind are terminated and it is assumed that these quanta contribute nothing further to the X-ray spectra or ionization state of the wind.," To deal with these quanta, a cut is introduced whereby the flight paths of Monte Carlo quanta which propagate sufficiently deep into the base of the wind are terminated and it is assumed that these quanta contribute nothing further to the X-ray spectra or ionization state of the wind." + A very conservative cut has been applied in the simulations presented here: quanta are terminated if they penetrate deep enough into the base of the wind that the Compton optical depth to re-emerge from the wind is greater than twenty in all directions., A very conservative cut has been applied in the simulations presented here: quanta are terminated if they penetrate deep enough into the base of the wind that the Compton optical depth to re-emerge from the wind is greater than twenty in all directions. + As described in Paper IL the ionization and. thermal structure of the wind are determined iteratively from the radiation field properties and the assumptions of ionization and thermal equilibrium.," As described in Paper II, the ionization and thermal structure of the wind are determined iteratively from the radiation field properties and the assumptions of ionization and thermal equilibrium." + The ionization balance accounts for photoionization (including K-/L-shell ionization followed by ejection of Auger electrons). collisional ionization. radiative recombination and di-electronic recombination.," The ionization balance accounts for photoionization (including K-/L-shell ionization followed by ejection of Auger electrons), collisional ionization, radiative recombination and di-electronic recombination." +" Heating by photoionization, Compton down-seattering of X-ray photons and free-free absorption are balanced against bremsstrahlung. Compton cooling by low energy disk photons. bound-free recombination. bound-bound line ransitions and cooling due to adiabatic expansion to estimate the ocal temperature."," Heating by photoionization, Compton down-scattering of X-ray photons and free-free absorption are balanced against bremsstrahlung, Compton cooling by low energy disk photons, bound-free recombination, bound-bound line transitions and cooling due to adiabatic expansion to estimate the local temperature." + Note that our treatment of Compton cooling remains particularly approximate since we do not simulate the ransport of the accretion disk photons in detail (see Paper ID., Note that our treatment of Compton cooling remains particularly approximate since we do not simulate the transport of the accretion disk photons in detail (see Paper II). + The assumptions of ionization/thermal equilibrium are not perfectly valid in regions of the wind where the density is sufficiently low hat the recombination/cooling timescales are long compared to the flow timescale., The assumptions of ionization/thermal equilibrium are not perfectly valid in regions of the wind where the density is sufficiently low that the recombination/cooling timescales are long compared to the flow timescale. + However. it alleviates the need to introduce explicit ime-dependence in the calculation — a major computational saving.," However, it alleviates the need to introduce explicit time-dependence in the calculation – a major computational saving." + In general. we would expect that the most important consequence of departures from equilibrium is that the ionization state becomes Tozen-in in the outer. low-density flow regions since recombination may become too slow to maintain local ionization equilibrium.," In general, we would expect that the most important consequence of departures from equilibrium is that the ionization state becomes frozen-in in the outer, low-density flow regions since recombination may become too slow to maintain local ionization equilibrium." + As we shall show below. however. the equilibrium assumption already leads to near fully-ionized conditions in much of the outer wind — thus accounting for any further effective reduction to the recombination rate is unlikely to dramatically alter the typical ionization state.," As we shall show below, however, the equilibrium assumption already leads to near fully-ionized conditions in much of the outer wind – thus accounting for any further effective reduction to the recombination rate is unlikely to dramatically alter the typical ionization state." + The radiative transfer simulations were performed using the same set of atomic data as described in Paper II., The radiative transfer simulations were performed using the same set of atomic data as described in Paper II. + This includes the K-shell ions of the astrophysically abundant metals. the shell ions of the important second and third row elements and the highest few M-shell ions of Fe and Ni.," This includes the K-shell ions of the astrophysically abundant metals, the L-shell ions of the important second and third row elements and the highest few M-shell ions of Fe and Ni." + Note that this data set does not include M-shell ions of iron below Fe — thus when the computed ionization state favours this ion it is likely that the true degree of ionization is lower., Note that this data set does not include M-shell ions of iron below Fe – thus when the computed ionization state favours this ion it is likely that the true degree of ionization is lower. + Similarly. a lower limit of logZK]=4.0 is imposed in the radiative transfer simulations since (i) the atomic data used is likely inadequate to describe the cooling to lower temperatures and (i) the uv radiation of the disk — which is neglected here — should prevent the inner regions of the outflow from dropping to significantly lower temperatures.," Similarly, a lower limit of $\log T_{e}[\mbox{K}] = 4.0$ is imposed in the radiative transfer simulations since (i) the atomic data used is likely inadequate to describe the cooling to lower temperatures and (ii) the uv radiation of the disk – which is neglected here – should prevent the inner regions of the outflow from dropping to significantly lower temperatures." + The relevant physical and numerical parameters adopted in the simulations are given in Table |.., The relevant physical and numerical parameters adopted in the simulations are given in Table \ref{tab:pars}. + Most of these are carried over or derived from the parameters adopted in the radiation hydrodynamics simulation (2... PKO4).," Most of these are carried over or derived from the parameters adopted in the radiation hydrodynamics simulation \citealt{proga00}, PK04)." + For this study we have selected two snapshots of the wind structure: specifically we chose the wind conditions from timesteps 800 and 955 from the PKO+ simulation., For this study we have selected two snapshots of the wind structure; specifically we chose the wind conditions from timesteps 800 and 955 from the PK04 simulation. + These timesteps were chosen since they are well-separated in simulation time (timestep 955 is later than timestep 800 by Al~5 years)., These timesteps were chosen since they are well-separated in simulation time (timestep 955 is later than timestep 800 by $\Delta t \sim 5$ years). + This allows us to study two independent realizations of the flow pattern and investigate how the spectral features should vary on timescales comparable to the typical, This allows us to study two independent realizations of the flow pattern and investigate how the spectral features should vary on timescales comparable to the typical +"In addition. based on the flat spectral slope between 1.4 and 3.5 GIIz measured at /=3.3 davs. we conclude that for both the reverse and forward shocks 54,<1.4 GlIz.","In addition, based on the flat spectral slope between $1.4$ and $8.5$ GHz measured at $t=3.3$ days, we conclude that for both the reverse and forward shocks $\nu_a\lesssim 1.4$ GHz." +" Otherwise. (he emission [rom the reverse shock would be severely attenuated over this [frequency range bv the lorwared shock. F,,,/,=Freeme77. resulüng in a significantly steeper spectrum: here 7, ls (he svnelirotron optical depth."," Otherwise, the emission from the reverse shock would be severely attenuated over this frequency range by the forward shock, $F_{\nu,{\rm obs}}=F_{\nu,{\rm +em}}e^{-\tau_\nu}$, resulting in a significantly steeper spectrum; here $\tau_\nu$ is the synchrotron optical depth." + Usine the conditions inlerred in relsec:racl we model the radio. optical. and X-ray data with a model describing sell-consistentlv ihe time evolution of the forward and reverse shocks in a uniform. density. medium.," Using the conditions inferred in \\ref{sec:rad} we model the radio, optical, and X-ray data with a model describing self-consistently the time evolution of the forward and reverse shocks in a uniform density medium." + We consider (he optical data only al /«10 days since the emission at later times is dominated bv a much redder component. possibly à SN (Priceefal2002).," We consider the optical data only at $t<10$ days since the emission at later times is dominated by a much redder component, possibly a SN \citep{pkb+02}." +. We return to this point in re[sec:prog.., We return to this point in \\ref{sec:prog}. . +" The time evolution of the reverse shock spectrum (E,xpi [or p|(1211g)/*(12g). and the time of peak emission. /,—max[Fau/(14-z)./q«] (IXobavashi&Sari 2000): here lane= GOs is the duration of (Priceefαἰ. 2002)... Aq=(3:/Ημ...an Ty is (he initial Lorentz factor. ancl ny is the circumburst densitv."," The time evolution of the reverse shock spectrum $F_\nu\propto +\nu^{1/3}$ for $\nu<\nu_{m,{\rm RS}}$ and $F_\nu\propto +\nu^{-(p-1)/2}$ for $\nu>\nu_{m,{\rm RS}}$ ) is described by $\nu_{m,{\rm RS}}\propto t^{-3(8+5g)/7(1+2g)}$, $F_{\nu,0,{\rm RS}} +\propto t^{-(12+11g)/7(1+2g)}$, and the time of peak emission, $t_p={\rm max}[t_{\rm dur}/(1+z),t_{\rm dec}]$ \citep{ks00}; ; here $t_{\rm dur}=60$ s is the duration of \citep{pkb+02}, , $t_{\rm +dec}=(3E/32\pi \Gamma_0^8n_0m_pc^2)^{1/3}$, $\Gamma_0$ is the initial Lorentz factor, and $n_0$ is the circumburst density." + The parameter describes (he evolution of the reverse shock Lorentz factor. Doxr.7. aud the limits correspond to adiabatic expansion (yg= 3/2) and pressure equilibrium between the forwarcl and reverse shocks (g= 7/2).," The parameter $3/2\leq g\leq 7/2$ describes the evolution of the reverse shock Lorentz factor, $\Gamma\propto r^{-g}$, and the limits correspond to adiabatic expansion $g=3/2$ ) and pressure equilibrium between the forward and reverse shocks $g=7/2$ )." +" To evaluate /,. 9;ns(/5). and Pions(/;) we use the physical parameters of (he ejecta and cireumburst medium as inferred from (he lorwarcl shock emission (see below and Table 2)). in conjunction with equations 79 of Ixobavashi(2000) for the {hick shell case (i.e. when the reverse shock is relativistic and effectively decelerates the shell). and equations 1517 lor the thin shell case (ie. when the reverse shock cannot decelerate the shell effectivelv)."," To evaluate $t_p$ , $\nu_{m,{\rm +RS}}(t_p)$, and $F_{\nu,0,{\rm RS}}(t_p)$ we use the physical parameters of the ejecta and circumburst medium as inferred from the forward shock emission (see below and Table \ref{tab:ij}) ), in conjunction with equations 7–9 of \citet{kob00} for the thick shell case (i.e. when the reverse shock is relativistic and effectively decelerates the shell), and equations 15–17 for the thin shell case (i.e. when the reverse shock cannot decelerate the shell effectively)."